Sorry for your theory and all, but you can't force people to like things they don't like.
I was very bad at math in school, and this being the 60s....there was no shortage, I assure you, of "drill and kill"....we recited multiplication tables and all that.
I got lost somewhere in 2nd grade, and never came back. It was only much later, in my 30s, that I was officially diagnosed with DYSCALCULIA -- think of as as math dyslexia. It was such a relief to know it was a real learning disability -- because ALL MY CHILDHOOD LONG, I was told I was lazy and shiftless, and "only wanted to do fun easy things" (which was never true). I was beaten, punished, sent to bed without TV....forced into summer school....forced to do endless flash cards with my angry, frustrated parents who couldn't understand why I just "didn't get it".
I suspect far more people (both men & women) have dyscalculia than we realize....nobody really tests for it. Schools just accept that "little Susie or Joey is bad at math".
BTW: I don't think it has anything to do with being female whatsoever. My dad was an engineer, would have been THRILLED had I gone into that field, or mathematics! But I couldn't do it anymore than I can flap my wings and fly -- or breathe underwater.
Ms. Oakley: you could have waterboarded me in elementary school and it wouldn't have made me like math or be good at it. In fact, all the "punishments" -- hectoring, nagging, etc. -- gave me a complex over math -- let's call it "math phobia".
9
Finally, a rebuttal of decades of Dewey's theories. The way math, reading, and everything else is taught today needs significant revision. There have been a succession of "new maths" and "new reading", none worked, all did a disservice to children. Read some letters of young people during the Revolutionary or Civil War, a 10 year old had a better grasp of quantification and the English language than many adults today.
As a comparison, there is no athlete today, nor musician who didn't spend years practicing. Read your kids their biographies. They all grew up banging tennis balls agains the side of the house, or throwing a ball through a garbage can, or running around the block, or swimming any chance they got.
Our problem today is that the teachers' colleges are not teaching the teachers how to teach, and the teachers' teachers don't know how either. We don't need bibles in schools, we need teachers who are passionate about giving kids intellectual survival skills for this century.
6
I love that we are still trying to "fix" girls -- when all evidence points to boys' much greater struggles, ultimately, with education: https://collegepuzzle.stanford.edu/tag/women-exceed-men-in-college-gradu...
"Make your sons go to college -- they might have a better chance of finding a partner" (https://www.thedailybeast.com/why-college-educated-women-cant-find-love?...
There's a headline you'll never see.
9
I'm a new father of two toddler daughters...so no school experience yet. I feel it would be a disservice for any parent to just focus on one subject and not another, one sex and not the other.
Barbara Oakley is famous for her online course "learning how to learn", but why publish an article for girls? And leave just one line at the end for boys. Am I wrong to feel it's sexist and insulting?
Her article says, girls are boys have the same math abilities, and girl are better in language arts. Does she have an article to remind parents to read and write with your boys, because they have an adherent biological disadvantage in those areas? Or do we let boys just play sports and work at a warehouse later in life as girls take over? Why not have an article that says...have your kids, boy or girl, practice their school work?
I hope my daughters' do better than everyone else's son or daughter. I will work with them on their math AND language art skills... prioritize sending them to a Kumon Math & Reading Learning Center instead of soccer, or swimming lessons...the same way I would do if I had sons. As a parent, that is just what should be done!
4
"becoming an expert at anything requires the development of neural patterns that are acquired through much practice and repetition" - it is truly sad to see an engineering professor write this completely nonsensical platitude. Becoming an expert requires aptitude, interest, drive, and desire - what professor Oakley describes is the recipe for training Marines.
8
My major (Engineering) in college required "a ton" of math. I like math and have always done very well at it.
I agree with the overall theme of this article - However my view is the crisis in this country is NOT that our students perform so poorly on international math rankings it certainly not a good thing but...
The real crisis is we as a nation have a horrendously poor math curriculum taught for the most part by instructors ill equipped and ill suited to the task of teaching mathematics.
Any idea what the "dropout/failure rate" of first term College Calculus students is (both men and women)?
Its abysmal
Almost all of it can be laid at the doorstep of poor primary math education/curriculum/instruction and even worse curriculum and instruction in colleges.
Yes there are some superbly gifted math instructors but there are far too many completely inadequate ones.
My first Calculus instructor in college was an absolute gift from God in terms of ability to teach - unfortunately my second term instructor was abysmal - I essentially taught myself integrals (back then there was no Khan academy) My Linear Algebra instructor was a complete joke - Brilliant guy! - just couldn't teach anyone how to light a match let alone math.
Got to Diff Eq's and got my 1st term instructor back - wasn't half as brilliant as the Linear Alg guy but could teach circles around him...
It takes TWO to tango!
11
Instead of making a comment myself, I'll allow George Pólya, author of "How to Solve It" to make a comment:
"A teacher of mathematics has a great opportunity. lf he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a taste for, and some means of, independent thinking."
13
Speaking as a male who suffered from severe dyscalculia all thru school with no help whatsoever, how about some help for the boys too?
8
"A typical little boy can think he’s better at math than language arts. But a typical little girl can think she’s better at language arts than math."
Any second year econ major would immediately recognize this as Comparative Advantage (filed under Ricardo). There really is no point to further comment until the author reads up a bit on why, in the real world, this is entirely sensible.
6
Our society is uncapable of free-thinking - something, that Americans used to be famous for and that propelled the US to success, culturally and economically, in the XX-century. As of last 20 yrs, all I am hearing is "STEM" and "every HS kid has to go to college". Both are complete nonsense. One of my daughters-in-law is a biology professor at the NYU. He classes are full of students (boys and gals alike) who absolutely have no desire or business to be there - but they have bought into the cool-aid dream. They derive absolutely zero value out of it, and we, as society, are paying dearly for it, while multiple well-paying blue-collar jobs (construction, anyone?) vital for our economy go unfilled. Same with math. Math is NOT for everyone. It shopopuldn't be. Moreover, many (most) professions do NOT require but basic knowledge of it (my hubby, as a doctor, has never used math beyond the 9th grade level, according to him); so why is it being pushed down the throats of every boy and (especially) girl in this country?!
5
After 40 years of teaching college math, I’m convinced the problem is cultural — girls are told they can’t do math. They come to believe it. Furthermore, they’re patted on the head and told “It’s okay” if they flunk a math test. They’re told “you’ll never use this stuff anyway” and “you won’t be popular with boys if you can do math”. Trouble is, their parents and many of their teachers also believe these myths. So, yes, make your children practice math and learn the multiplication tables and learn to take pride in it because it will make them more logical thinkers and problem solvers.
2
It is a marvel of pedagogy that innumeracy is not considered the same evil as illiteracy. I am reminded that some famous person once said; "Schools (K-12) are designed by women for girls".
I have read than innumerates can graduate from Ivy League universities whereas math is still considered one of the fundamental arts of "liberal arts" at Oxford and Cambridge.
I am good at math and I still despise the english teachers who forced to read truely awful books like "Silas Marner".
3
Here's what I did. I unschooled my daughter. I took her out of regular school because the education system is not aligning with the science on child development. Until puberty, a child is a concrete operator, incapable of abstract thinking, yet they were trying to teach her algebra in elementary school. That's traumatizing. Oh, and they skipped over memorizing math tables. That's insane. You know what cognitive scientists figured out why Asians more often excel at math? Their language structure. We say the abstract word 'twenty' they say something like 'ten times two' - in other words, because of their language structure, they are doing their math tables all the time. So, back to unschooling. I got my daughter a professional math tutor - a woman. I told her to never grade her, but to grade herself - it was the teacher who was failing, not the kid. I found one other friend to be tutored with her. At 14, my daughter started taking math (and other) classes at the community college (along with a bunch of friends, so no, she wasn't an outsider). She rocked all her math classes. She loves math. She got A's. She got an A in statistics at 16.
4
Teach your daughter had to blindly memorize massive amounts of fairly mundane visual information. Then, she can suppress her ability to think long enough to get through Pre-Med, which requires mountains of rote memorization, and, not much thinking. Once she gets to Med school the mind dumbing memorization continues. But, when she gets out, then, she will be confronted with complex systems that do not bear any resemblance to what she has memorized. Here, she can mis-diagnose her way to multiple Lake Houses and fancy cars. This, my friends, is a much better path for your daughter. Doc's can work until they are so old somebody has to help them find the bathroom. Math? That requires real and sustained mental effort.
5
Dr. Oakley is “spot on“ in her comments which apply to everyone. I now have a new book or two that I am adding to my wish list.
1
"...SEEM to indicate that SOMETHING like the above dynamic MIGHT be going on..." (caps mine).
so, yet another feeble attempt to retail a bag of tired tropes, in this case "genderization" that falls of its own weight while the real problem, "the way we teach math" gets pushed off the stage.
the "way we teach math" ever changing as the newest "best method" displaces the previous "best method,"
does indeed (no "may be" about it) hurt all students.
professor oakley is right to suggest that drill is a neglected element in the study of math, as it is in languages and, on closer examination, writing, oral expression and critical habits including the fundamentals of argument and debate, (the manifestations of these last obvious to anyone who hears the congress or the cable news in action).
the lack of appetite for rigor, a "pedagogical disorder," so to speak, shows no signs of abatement.
the problem with math is that, unlike languages, the instructional foundation,
the equivalent of parts of speech, the verbs and adjectives, their cases and tenses, is nowhere near as effective as it is in languages.
a substantive plan for improvement in early math instruction (which might include music, with its frequencies and amplitudes, as a correlative) would be worth an entire op-ed page, at least.
Totally agree! Sadly, I tutor young girls in math in an after school homework program and they don’t have a clue. Many of them hate math. Our pathetic teaching programs have condemned these young girls to a life of dependency on others.
It makes me furious and terribly sad at the same time. Math is fun and stimulates analytical thinking. Our failure in the school system to address this problem creates robots rather than free-thinking citizens.
Thank goodness for those parents and grandparents who relentlessly challenge their kids with math. Whether they thank you or not is another question, but they will be better off.
This is not a knock on teachers. It is a plea to those in authority to challenge our students on the basic principles of math. Practice, practice, practice and don’t accept anything less than excellence.
1
My father was a civil engineer and math aptitude was highly valued in our family. After supper he would sit down and tutor me, demonstrating the secrets of a slide rule and describing the straightforward logic behind calculation. I don't recall Dad doing my work but instead his patient guidance. Those are fondly remembered father-daughter bonding lessons for me, and math skill was a point of pride for both of us. My mother avoided helping me with math questions, thinking herself dumb. Thankfully I never absorbed that message. I felt comfortable in all STEM curriculum AND language/literature classes. Ironically, Dad always thought studying the humanities was a waste of time, but that didn't stop me from enjoying and doing well in them too. Looking back, Dad was invested in modeling his daughter's brain to learn. I wonder if he ever realized how loved I felt in the process?
5
One of the very few sensible articles on education that I have read recently.
1
This is an excellent column about learning math. There is no substitute for drill and for the old "math facts". The problem with the article, as with almost everything in the Times, is that it cannot divorce itself from liberal politics, in this case sexual politics. New Math, Discovery Math and all their siblings have harmed boys, girls, blacks, whites, and America as a whole. This has been shown through international testing for decades. Math and science faculties at the college level have begged the education establishment to go back to math facts and been roundly rebuffed by political correctness. It would be vilified as a Trumpian proposal to get rid of new math on a national scale, racist to the core because it would require a clear learning standard with the possibility of failure, require children to sit in their seats, shut their mouths, and practice. Interestingly the author is right that girls would do well with it due to their better concentration skills in elementary school. And it would also help the boys. The author at least makes the same point in her last parenthetical sentence.
1
Our society deems it honorable to be bad at math. People brag about it. Herein lies the problem.
5
I HATED math as a kid, and thought I did as an adult until I had to apply it. First in business school, then on home projects which involved geometry and now the field that chose me Analytics. Noone ever tells you that you will revel in statistics or trending analysis that involve a heavy reliance on...you guessed it...math!
I cannot thank Dr. Oakley enough! As a middle-school math teacher, and former student of her MOOC about Learning How to Learn, I’ve cited her countless times (ahem, pardon the pun). Math CAN be understood and mastered: the brain is like a muscle that needs training.
Kudos to you, Dr. Oakley!
3
My college boyfriend insisted I take a full year of calculus even though only one term was required for my major. Reader, I married him.
6
Kumon! The Kumon program treats math like a language, and basically presents students with “pattern practice”, a technique that burns the fundamental grammars of language (and math). It works!
2
Ok, call me dumb, but as somebody who grew up completely indifferent to math but excelled at foreign languages the minute I started learning them, I have some questions. Let me also preface my questions/comments with the background info that my dad, who died when I was very young, was a math whiz. So, had I been raised by him, perhaps I’d have a very different understanding of math.
I understand the value of rote learning because once we observe patterns in language, like agreement, case, conjugations AS WE USE THEM, we realize it is efficient to memorize said patterns so that we can put in the proper form quickly within a context when we want to express something. So, please explain to me in math class how we first observe those patterns in real situations and then I’ll gladly learn tables with forms. This never happened to me in math class.
One commenter here mentioned the key to dividing fractions by flipping them and then multiplying them. How did somebody figure that out???????? If somebody had shown me how that was done by some smarty, I’d be more interested. What real life situation led to that revelation? Oh, they turned the question around.... got it. Nobody ever showed me that.
How did people learn to use numbers as language? At some point, many of us turn off in algebra class because nobody explains that to us.
Ok, I had a really successful career, but I know I seem dumb to you numbers people. Sorry.
3
Sorry, forgive me for being language arts impaired, but what does STEM stand for?
1
The pendulum has swung in education. The girls are better students. They are able to behave and concentrate in class better than the boys. They make better grades, better test scores and are well over 50% of the higher education students. In my city the only all single sex public school is a girl’s school. They are the protected sex.
We need to be aware of this. The male population, compared to female, is becoming less educated. To make things worse, the women drop out of the workforce sooner than men(sexist comment but true).
It really is time to consider making the boys the protected sex. Encourage education techniques that might be inclined to interest boys more. Give them their own school for Pete’s sake.
It may become a bigger problem to fill the STEM jobs in the future as women dominate the education spots (but get out early to have a family-certainly see this in medicine)and there are not enough males who are well educated and the immigrant talent pool isn’t as excited to come to our country.
3
btw..I also have a teenaged son and he is equally put off by math 'contests' and highly capable in the language and useful concepts of mathematics.
Either of my kids could be successful in any field they choose...this gender-based nonsense on aptitudes is depressing and absurd.
When I first arrived Stanford as a foreign engineering graduate student, my English major roommate exclaimed, “wow, you must be very smart to be good at math! I’m simply not good at it!” This was the first time I heard someone claiming herself “not good at math”, and, me being good at math is because of “ being smart”. Where I originally came from, diligence was valued over talent. School teachers don’t differentiate students based on what they are good at, but how much they practice and improve. If someone is not good at math, it must be because she doesn’t work hard enough, not because she is lack of talent.
8
Draw a circle with a radius of ‘Pi’, then find the circumference without using a calculator. Magic!
“Everything is vibration.” -Albert Einstein
1
Yes! Thank you! You ACTUALLY understand this. This is not cool or nice to bois. I’m 11 and see both points of view but it’s seems sexist towards bois.
2
Math makes you smarter in general and there is nothing wrong with being smarter for the rest of your life, in fact over time, you realize it is quite useful and desirable.
60
As a high school math teacher, I take strong objection to this article. Girls are the ones who excel at the high school level. More girls take AP's, more girls than boys are valedictorians; it is boys who drop out of school in greater numbers. Instead, it is the math, computer science, and science departments in colleges and universities who are the ones turning girls off from STEM fields, and I suggest they begin to take a look at themselves, their attitudes, and their practices. Prior to college, many girls love and excel at science and math.
9
I find articles like this, which imply that all children learn best in one specific way, infuriating. Children (just like the rest of us) are all unique individuals, and are all on a spectrum of differing cognitive biases and abilities. They all have different learning styles and some approaches to math will work well for some kids and be terrible for others. My son in is NYC public schools and has been made to do 2 hours of math a day since he was 8 years old, and all of his homework since third grade has been math. The result? He hates math. And it’s not because it’s not “fun” as this author so dismissively implies is what is intended by a more progressive approach to education. He is an intuitive learner and loves when instruction and material is approached from a perspective of the big picture and forming connections from disparate realms. This doesn’t mean it’s not productive or hard work. It’s just a different approach which he- and lots of other kids- connect to better and therefor learn more from. Drilling is fine for some if they learn best that way, but for others it is like beating a dead horse. I think we need options for our kids and the acceptance that not all kids learn best one way.
5
I agree with making the girls (and the boys!) practice math. But I maintain one difference, as follows.
Practice makes habit. If you practice the wrong things, you become more fluent at the wrong things, but if you practice the right things, you become more fluent at the right things. If you practice the right things, you improve, and then practice makes improvement. This is a hard lesson I had to learn while practising music, and while learning mathematics and physics. I really had to struggle, and only grim determination and persistence got me to advance in any of those areas. The long and short of it: Practice and keep trying to find the right thing and the right way, and be mindful.
Rote practice is what video games are good at. My kids would play math-based video games for fun. Or do workbooks where the answer to a math problem would be a clue to coloring a picture or getting the punchline to a joke. Minute math worksheets convinced my kids they were bad at math, since they couldn't do the problems fast enough. A computer will cheer any improvement.
My son could never do half of his minute math problems in the required 2 minutes. He probably still can't. He wasn't 'fluent' by elementary school standards. He got the second highest possible score on the Math SAT, the Math 2 SAT subject test and a perfect score on the Calculus BC AP test. He's heading to RPI to study engineering.
1
People inherently have a certain type of mindset that either makes them grow or holds back their potential. Stanford Psychology Professor Carol Dweck’s groundbreaking work on fixed vs growth mindsets shifted the way that educators motivate students to learn (I found this article very simple in explanation of her work https://bit.ly/2MtcDki). She found that those with the fixed mindset mostly believe in possession of natural talent, meaning that little girls would think that they are naturally not good at math while boys have a natural talent. Such people believe that their intelligence and skills are intrinsically linked to themselves as a person and as such, their skills and talents are fixed and cannot be improved. Those that have a growth mindset, on the contrary, believe in constant improvement and development of their intelligence and skills and that talents can be developed as well. So it's very important to help your kid develop the right mindset from the very childhood as it determines their further development path.
2
In addition to practice, I would advise parents - and especially mothers - to avoid saying that they are bad at math. I have too many friends who are quick to joke about this in front of their children or utter it in frustration during homework sessions. Don't. You aren't bad at math, you just haven't practiced as much as, say, the math teacher who gave your child that challenging homework assignment. By declaring your supposed inability in front of your children, you are modeling low expectations and reinforcing the stereotype that it is somehow normal or OK to be "bad" at math.
3
Help your children of both genders learn math! My father was a math/physics professor at a junior college. He recognised that most of the students in his classes were young men who had never quite grasped basic math in high school and had no intention of continuing to college, yet suddenly found that they could not progress in a blue-collar trade without knowing basic math. He made a mini fortune by writing simple, basic math books for adults who somehow managed to graduate high school without basic math knowledge.
1
Mental math! For day to day questions--multiply the recipe times 3, decide how many sections of fencing are required for the garden plot--don't pick up the calculator. Do it in your head, and have your children do it too. Not much higher level math involved, of course, unless your life is far more complex than mine. But mental math develops a concrete understanding of the basic concepts, awareness of the essential role numbers play in everyday life, and, perhaps most important, confidence that this is something you can handle.
2
Rote learning is underappreciated. Students simply do not get enough practice to achieve mastery. This is true in both mathematics and language arts. The comparison I make is to sports. Students take without question that to excel in a sport, they must drill, must run the same play day after day. It is similar in academics. A great teacher knows how to balance this needed practice with an engaging environment as does a great coach.
1
When you empty all the day’s change from your pocket and start figuring how much it is (i.e. 10 nickels plus 6 quarters plus 2 dozen pennies and then add it all up) you’re doing algebra whether you realize it or not. I actually calculated how much money I save over a ten year period by driving the speed limit (and my driving habit of coasting up to red lights). The cost savings in gas and maintenance is around ten thousand dollars. And when I crossed referenced that figure with how much time I lost by not driving faster (for most commuting drives) it was apparent how driving the speed limit and the savings realized far outweighed the few minutes gained in s shorter drive. If only people did the math!
2
Hear hear! I was generally a good student who excelled at most subjects. When I started struggling with more advanced mathematics, I was told (even by teachers!) that "math just isn't my strong suit." But what do you know, I grew up to be a biologist and statistician who now works as a data scientist. People comment now "oh you must be so good at math!". And my reply is always something like "I practiced and worked hard for many years, including 7 years of graduate school. I'm good at math now because I devoted years to practice." Keep it up kids!
1
I agree with comment by Tamar R. Our country needs to invest in teachers: hire more, pay them more. The shortage of teachers, particularly STEM teachers, is a crisis which could be resolved with better pay.
1
I strongly agree, practice is critical in math. However, I disagree that it cannot be fun. Figuring out how to make it fun, which good math teachers do, is the solution.
As a retired (private school) educator, I'm afraid I can't get with the program here. I've seen great math teachers, but I've seen too many who expect kids to learn under the conditions the author sets out -- and generate frustrated, under-performing, sullen kids who still "don't get it."
The problem: well-meaning teachers who just cannot connect math to the world we live in, and expect kids above fifth grade to begin dealing in mathematical concepts that remain abstract and self-referential. I believe in drill, memorization, and the like -- but only when kids see a purpose. This isn't 60s relevance -- it's real life that we often ignore in school.
Too many dedicated (math) teachers forget that students just do not share the adults' passion, neglecting methods that would inspire along with instruct. Math curricula have long lost their way - returning to the author's methods, as with phonics-only in language arts, isn't the answer.
Kids and teens deserve enlightened teachers who don't expect everyone to become engineers -- but expect citizens who grasp important mathematical underpinnings of everyday life, of science, and much more -- including a can-do attitude, of hard work, and critical thinking.
I'm afraid the author is going to further fortify teachers and parents who expect more drill-and-kill, without the hard work that goes into bringing real life issues to school and energizing individual motivation to learn how and why math is important.
3
Thank you Florine Gordon, the only female math teacher I had in my schooling. When women teach math, their female students know "girls do math." She made me love the numbers and the beauty of an equation and later I fell in love with geometry because I could see it all around. While I did not major in any math based profession, the analytical skills were useful in law where dealing with expert witnesses in science and math is necessary. So, you don't have to be an engineer, an actuary, or some other math-y person to appreciate the lessons of math. Maybe encourage that whole brained approach to help the math phobic.
Yes!
At the risk of sounding like “things were better in my day,” I attended a middle class (children of auto workers), average, public elementary school in the 60’s. In late elementary, we had pages of math homework practice every evening - multiplication, long division, fractions. And those of us who did the work really understood math and had a great foundation for the algebra, geometry and trig in middle and high school.
My hardworking classmates were all well-positioned to do whatever they chose for careers - some in STEM fields (like me), some in other fields, but all of us had a spectrum of good choices available to us because of our mastery of math.
Girls are certainly stronger in language arts at younger ages which naturally builds their confidence and leads to their being recommended for more advanced classes and experiencing better teaching. The same goes for boys and math. I am seeing more leveling as girls get older and the culture pushes them to achieve more in STEM fields; too many boys, however, continue to lag behind in language arts as they get older because they simply stop reading and never acquire the love for it.
I am supportive of changes that will increase math and technical skills for all Americans. All of our lives improve with better education.
1
In the 50s and 60s when I was in school in India we were made to recite tables by heart without looking into the books everyday after class .We also used to have oral exam in math where in the teacher will give out questions orally and we have to write it and submit.
1
Ms. Oakley's last bit: "(And, by the way: the same applies to your son.)" is important because despite all the worry over our daughters, it's our boys who are falling behind (graduation rate, drop out rate, incarceration, etc.)
In High School, according to the National Girls Collaborative Project, our daughters achievement in mathematics and science is about the same for our sons. However, "gender disparities begin to emerge, especially for minority women" in college. And women only make up "29% of the science and engineering workforce."
Of course, personal choice matters too, which is to say looking for equality by gender (or race or religion) fails to consider that for many men and women, finding a job that fits our work/life goals is most important.
Still, Ms. Oakley, and many commenters, make an entirely different point: involved parents make a difference. That's true across gender, race, and socioeconomic circumstance.
https://www.theatlantic.com/business/archive/2017/11/gender-education-ga...
https://ngcproject.org/statistics
More than that: teachers tell girls they aren't good at math, from a very young age. In kindergarten and 1st grade, the teacher would pick out a few kids who could do harder problems. Every time, the group was composed of boys. Then I'd work with each kid, and find there was always at least one girl, and usually 2-3, that were better at math, and enjoyed it more, than the boys chosen. Usually, the strongest math student was actually a girl. In K-1, some girls would demand to work at the proper level. By 2-3-4, they give up.
As a scientist at the 30 year mark of her career I could not disagree more.
I love the use of precise, descriptive, concise language to define a problem and the essential characteristics of a discovered solution with a validated hypothesis. A large part of my career has been doing this in words...to persuade my peers in journals and proceedings and enjoy the award of patents...but the representative language of mathematics is pure poetry.
As a young student I excelled in math and was often called upon to be a tutor to my peers, but I regularly choked in competitive multiplication face-offs that were supposed to be "fun"
Turning math into some sort of a sports contest of memorization rather than a problem statement reduced to the linguistic elegance elemental representation nearly put me off science..as it did my teenaged daughter...highly math capable...35 years later.
Think, define, validate, create...don't drill, don't memorize, don't make everything an idiotic competition.
82
Let's not get into another war on how to teach math as we had with reading. Children need to practice math skills and they need to develop an understanding of the concepts behind the rote memorization. With reading, the war over how to teach reading led to throwing the baby out with the bathwater when whole school systems not only discarded teaching phonics but in some cases forbid it.
When I learned to play an instrument, actually two of them, practicing difficult passages over and over to perfect them was important. Also important was understanding scales and how chords were formed as well as how to read the notes and the rhthms. That knowledge, though, would not make me a great musician without practicing playing my instrument every day and becoming more facile with it.
Let's not create an either/or situation. Let's work on how to integrate the two so that girls have quick skills in math and an understanding of the concepts behind the rote memorization and how math knowledge and understanding is critical in everyday life.
2
I think the US education system would do well to de-empasize "natural ability" and put more emphasis on practice in general.
3
The point about drilling, and practicing, OVER and OVER is exactly right. No child can discover concepts or patterns on their own, absent well-ingrained-deep-mastery through doing repeatedly, knowledge of the various instances/examples from which patterns emerge.
Another important point regarding girls, when I was growing up at least, is that the other girls didn't know that it's OK to not understand something for quite a while -- that learning HOW to do something first, without understanding it, is (usually) fine, because understanding can often come after the practice. But for some reason I did intuit this so that in A.P. Calc, the integration techniques I didn't get right away didn't make me worry, and eventually I understood the concepts behind all of them. (Ultimately this female got a Masters in Math from a top-10 grad school.) Whereas (again, at the time) boys didn't so much have the cultural option of dropping out, so they stayed in and many also attained understanding that way.
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K-5, my daughter loved math. Middle school changed that. Now at least 50% of math is using online programs (ALEX and Buzz Math). There is little instruction and little toying with problems to figure things out. Her homework consists of playing low-stakes math games, guessing, gaming the system, and doing none of the activities that make learning stick. She is in an honors/accelerated program, in STEM, and on a robotics team, but I worry that she will lose interest in math. Fingers crossed that the 7th grade curriculum & teachers are better. (PS. Boaler's _What's Math got to do with it?_ is a good read on math education.)
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Retired foreign language and math teacher here. How do young brains develop? No one really knows, but I bet millions of circuits are available for the young learner to capture and dedicate to her needs and interests. If we believe math is important, we should communicate that value to kids via interesting and engaging activities.
Generally speaking, learning one "system" such as musical notation, a foreign language, geometry, etc. makes it easier to learn an additional "system". I'm guessing the brain uses parallel circuitry development to add a new "system" to the repertoire.
Thank you for having the courage to suggest that learning requires concentration, effort and that hateful word, memorization. A mind unfurnished with information has no resources with which to think. This applies as well to mathematics as to every other subject i have ever studied. Unfortunately, kids have been deluded by the scholastic system into believing that little effort is necessary.
Agreed on the “rote” method. Academia sometimes gets so wrapped around promoting free thinking that repetitive practice/drilling is perceived to be counterproductive to creativity when it is actually necessary for building a foundation that can be developed and refined over time.
As a high school math teacher, I take strong objection to this article. Girls are the ones who excel at the high school level. More girls take AP's, more girls than boys are valedictorians; it is boys who drop out of school in greater numbers. Instead, it is the math, computer science, and science departments in colleges and universities who are the ones turning girls off from STEM fields, and I suggest they begin to take a look at themselves, their attitudes, and their practices. Prior to college, many girls love and excel at science and math.
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My 5 year old son is profoundly deaf. He was born hearing but lost his ability to hear through a drug mistake in the NICU. When he was diagnosed as deaf they said that if he were on a runway at an airport he wouldn't be able to hear the planes land or take off.
He was bilaterally implanted with cochlear implants at 12 months old. It has been quite a bit of work at times but he is now hearing and speaking beautifully. He sings, dances, plays sports and does everything any other 5 year old does.
It is my opinion that the cochlear implants are a miracle of Biblical proportions.
How any teacher can defend the current system that has the USA ranked so low in math scores is beyond comprehension.
When the "method" used and not the right answer determines a passing grade the system is totally broken.
The average high school graduate today does not know the multiplication tables, does not know what a cubic yard is and is unable to simple math problems that 6th grade students could in the past.
We spend more money, per student than any nation on earth with dismal results. It is time for a complete and total overhaul with heavy emphasis on the three "R's".
Your child's education is too important to be left in the hands of teachers who have no vested interest in the outcome and place a higher value on social engineering than on teaching life skills.
Without a foundation in math, which does require some rote, a child is handicapped for life with the current broken methods.
Such an excellent piece. I'm raising two daughters and this spoke so directly to me. Instinctively we've been dealing with math the way she says to, but it's nice to hear it was the right choice. Thank you Professor Oakley for writing this.
Great article, but I think there is a little more to this. My daughter never really cared for Math until she found herself in a class with a gifted educator. This one teacher convinced her that she was good at Math, and it became her favorite class - for one year. Then, an inexperienced teacher followed by one of the school's 'shouldn't be a teacher' teachers brought her back to hating the subject again.
She's a clever kid, in the 8th grade, and already firmly of the view that she can't do Math and can't wait to not have to study it again even though testing shows she beats the district averages and scores above the 95th percentile on standardized tests, and she gets As in class consistently. She definitely can do it, and her loss of confidence is down to who taught her, and their failure to encourage her. I think more practice is a valid point, but also, let's look at who is teaching Math and how they are doing it, as well.
My husband and I did this with our daughter--it is the best advice. Our daughter was low-average in math and from first grade on we got her a math tutor, even though this was an expense. By the time she was in sixth grade, SHE was utterly convinced she was a math wiz. She passed AP calculus in high school and went on to have three more years of math in college, which eventually lead to great GRE scores and a Ph.D.
When I witness the emphasis on sports for kids, I just sigh. Math is and always will be the door opener in life.
I had the immense good fortune to have Max Beberman as my high school math teacher, at University High School in Urbana, Illinois, in the early 1950's. Although Beberman is often touted as "the father of the new math," he went on to soundly denounce the way it was interpreted by educators who didn't really understand the concepts he was pushing. He was, indeed, emphasizing deep concepts -- for example, he insisted that we all understand the concept of "number" deeply.
But Beberman also understood all too well the importance of rote practice and building up "muscle memory" by practice, practice and more practice. This is the point that lots of educators missed, perhaps out of laziness or a lack of understanding on their parts.
Kudos to Barbara Oakley for this article, which is sadly still much needed.
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22 of the last 27 years I've taught entry level ESL, Special Education, college preparatory, as well as AP and IB English, and currently I am a Gifted and Talented consultant for literacy and numeracy. I help teachers to challenge their G&T numeracy students by finding puzzles and multi-step problems.
Most of this G&T puzzle-work involves a lot of language decoding. My middle school students who can manipulate numbers and use algorithms in their heads sometimes get caught up in the language of the problem rather than the algorithm or computing.
Divorcing numeracy from literacy is a huge mistake that we repeat in this country ad nauseam. Life has never and will never present a scientist, engineer, etc, ... with the problem: what is the square of a prime number divided by blah, blah, blah; what is the function of a parabola...
Therefore, word problems that mimic real life should be a goal of all educators, education. Discreet studies within a discipline have their place but the goal should be to combine all the disciplines that help our citizens (in training) more fully comprehend the world and its complexities.
Our daughter started playing cribbage with my husband when she turned 5. I credit this and my daughters desire to know how math “works” for her success as she pursues her career in data science. She always wanted to understand the process in solving math problems telling us it’s more important than the answer. Memorizing was never her priority.
I thought this was poorly conceived, awkwardly written and it failed utterly to make a legitimate point about "daughters," with whom I have first hand experience. Sorry, Professor, no offense, but of course women and men have similar aptitude in mathematics, and of course if you immerse yourself in mathematics as a way of life, you are likely or nearly certainly to be very able in a variety of fields in mathematics unless someone is making you take the class because they want you to be a techie or engineer... See where I'm going with this? The mantra for our kids was that English (language arts) opened their minds to the world, and mathematics opened it to the universe. The bottom line is to encourage your kids to take math and composition as high they'll teach it and read on your own as much as you can and get to like history and the classics. Literacy in mathematics and composition generally is a serious issue not to be treated lightly. It is a vital national security interest.
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Teaching children of various ages was part of my career over 30 years. I can't understand why, when I started, students were expected to, and did, memorize information. Memorization was a skill to be developed and used, employing a variety of techniques to take advantage of different learning abilities. it was seldom fun, but viewed as necessary for life.
By the time I retired, memorization was anathema to teaching in any setting. Now we, as a country, are near the bottom of the scale in math, have little sense of history or world context, and are, apparently, unable to differentiate between truth and falsehood. It seems to me we would be better off if we could relearn how to develop and use our memory.
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Would like to thank the author for sharing her perspective. I completely support her recommendations. I came to know of her via a course she taught on Coursera - "How we learn" something like that. In that courser I came to know of her life story which I have shared with many people.
I believe most people confuse pace of learning with intelligence. For some it takes longer to warm up.
Before we can build higher level constructs, one must be fluent with the basic building blocks. A lot of math can be made accessible via numbers and their properties including the use of contrived examples.
Using your head the biggest calculator should be encouraged. I volunteer at a elementary school helping kids with math and the one thing I ask them is to master tables. I often see kids getting lost in doing problems because they are stuck in multiplication / division part of a problem.
So...the thesis here is that girls equal boys in math ability, and surpass them in language ability, yet this is a disadvantage for girls? I don't know if the first part is true, but even if it is, the second part doesn't seem to logically follow from the first. Couldn't you just assert that girls have equal potential in mathematics, and that they should be equally encouraged in it? Was it necessary to make this into a zero-sum scenario? Also, the sub-headline is not developed in the essay--how exactly does the "way we teach math in America" hurt girls the most? It sounds like it's a lack of social and parental encouragement that may be diverting more girls from following STEM careers, not the way that math is taught.
No doubt our approach to math education needs work, but I don't think gender is that relevant to the problem there. Yes, concrete practice is essential, of course. Chinese classes are known for focusing on that, and they get better results than our own. However, it seems a lack of motivation is the real problem. Chinese schools are highly disciplined, and they rightfully recognize mathematical ability as a national resource that their patriotism encourages. The US fails to instill that message; instead, parents routinely tell their kids they hate math, and math is presented to kids like it was a useless torture that even their teachers don't like. Until we change that negative attitude toward math, we will lag behind other countries.
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Art is the language of the soul, Music the language of the heart, Writing the language of the mind, and Mathematics are the languages of reality.
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This is very good advice. In 4th grade, our daughter started saying she didn't like math. Instead of letting it go, we got her a wonderful tutor (a quirky, brilliant female grad student with whom we are still friends) who came once a week and showed her how fun and interesting math could be. She quickly got up to speed and came to self-identify as "the girl who was best at maths".
Ms. Oakley makes some great points. However, beyond rote 'fluency' learning one needs to consider the changing cultures that makeup many of today's public classrooms where too often male student(s) dominate and subjugate learning for his classmates with behavior antics or demands that have little to do with classroom academics. And
during recess, females are walking the side-lines while male students play with the real equipment, soccor and basketballs, etc. This I sense also carries over into the tech world and education.
Additionally, technology can become a culprit for math learning as students use smart phone calculators for what should be memorized knowledge. This is a tough battle as many of today's youth are almost addicted to their smart phones and Ipads.
I taught a class of senior and first year master's elementary education students once. With few exceptions, they complained that they hated math. Computations in class were minimal, involving 2-3 two digit numbers, but they were unable to add or subtract them without using calculators. Nothing had value if it could not be made to be fun. Not only was it the most frustrating teaching experience of my life, I worried about these teachers' future classrooms of children. With such negative attitudes toward math and anything that was not entertaining, I had little hope that their students would develop the interest in math that is essential for success in many careers and adult life in general. Maybe the problem is not with the curriculum or assumptions about students; maybe we need to take a closer look at the preparation and attitudes of those who are preparing to teach in elementary schools.
Math isn’t arithmetic: times tables, adding, multiplying, and so forth. Math is about imagination, a way of framing problems, of seeing things from various perspectives.
None of which is much appreciated in the sound bite era.
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A perceptive essay that points out one of the principal and pervasive weaknesses of modern thinking about education and the mastery of complex subject matter and skills. The author only goes astray by unfortunately thinking she has to make her point more salable by emphasizing a speculative gender learning difference angle she asserts is applicable only to girls, while she ultimately concedes in her final sentence that her principal thesis is equally applicable to boys. An otherwise excellent argument unfortunately diluted at its rhetorical apex by ideological bias.
I'm always a bit dismayed when I see fluency in arithmetic (certainly a good idea, but terribly concrete) confused with 'mathematics,' which is an abstract science. I wasn't particularly good at arithmetic (the rote stuff: I made stupid mistakes, it was boring) but I was always great at mathematics--the proofs, derivations, and logical systems; I majored in it at an Ivy, and it was a bit of a gut. Everyone should have an opportunity to excel at both interpretation, but please offer abstraction early, to allow identification of those kids early.
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News flash. Boys say the exact same thing. “I am not good at math.” The rejection of math and science impacts both genders. As a college professor of 40 years in the hard sciences, I can assure you that this problem is pervasive.
I went to public school in the olden days with old fashioned teaching methods. In middle and high school I was fortunate to have wonderful math teachers. I was very fortunate that my father was trained as a math teacher and could help me. Sure, I grumbled about homework like any other kid. But math and science became my favorite subjects. I went on to medical school at a time when women med students were a very small percent of med school classes.
Another problem with girls learning math is the attitude that girls aren't supposed to do better than boys in math and science. Girls do better in math girls only schools where they aren't competing with boys. I'll bet that attitude persists, hopefully to a much lesser extent than my school years.
Math matters, surely, but the writer's analogies with music are problematic. In fact, the kind of music teaching she talks about is associated with negative outcomes: never really learning much of value other than some basic skills and tunes and than dropping out. Most people who play music in school give it up within a year or two of graduating HS (or college, if they play there, too).
In contrast, many today in music education promote more holistic approaches, where a pleasurable connection to music increases motivation, curiosity, and a disposition that keeps students engaged long after they have left school. Scales and chords might be present, but not prominent, as conversations about music and lyrics and meaning are wedded to meaningful participation opportunities. And students are encouraged to improvise and compose instead of merely learning the compositions ratified as already great masterworks. In fact, Jackie Wiggins, who teaches at the same institution as the author, is one of those in music interested in more constructivist approaches.
Math matters, and practicing matters, but I oppose those who put down joy in learning or think that the faintest whiff of pleasure signals softness. See Gardner's columns of math questions, or Asimov's book on numbers, or Lewis Carroll's fascinating logic. That's the truth for music and math.
I've seen tiny girls in primary school - with a sheet of one of those (Kaplan?) school exercises - all boxes like 21-8= (fill in the answer) - and watching tiny girls assiduously working through them - very nice.
I've also seen them keenly playing Mathletics on computers - seeking better scores than their classmates whose scores they can see - so social relativity as a driver - yeah that works !
I was always good at math - and quite possibly liked it in my youth because it was one thing I could do better than boys :)
Whether it was memorizing multiplication tables or grasping advanced calculus years later. I went on to work with computers, where mathematical and logical abilities are very handy.
I had assumed that all science/STEM majors would have a solid foundation in math, only to realize that, at my current professional setting in research labs, that not all do ; leaving them at a disadvantage in the days of increasing data analysis for all kinds of problem-solving, and what is called ‘big data’.
My experience of learning the times tables as a child was unpleasant and in retrospect I think harm was done. I had to start out at the beginning 1 x 1 all the way through the twelve sets of tables. If there was a mistake I had to start at the beginning all over again. This went on for hours. One day in my miid-twenties I pulled out a calculator, which not exist when I was a child and I punched in 8 x 7 and 56 was the answer. I asked my father what was the point of learning by rote the times tables if a calculator could provide the answer. No, no he admonished you have to know it by rote. I was also subjected to complex algebra equations, which I now realize were more suitable for a high school student than an eight year old girl. I could not comprehend how to do them and was not successful. This instruction from a man who could not balance a cheque book. I am sometimes told I repeat my self in conversation and have only recently realized that it may have something to do with always repeating and redoing the times tables for that impossible quest for perfection, that I could never attain. I do know that 8 x 7 = 56, without a calculator.
My whole life I "struggled" with math. This perception was not helped by my mother who, despite being a teacher herself, would harp on about how hard and boring math was, and tell me repeatedly that she herself was terrible at it! English and music were her specialties so perhaps not surprising that these also became strengths of mine as we focused on these subjects outside of school hours! Those formative years have forever impacted my confidence around math....despite ending up in careers where it's a required daily skill and finding out I'm actually quite good at it! Safe to say, with my first daughter about to be born, I shall be following this author's wise recommendations!
This is article is 100% true. Math department chairs in the schools are ex teachers who never really liked math for the sake of math, but wanted a larger salary. High school teachers must teach at the whim of uni education departments who develop their theories after spending three weeks with 20 kids. MS/HS teachers know the uni education department is a joke becuase no other department on campus cares about it and its theories. Teachers can't do rote and drill anymore and the kids are in fact suffering. Everybody is not going to be good in math, and classrooms should never be just chalk and talk, but let kids memorize.
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Showing enthusiasm and a smile after work was perhaps the most significant thing that I did for many years to support my daughter. Learning Math and Science requires love as well, sincere love for solving problems that is. My daughter is now an undergraduate student at Caltech (California Institute of Technology). Her major is Physics. I never hired a tutor, but rather sat down with her to occasionally discuss alternative ways of solving problems. I could never compete with her ipad, but for example I might encourage her to graph a trigonometric function on millimetered paper and use thin colored markers to represent it in both Cartesian and Polar Coordinates. She took it as a game of sorts. It's also nice to witness the aha moments when maybe Combinatorial Algebra or applying intergrals to calculate volumes became something cool for her to do, rather than something too difficult.
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Several of the teachers at my children's elementary school quip 'oh, I'm just not a math person' and somehow think that it is OK to be innumerate in a way they never would tolerate someone saying 'oh I'm just not a words person' and being illiterate. Math is as core a life skill as anything. (at least if you ever want to finance college, get a mortgage, save for retirement, etc.)
I couldn’t agree more - but what child will let their parents drill them? Not ours! Solution: we took our daughter to Kumon. She spent a few months doing math drills - - mainly arithmetic and multiplication, something that’s out of fashion in American education. No more counting on her fingers - once memorized you never forget. Now she’s a terrific and confident math student.
A long time ago, after receiving praise for math skills from my school’s principal and first grade teacher in a letter to my parents, my mother told me I was not supposed to be good at math; being good at math was something for boys. I did not understand why I could excel and it be disregarded by my own mother just because I was a girl. This was how things were for me in the 1950’s. It took many, many years to earn a Ph.D. In Chemistry, which required a lot of prerequisite math courses. Math does take practice and persistence. I did some university-level teaching in the mid-2000’s for several years and found I had a better foundation in math from what I learned in primary and secondary schools than about one-third of all my students. Something was wrong with the way math was being taught to boys and girls.
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Yes the US is below average on the PISA. However when you look at the details, our students do fine one one-step computation problems - the kind that can be improved via drill and practice. Where they fall down is on multi-step problems, the kind that require conceptual understanding.
This is something of an oversimplification, but less so than Dr. Oakley’s opposition between drill and understanding in mathematics learning. Mathematics, when it makes sense, is enjoyable, and, yes, there is also a (relatively) small body of material that need to be committed to memory. But even this can be done via fun kinds of individualized practice. It’s long past time that we should be urging anyone to “make” girls do math - girls and boys should look forward to doing math, and we need to help teachers learn to teach so that they do.
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Desirable difficulties...so force them to...
Hmmm...
I was shocked to learn in my late 20’s that “girls are not good at math”. In my class at school, it was the girls who excelled in math and science. It was a competition between the girls for who would be valedictorian. I thought this was normal. It turns out that I was fortunate not to be exposed to the stereotype that holds back so many girls from excelling in STEM subjects and leadership roles. My wish is that more girls had the same experience that I did.
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When I was driving around with my kids I would ask them to answer these questions:
2x3=?
3x2=?
6/3=?
6/2=?
And when they could do a times table in order, I'd skip around until it was ingrained in them. I wanted to make the reciprocity of mathematical functions intuitive to them.
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What I tell my kids is there are different kinds of math. Just because you don't like trig doesn't mean geometry won't be your thing. I didn't like trig much, liked algebra and geometry okay, but discovered I loved calculus. Our teacher always told us how important intuition is in calculus-- now, if we believe the stereotypes, then we should know that girls are good at intuition. One more reason for girls to stick with us.
But perhaps the most important factor is the teacher. My school was nothing special except for our math teachers. I had two who were brilliant teachers. They loved math. They truly believed it was the most fun a person could have and they encouraged all of us -- boys and girls alike -- to love it too. In my senior year we had math first thing in the morning. Our math teacher would bound into the room with a broad grin and tell us the only thing better than coffee in the morning was calculus! We didn't quite believe him, but his class was certainly the best. Hmm, so maybe we parents shouldn't tell our kids to work at math even though it's not that much fun. Maybe we should tell our kids to do math because it is fun. And then act like we mean it. Just a thought.
Ms. Oakley's piece makes a lot of sense in our household of three busy elementary and middle-school aged girls. Figure skating and piano are two pursuits that obviously require a lot of repetition to excel. I often say that "practice is magic" or "practice is progress." Sometimes it really does seem like magic!
For some reason, however, learning math no longer seems to follow the same model, at least in schools. The solution of many parents where I live is to enroll their kids in an extra-curricular math school. It encourages learning and practicing strategies, creative thinking, and problem-solving, with a completely different curriculum than the local public schools. After a year of classes at the Russian School of Mathematics (in the least advanced of three levels for her grade), what my rising fourth-grader can do is impressive. Now school math is easy for her, and she is no longer afraid of it. Public school curricula in math is just not enough for American school kids to compete with their peers from other countries, which is a real shame.
Learning math gives girls, and all students, options. If they want careers in science, engineering, medicine, finance, research, or any other technical field they need math. Not every child will choose a career that requires math, but those who don’t know math will not have the opportunity to make that choice.
From what I’ve seen (as a college instructor), a big part of the problem in K12 education is that many teachers lack basic math skills, and their lack of comfort and enthusiasm for math is passed on to students. If we really want students to be better at math, then we should require all teachers to demonstrate competency as well.
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Even if I this argument we’re borne out by data, it is by no means every boy and girl, or even close. I know many boys who are much better at verbal skills, and many girls who are much better at math. When I think about the kids I know, there are about equal numbers of girls and boys in both categories. This is the problem with teaching to a stereotype instead of to individual people.
Fluency in English is just as important (maybe more important) than math fluency in pursuing a STEM career. Excellencence in mathematics requires proficiency in language, not necessarily arithmetic. After all, mathematics--like all human knowledge--is an expression of ideas, and ideas are expressed in language.
Telling oneself "I am bad at this" or "I will never be able to do this" etc.. by anyone and about anything and at anytime in life - academics, relationships, dieting, exercising, etc... is self hypnosis and WILL affect our ability to succeed. These phrases we all utter need to gain our awareness we must train ourselves to stop. Bad habits.
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I don't know why we continue to lie to ourselves about the innate ability of males and females. We are different, there is nothing wrong with that. The article claims girls are better at reading and writing. I agree; something in our DNA is obviously causing that disparity. Super !!
Boys are better at math than girls. We all know it, lived it and continue to see it. For 50 years boys have outperformed girls on the math SAT; and the gap is remarkably consistent; like scary so (about 30 points). And at the high end, meaning those scoring between 700-800, it's 69% boys and 31% girls.
This is not bias, it's not an accident. It's nature.
So yes, encourage girls to enhance their math skills; but stop misleading us on the starting point.
I was shocked when a note came home from my son's 3rd grade teacher that they would not be drilling the multiplication tables in school because there wasn't sufficient time. They asked us, the parents to do it. This is basic knowledge that everyone needs to know. Why wasn't there enough time to work on this in school? Yes, I drilled my son, but how many other parents did not?
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Very few of the math teachers I had or that my children had were actually good at communicating mathematical concepts, which came to them with very little effort. People with a natural talent for math often don’t have an equal ability to teach it to others. But math is the most abstract of the studies in the lower grades and young children do not have the ability to think “abstractly,” so it is really important that the teachers be extraordinary communicators. Practicing 2+4+6 dozens of times does not teach the underlying concept and as you advance in education, understanding the word problems becomes more and more important. Girls have an advantage in this but not if they don’t “get” the underlying concept, and that requires a better than average communicator as a teacher.
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Yes, this is very true. I am talented at math (and a good programmer) but it wasn’t until I discovered, in adulthood, that to be good at programming I needed to hone my math skills, that I practiced my mathematics.
When you practice it, you become facile, and it becomes, no shock here, fun.
In my admittedly limited experience (I have only my own to go from), a big part of the problem is that we don't acknowledge different learning styles. People's brains work differently.
Even though I was a boy and it was the 1960s and 70s, I was always good at reading and bad at math: I skipped 1st grade because I could read, then had to repeat 3rd grade because I couldn't do math.
The couple of helpful math teachers I ever had, whatever their personalities, always had in common an attitude of: "You're not stupid. We can find a way for you to understand this." Sadly, it seems like there is no time for an approach like this now (not that there really was then, either, but a teacher could afford to care once in awhile).
outrageous that author claims girls are better at reading. That's also an artifact of sexist upbringing/stereotypes. Same as the math, the other way. Diversity training for author, now.
Math practice, like any practice (piano lessons - a waste of money), requires focused interest. Focused interest requires a reason to be interested and usually, a mentor. I remember being a little girl in the late 1960s proud of a math project for open house, telling the teacher and my mom: "I want to get a PhD in math!" and hearing them sigh, "She doesn't know what she's talking about." I accompanied my father to the Seattle public library many times; while he researched his patent idea I pulled books off the shelf and sat reading about matrix algebra because, ciphers! A book report in 9th grade math class was surprisingly well-received, but, whatever, it was something to do. After many twists and turns including an aborted science career, I became a lawyer because using language arts to frame and solve problems is something I love to do. Nurture a child's interests but always trust a child to find something s/he loves. Just because.
So let's see. Young girls and boys are basically equal in math, but girls are significantly better in reading and writing. At the college level, women are now outnumbering the boys in enrollment and degree completion to the tune of 60 vs 40%. And we're supposed to be worried about the math education of girls? It's the boys who need the extra attention. What, that's too politically incorrect for your digestion?
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It’s not only American girls who can’t do math, but boys too. There are almost no Americans in graduate level studies that requires math. And they are predominantly Asian, now. And there are lots of reasons why. In the US, the Public Schools are now run, managed and staffed over 90% by women. It’s the largest employer of women folk in any state of the union. And you can easily say it’s is the most dysfunctional organization in the land. Here, in the city of Seattle, the city council just raised property taxes by up to 35% to feed this feminist monster, and gave nearly 700 million of tax-payer money keep it from collapsing. But our public schools’ bureaucrats clearly know—the more they fail our children, more dysfunctional, chaotic they’d become, the money they and can extort out our tax-payer. I’m sure the teachers union knows this too. All this because along the way, we have abandoned how children learned the best, and embraced politics and social engineering. All the post- modern nonsense invented in the American academia have infected our public schools like a debilitation disease. In our public schools our children do lot of race, gender and cultural projects that has nothing to with acquiring learning skills. They have given up learning real subjects like math, altogether. But our feminists are insisting that they want to do the same ─to America’s last hope and our saving grace ─our universities.
"Unfortunately, the way math is generally taught in the United States — which often downplays practice in favor of emphasizing conceptual understanding ..."
Unfortunately it is now up to the parents to insure the student practices enough. Why do I say "unfortunately"?
Because those with parents who care enough to do so are labelled as "privileged".
As a scientist, and physicist, I have a bit of a different view.
Innately talented, I was pushed to study math, even when I openly expressed that I didn't want to, and ultimately I flunked out of math on purpose in my senior year, just to get away from being bullied by the boys, and being constantly pushed by the girls to let them cheat off my tests.
YES, teach your daughters math, and the language of math, because it is it's own language, and it's language is very precise, and all students benefit from learning that kind of precision in language.
YES, teach your daughter equations, plots, etc.
THEN let them take a break if they want too. Success or failure in math is not determined solely by their Grade/Middle/High School performance!
In my personal life, when I exit the math and science world, and enter the world of the "general public," I am OFTEN confronted with women that say:
"Oh, I wasn't good at math."
And then every other women in the room agrees, and supports this woman's "confession," while I remain silent.
Do women realize that saying that is equivalent to saying:
"Oh, I wasn't good at punctuation, those comas were just too hard."
When, as a society, we accept without question, women who declare math ignorance and use it to bond with other women, we diminish the real capabilities that girls and women have.
If we accept math ignorance from women, then by default we also accept the ludicrous statement that punctuation was "just too hard" to learn.
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Please teach your daughter about finances.
Girls who are the best in English and are outstanding in math are unlikely to be confused about their abilities. If you're the only one who can do a geometry proof and the only one who understands derivatives right away, the fact that you're the best in English is not going to make you think you are stupid in math.
News flash. Boys say the exact same thing. “I am not good at math.” The rejection of math and science impacts both genders. As a college professor of 40 years in the hard sciences, I can assure you that this problem is pervasive.
Arithmetic requires practice, which few people do today when we have automated the process; mathematics requires logical rigor.
I am sure you are probably right but I am the mom who did this. Every day in the car, every summer, winter, and spring break. She was in private school, math class customized to her, homework help in small groups after school for three years. Two different tutors. Now she enters HS, and I don't think she is math literate, which means she will struggle in math and science. Meanwhile, I have seen her writing skills take off through middle school and standardized testing shows that she is great at all of her skills except those math related. I bought in fully to the idea that everyone can lay down these basic skills with enough practice and effort, only to have it not work for math for this kid. I'd love to hear about alternatives.
Learn your times tables from Multipication Rock!
3 is magic number
Doesn't anyone care about the boys or men?
Girls are better than boys at reading and writing and equivalent to them in math? Are boys really so stupid and intellectually disadvantaged?
In microfinance, men are deliberately ignored because women are posited as somehow being better credit risks.
And now American educators and schools conclude that boys can't best the girls in reading and writing and sometimes do better than them in math, only because the girls let them!
Guys, it's up to you! The system is geared to taking you down, belittling your abilities and dedication, and when and where you thrive, telling you it's only because the girls let you.
Fitting in a Trump age I suppose.
"Dislike-avoidance-further dislike," combined with a math teacher in 10th grade who told me I was stupid finished off math for me. Despite years of tutoring, and an understanding of mathematical concepts, I was never able to build the arithmetic skills that I needed to pass statistics in college (back in the dark ages when no one had calculators).
I had math anxiety writ large.
Why is it not okay to be a girl? Why do girls have to succeed at things men are better at? Why aren't men trying to do girl things? Why are things like art, crafting, and quilting "girl" things and therefore unimportant and not as worthwhile. Why are athletics more worthwhile than quilting -- which actually provides coverings to people in need -- rather than a selfish athletic activity that breaks a previous record?
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Girls need to know they can do math *and* language arts. I loved math and was one of the top students in my high school calculus class. That class was taught by a woman, and she taught us so well that I placed out of my first year of advanced math in college and coasted through the next three semesters. But I was also good in English, winning my high school's language arts award and editing its annual magazine. I went on to get degrees in biology and journalism and have had a successful career as a science writer. Yes, girls can do math and language arts--and anything else they want to do.
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Thank you! I do this for a rather unfortunate reason. My daughter has an affinity for Mathematics but her friends think it’s so uncool and her school will only do the bare minimum.
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I get so tired of the response to sexism being sexism.
All of my kids know all people should be respected no matter what is between their legs, and that what is between their legs is unrelated to what is between their ears.
My family is good, no, excellent at math. We have a professor who teaches quantum physics and a rocket scientist. One is female and one is male. I believe, like in many other cases, the "differences" in these studies are not real, but only pure sexism. Just as it would b pure racism to say blacks ae worse than whites at math, so we need to "tell our kids to practice math, if they're black".
Did I mention both of those mathy family members are biracial, and their kids are three races in terms of background? And that the mom has been mistaken for her children's babysitter, likely due to different skin colors? Let's stop saying women are bad at math, and help all kids acheive. Not to mention where do articles like this lauding sexism are offensive to those who believe in transgenderism.
Our daughter went to an all-girls middle school (best decision we ever made) known for keeping girls interested in math and science. Back to school night, the math teacher said, “whatever your experience was with math, zip it!” Do not tell your daughter how bad you were at it or couldn’t understand it. That is setting them up. Re: math homework, spend no more than 30 minutes a night on it and no more than 15 minutes on one problem. If they don’t finish it, send them back with what they covered, that way the teacher knows what they understand and don’t. And, if you do help them, have them teach it back to you so you know they understand the concept. There were times that we’d get an email saying the teacher was going to reteach a concept because it was obvious from quizzes that the students didn’t understand. It was on the teacher to reteach it. Imagine that!
And btw, this was not a rich kids, all-white school—50% of students were people of color, a third received financial aid.
-what we did have in common was a buy-in of the school philosophy—largely in sync with two books—Mindfulness by Dr Carol Dweck and The Blessings of a Skinned Knee—you have to let kids fail sometimes.
There are great schools out there; too bad we don’t observe what is working.
Oh ya, no teaching to the test (and very little multiple choice). Mostly short answer—how else do you know how well they are grasping the concepts.
I could go on and on.
My daughter is a rising junior math major.
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My father was a math professor when I was born, so math lessons started very early. I was good at math and even came up with a way to calculate matrices when I was 12 or so. Unfortunately, my dad ruined math for me by overdoing it. Every Saturday, I had to write out the field axioms and the decimal equivalents, the Greek and Russian alphabets; later, the laws of algebra and trigonometry. There were full days of math on weekends and during the summer. I was expected to be several grade levels ahead of everyone else, even in elementary school; he had me learning calculus at the age of 11. There was always some kind of math or science lecture going on, spoiling car rides and summer afternoons and depriving me of the opportunity to just be a normal kid. I did pass college calculus, but never took another math class. I'm glad that I'm not "afraid" of math or science like so many women are; my familiarity with these subjects have helped me become an effective technical writer and editor. But it's important to listen to children and set limits on drills so it's not just a never-ending punishment.
The thing I most appreciate learning is how to use "easy" versions of word problems as examples for solving more difficult ones. A 63% increase isn't an intuitive concept, but 50% or 100% is. Use the easy version with your variables and use your common sense to check the answer. Then substitute the new figures in your equation and solve.
Absolutely! I was a strong math student and pursueed a PhD in Chemistry. It is ALL based on math. Girls can do math. Don’t let anyone tell them that they cannot.
Math is NOT sine qua non for all STEM fields. Probably it is for engineering, but we're not all interested in engineering. It's perfectly possible to excel in the life and medical sciences while loathing and avoiding math. In fact, great reading and writing skill will take you much further in the life sciences than math. Please stop shoving math at everyone just because you find it enjoyable or useful. OK, rant over. Aside from this point, I liked the article!
What a weak commentary!
Practice math?
It's like saying practice Science. Or Biology or Phsiccs?
Working on "Understanding" is whats required and then executing results from that understanding.
It's 'Understnding" basic underlying concepts (the language) of math where things go wrong.
That's a function of poor teaching -where most teachers have no rerequirements for being abe to communicate core math concepts:
Like -i'm sorry to say -YOUR ability to communicate the real issue related to math acumen.
Could not agree more. Not being able to immediately recall the product of any two single digit numbers greatly hampers a student's ability to understand fractions which in turn makes equation manipulation arduous at best. At that point, science and math classes are pretty close to useless exercises in rote memorization of apparently meaningless drivel. Paradoxically, a lack of rote memorization put this snowball of ignorance in motion.
So, the article states that boys are innately inferior at language and reading, but girls and boys are innately equal at math. One wonders how accurate these generalizations are. Anyway, if you want to recommend girls practice math, fine. But what about the boys? There seems to be no concern about their "innate" inferiority in reading and language. Shouldn't you encourage them to try harder in these areas?
Do the following with your kids:
Ask an Indian friend to bring back the math text books from a good school in India. Or obtain one online - it's easy with a bit of Googling.
Then, sit down with your kids and make them finish the math over summer, ahead of the next grade. If you can't do it, hire a tutor.
Use the actual school year to review the math and see another way (the American way) of looking at the same concepts.
This is the most accurate and straightforward assessment I've read on this subject. It also describes my own childhood history with math. To this day, I panic when I have to do math on the spot, and it has definitely limited my career options. I am trying to right that wrong with my own girls. We do a supplemental math program (Kumon) and fortunately, it's working -- but I worry about the kids who can't afford that. I hate to blame schools for all the ills of the world, but in this case, they have the power to stop this craziness and they refuse to.
I take issue with this article. While I agree that practice is important in math, rote is not necessarily the way. I have taught fourth grade, GED, and I now teach remedial math at a local community college. As a math teacher, I encourage my students to make mistakes, and I encourage them to think of math differently. Allow me to explain: the author talks about girls having better language skills than boys, which gives girls an out on math. She suggests that math be taught in a manner similar to how guitar is taught -- practicing chord after chord. A good point since chords are the foundation of music. Math has its own chords -- the times tables, addition facts, etc. -- that students need to master. But math, like music, is about more than playing chords. It is about how and when to use those chords to make beautiful music is vital. That is where concept comes in. There is a quote attributed to Count Basie in which he is said to have said that sometimes the best note is the note never played. I agree that math is not taught well these days, and I believe that is tied to our results oriented culture. Students worry to much about the answers being right. But how can one answer a question if one does not know what is being asked? I stress math as a language, and solving a problem is about asking questions. By the way, the top 7 students in my class of 19 are women, many of whom said they hated math several weeks ago.
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As an engineer myself, this article is probably on the money. But how we teach math in public schools is a disaster. No longer do kids come home with a good textbook with a nightly homework assignment to do 20 -30 problems on a given topic. Nor do they spend substantial time on a given subject before it's mastered. Now they get 'worksheets' with a handful of problems to solve. They waste interminable time on fuzzy areas like 'mental math' and 'estimating' in the earliest years of primary school. This is ridiculous - in the earliest years, they should be doing rote memorization and practice, practice, practice.
And don't get me started on common core math. The absurdities that I've seen demonstrated with today's 'modern' curriculum will only further ensure the deterioration of primary school math skills.
US public ed needs a major overhaul. Dispense with the fluffy feel-good curriculum. Get back to solid fundamentals.
Thanks for this piece. Sick of reading quilting books that pitch some way to resize a block or figure yardage but always preface their tips by "Don't worry if you're no good at math, this takes all the math out of it and makes it super simple."
Meanwhile they presume they're addressing a woman who while she doesn't think she's any good at "math" also doesn't realize a) that book is only using arithmetic, b) she's not fazed by "math" when it comes to knowing how to scale a food recipe up or down and c) long ago learned that it's not always about scaling every ingredient in the same proportions.
I teach Introductory Physics in community college and I can attest to the truth of everything in this article, for all students, not just girls. The ripple effects of shaky Math continue into all basic science courses. My work is made doubly hard when my students don't have a good mathematical foundation. Given the limited time, I have had to forgo teaching interesting but mathematically complex Physics problems because my students cannot handle the Math. All of my students have been taught the basics of Algebra & Trigonometry but they have not had enough practice to make problem-solving in these concepts second nature. Growing up in India, I had a better proficiency by 10th grade than my students in the US have in college.
I am having a great deal of difficulty imagining my daughter thanking me for making her do anything.
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Got it!
So now it is not only politically correct, gender sensitive, etc. and even acceptable for publishing at the nation's "paper of record" that - of course "based on studies" - quote:
"She (i.e. a statistically typical girl) actually is just as good (on average) as a boy at the math — it’s just that she’s even better at language arts."
So, boys are not as good in language arts (important for interpersonal communication w/in family, work teams, civil society and international institutions, etc. etc.) yet they also don't have competitive edge over the female half of humankind in math (foundation of STEM, high finance, etc.).
One would expect that, stating such fundamentally and alarmingly important (and, again, studies-supported fact) author would offer her giving immediate and extra attention and chance to build those "new neurological paths" in their brain to "little boys" as boys (of any age) are, proven here yet again, by far the largest "at risk" and "underserved" population.
But we find here (or in essence anywhere) nothing like that.
Half of our children are, yet again, written off as it is "in" and worth to publish yet another call for investing in girls.
Concerning authors (in my mind correct) assertion that the way math is taught in our schools is ineffective and often counterproductive and even harmful, she doesn't give a hint why it is so, thus where to start with improvement.
My kids (top 0.1% PSAT scorers) and I (MS in Engineering) can tell.
This is completely the wrong approach. Girls do not need to do more. That is not what is holding them back in Math. What holds them back is decrimination and lack of opportunities to excel in the field. Having girls study more will not accomplish anything significant; addressing the discrimination will benefit everyone.
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"Unfortunately, the way math is generally taught in the United States — which often downplays practice in favor of emphasizing conceptual understanding"
"All learning isn’t — and shouldn’t be — “fun.”
I don't know how math is taught now in the US, but I am 66 and I remember the 5-6 grade (in NJ) when the "new" math was introduced. Drills out, concepts in and that worked fine until later grades when the concepts were harder and basic skills were lacking.
As for fun, try convincing parents that school and learning have to adopt certain boot camp elements to succeed. Discipline and drill is necessary not only for math. But many parents look at this askance thinking it damages the psyches of their little geniuses, boys or girls.
As for math, though, the key is good teachers, and that is not easy to find anywhere. If you can do the math, you will not be a teacher but an engineer, doctor, high tech, finance etc.
What a powerful call to action by a female scientist who defied the myth that girls “can’t” do math! In 4th grade, I had trouble with math and my immigrant father struggled to afford a tutor for me, because he wanted to be sure I would get into college and always be able to support myself financially “with or without a man.” Not only did I do that, but earned an MBA in Finance, had a long career in business, went on to teach university business courses, and now help nonprofits and colleges develop strategic plans to ensure their financial solvency. My father was the most influential mentor in my life.
Well, at the high school here in Ottawa (Canada) - the girls are all coming up on top.
My kids were both taught every day math, which involved a spiraling program, coming back to skills throughout the year in an attempt at a second, third, etc chance to learn something. They were told not to memorize facts, that it would come to them through practice. They learned to multiply using some complicated lattice system I never understood. My daughter did eventually learn her facts through osmosis (and I taught her to multiply the old fashioned way). My son struggled, and I brought him to a learning center. The first thing they did was teach me how to properly drill him on math facts, and to devote 5 minutes a day to it. His confidence soared, and he finally felt smart in math. Now he is in college learning calculus 2 and other higher math. I think we do a huge disserve to our chidren teaching them higher math without drilling them in basic facts when they are young. I also never allowed other family members to disparage math around my children. Such talk as "you will never use this" makes math seem unimportant and not worth the effort. I always told them that even if you don't use it in daily life, math is the best way to train your brain for problem solving. No other academic pursuit is as useful.
YES!! I've been saying this for about 30 years now. It's nice to read that now there's research backing up what anyone who was paying attention knew. Whether it's math or music or marbles or martial arts, repeated and intense practice is an essential component of learning.
When my daughter transferred, after 2nd grade, from a lousy public school to a private school with a very traditional curriculum, she was way behind, so we drilled her in 'math facts' all summer, to get her ready. Sounds old-fashioned, I know, but she aced her first timed math test, which gave her confidence that she could handle a very competitive environment. Best summer investment I could have made. She works at Apple now.
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It sounds like such practical advice. But Oakland University isn't exactly MIT. Having attended a nearby fabulous private high school, Cranbrook, I'm drawing a blank on Oakland University attracting the attention of anyone remotely capable in the STEM fields.
Most people who will go on to be talented musicians don't really get there from practice and repetition. It's an innate gift. "Guitar teachers" and those who teach any instrument recognize this immediately. Some students are shown a few chords and a month later they've written their own songs. Others struggle with those same basic chords their entire lives. My father had true absolute perfect pitch, my mom was tone deaf. Most of us fall somewhere in the middle. The prodigies who make it to Carnegie Hall before they're old enough to vote had a natural facility that made practicing the scales and arpeggios tolerable. Gil Shaham is a cousin of mine, I know of what I speak.
It's the same thing with languages. Some people just have the knack, they pick them up effortlessly. Others struggle despite doing the homework in high school and college. Might be connected to the hearing, my father spoke ten languages fluently.
Math is absolutely no different. My classmates that excelled in math and science, it just came naturally. We didn't spend any more time on the homework than our peers. In fact we probably spent less time as it came to us effortlessly.
Sounds nice, but it's not how the real world works.
Isn't our industrial-technological society fantastic. How, we force children to learn things they don't want to. But I guess that is just what "progress" looks like.
Although girls are not naturally good at math and science, it is important for them to learn it. These skills come in very handy on standardized tests, which evaluate competence in areas most people will never encounter for the rest of their lives.
Reminds me of how kids will say, 'I never got math.' My guess is that we've all heard someone say that - and yet, when was the last time we heard someone say, 'I never got words.'?
It's pretty obvious that this was written by someone trained as an engineer rather than a mathematician, since no true mathematician would bemoan a relative emphasis on conceptual understanding of mathematics over rote practice of arithmetic operations. (Also, I'm eager to know where the author got the idea that U.S. schools do emphasize conceptual understanding; that would make my day if it were true.) I think the author may also do a disservice in suggesting that prioritizing automaticity in operations over a solid conceptual understanding will lead to a secure future in STEM fields. Rote operations can already be performed mechanically and the STEM future will likely belong to those who understand mathematics on a deep level.
I've been tutoring math for 27 years, and I'm the author of five books on math. I've seen a huge change in the years I've tutored in students fluency with math facts, and the number 1 factor is the now all-pervasive use of calculators. When calculators first started being used in schools they were hailed by many as a great tool for helping students deal with higher-level math problems, and it's true that calculators, used judiciously, can help students do just that. But today students use calculators so much that most students I work with have become overly dependent on them. ELEVENTH-grade students I work with — and they are not all terrible math students, many of them are just average — reach for their calculators for problems as simple as 7 + 5, 6 x 3, 2 to the 3rd power, 10 – 3 ... I kid you not! Somehow schools need to regain a balance between appropriate and inappropriate use of calculators. We are raising a generation of students who have lost virtually all ability to do what used to be called mental math and it is very very sad.
Sent both kids to the Russian School of Math (after school) which is both instruction and hours of homework every day. Painful hours of homework, but the kids were having the bonding experience of knowing that their classmates were also slogging through the same problem set.
An interesting upside, beyond the proficiency that comes from hours of practice, was a halo effect at school. Youngest daughter was adept at math, ergo teachers felt she'd be adept at x, y, z, and encouraged her, respectively.
The other upside, of course, was that the investment of time in math at a younger age meant than HS classes (eg BC Calc) were breezily easy & required minimal after school prep.
My late mother made me recite the tables from 2 to 20 and father helped me solve arithmetic problems, guess what I unexpectedly topped in my high school class. Not all learning can be left to teachers, parents should play a complimentary role in the learning of their children, both son/s and daughter/s.
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I’m a former math teacher and well remember long hours of practice, so I can’t disagree there! However, in my observations, it has been lack of comprehension that drives people away from math. Basic arithmetic and grade school math were so badly taught for a long time, alternating poor explanation with endless hours of make-work repetitive work sheets. Many never recovered from that experience! At least with an emphasis on comprehension, grade school teachers have learned something and are not permanently discouraging children, making them think they are ‘bad at math’. Then in high school and college young people will find good teachers and discover the rewards that come with putting in the practice. Hours of practice for a mathematician are like the hours of practice a good pianist puts in, hard, sometimes very hard, but not horrible. And the rewards are great.
Unfortunately, many parents will take this article as an excuse to return to the old ways of demanding that children spend hours on incomprehensible and toxically dull worksheets. After all, that’s the way the parents and grandparents learned to hate math, and the old ways are best!
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We should implement whatever math programs work on the most successful countries. We should tier math so students move at their own pace. It should not be a mark of shame for classroom teachers who struggle with harder math themselves to have math specialists lead the more advanced students. Tutors should be available for all levels. Fear of math is very real and must be dealt with early on, in creative and individual ways.
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My goodness, a thousand times YES! It works, just do it. Forget about fun stuff and experience the pain of learning. If that means failing sometimes, so be it. You can’t grow if you never stumble or fail. I discovered a love for chemistry and the ability to solve differential equations in high school, ended up in engineering school and am darn proud of my career as an engineer in a few intersecting fields. The fact that I am a woman is incidental to all this. Engineering is not just a profession, it puts its imprint on how you approach and live life. Now retired, I’m still an engineer and if given the chance to do it over, I wouldn’t change a single thing.
I did and today my daughter successfully defended her master’s thesis in geology. Along with encouraging math, I helped her master several musical instruments, including the violin. Music and math go together.
For some odd reason being good at math really opens doors. I've read a whole bunch of biographies where the person in question (both men and women) got plucked out of the teeming mass of humanity because they were good at math. You never hear that about people who are good at, say, reading.
RE: But studies revealing developmental differences between boys’ versus girls’ verbal abilities alongside developmental similarities in boys’ and girls’ math abilities
This simply can't be true. Remember the self appointed PC police had Larry Summers fired from the presidency of Harvard for saying men and women had different innate mental abilities.
How about helping these kids learn communication skills? STEM isn't the be-all and end-all. Many kids (and even self-identified professional writers) I've dealt with simply can't write and can't write simply. Their reading comprehension is abyssmal, too.
On the other hand, I agree that math needs to be taught properly. The subject can alienate many kids, especially girls, and especially in junior high. I remember, with a shudder/cringe, an 8th-grade math teacher who'd return graded tests in reverse order: lowest score first. I was often near the bottom. Pretty damn humiliating. Despite this, my SAT math scores were decent, but I much preferred English.
Even before I got to the bottom of the article I just knew it was an engineering professor. Math beyond decimals and percentages is worthless for 98% of American kids. Less than 2% of kids enter STEM careers.
Many studies show that one of the main reasons that kids flunk out of high school is that they cannot pass geometry and Algebra 1 and 2. 99.9 % of people never use those math principles ever again. Never! They need to teach consumer math in high school not worthless courses no one will ever use in their life.
Somehow, when I was in school most boys were better at math than most girls. And most girls were better in languages. Unfashionable, but true.
Excessive drill is a sure way to make her hate a subject. If she is good at it, it is humiliating to be drilled in something understood long ago, and if not good at it, it is frustrating. Same for boys.
This author must never had tried to teach a child.
I can still remember the somewhat typical words of a math professor back in my college days: “There are 40 problems in the back of the chapter….do all of them.” A key element to learning math needs to be—not only learning the concepts—but to include practice until one’s eyes feel like they are about to bleed. OK, a bit of an exaggeration, but...
It is rare that I agree 100% with someone when talking about education and specifically math education. This article is just correct on all issues in my opine. In my teaching days, I found the difference between males and females in math skills to be non-existent. What I did find, and a bit disappointing, was that females tended not to want to study STEM subjects at the same levels as males. The exception was biology. I really don’t know any basis for it and I never saw evidence of any general discouragement for women to study STEM subjects—although that may have been fairly prominent in the past. I also informed my students that income just happens to be proportional to math skills. Hopefully it helped a bit.
"Practice and, yes, even some memorization are what allow the neural patterns of learning to take form." Unsurprisingly, the brain (mind?) utilizes muscle-memory through training too.
Brilliant! My daughter and I (a putative spatial analyst) thank you!!
The way math is taught in schools now is dreadful. I'm a female engineer and when I would sit down with our daughter to help with math, I was furious with what they have done with it. Instead of a straight forward 3 step problem, they have turned it into a 10 step busy work problem that only causes more confusion and more mistakes. If math were taught like this in my day, I never would have become an engineer. I always thought math was fun; but they have sucked all the fun out. It is tedious and mind numbing now.
Luckily, our local public school had excellent math teachers, both male and female. But most of our daughter's math teachers were women, as it happens. Our daughter excelled. Girls (and boys do fine as well) when they have female math teachers.
http://blogs.edweek.org/edweek/curriculum/2016/03/more_female_math_and_s...
I have this one acid test: if the school system is not making the kids (and yes, I do mean making them) memorize their times tables at least up to the 10s, then they are failing the kids. All kids can do that, gain that skill. Some kids can understand more advanced concepts. But all kids can acquire the skill that gives them an advantage at the grocery store, when bargaining on a car, and in any business deal. US in 30th place indeed. Shame on us!
It is true that the number of famous women mathematicians has so far been very small in comparison to the number of men. The effect is environmental, by no means generic.
"Math is [MUCH MORE that] the language of science, engineering and technology". It is a foundation of logical and precise thinking. If math could replace the ordinary verbal and written language, there would have been infinitely fewer misunderstandings in life.
Excellent essay. May I add that advanced skills are built upon previously learned skills, so it's critical to not just get through a class, but try to master the material. Don't move on to the next thing, until you understand the current material. Bug your teacher, try Kahn academy online. Sometimes the classes move too fast to get the understanding you need. Don't let that make you feel bad, keep trying and you'll get there.
I employed a tutor for my daughter and he did a great job, mind you, learning and being tested in maths, in Seoul is a trial by fire too.
I remember vividly my high school math teacher, Dr. Lambert. He grilled us unmercifully on the basics of algebra. My goodness, we suffered! But we learned it, and I went on to be a math major in college. By my senior year I discovered in my algebraic topology course that I was not going to be a mathematician, but learning math (as far as I got) has forever cemented in me an analytic way of thinking that has served me well as a doctor, and as a human being trying to understand the world.
I got far enough to begin to see how beautiful mathematical constructs can be, and how marvelous and subtle the universe is. And it led me by a round-about way to my current career.
No matter what you end up doing, learn some mathematics. It will help you in ways you can't imagine.
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As much as I like this article, in California, at the Junior College level, the powers-that-be are trying to REMOVE math as a requirement so that minority students can graduate in greater numbers. Even at the state university level, they are "toying" with math-alternative classes (don't ask, I have no idea what that translates into).
But in doing so, they allow students to take an easier path and shirk the harder classes. Obviously, STEM is out, but what else is lost? The willingness to struggle with hard classes, hard concepts, abstract thinking, "slowing down" and checking and rechecking ones work, having your classmates work together to come up with solutions, and experiencing the process of asking for help (yes, really!).
No, I have never factored a polynomial outside of algebra, so let's not go there. But it is pure foolishness for the state to "lower the bar"... these students will pay for it later.
Yes, I know the article is focusing on girls. But we humans tend to avoid that which hard; therefore, it is necessary as parents, and even as a society, to require more-and-better from our young women AND young men.
I'm a math professor.
I think rather than focus on gender and saying things like "girls are like this" we should focus on the individual child and see what works best for him or her.
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As a professor of science and engineering, I often volunteered at local elementary schools. One thing I learned very quickly was that too many math and science teachers were not proficient in the subjects they were teaching. If the answer to one math problem was incorrect in an answer key, the teacher would insist it was right even while not being able to actually calculate that answer. I have always believed in practicing math over and over again just like it's crucial to practice writing, reading, art, etc. Yes, parents should encourage their sons and daughters to keep practicing math. But, what we need most of all is competent teachers. We must change our teacher education requirements so there are no longer degrees in early childhood education but rather degrees in English, Math, History, Geology, etc.. with an accompanying certificate in education. We also need parents who are willing to take time every single day, starting pre-K, to work with their kids on reading, writing, arithmetic, etc. I worked long hours as a professor/administrator but always found time to work with my son on his homework while fixing dinner, eating, or driving to school, etc. I also kept a close eye on his teachers and if one wasn't competent, I stepped in and taught him, myself. Some kids need to practice repeatedly. Others do well focusing on understanding rather than memorization. But, neither approach is likely to work if the teachers aren't competent and the parents aren't engaged.
I often tell my students that their calculations may be correct, but their answer can still be wrong if they have made faulty assumptions. The opinion expressed in this column is based on the following faulty assumptions:
1. Math is mainly about calculation.
This was true (at least of school math) at one time, but calculating is now a skill with minimal value. Understanding that since 75% is halfway between 50% and 100%, it must equal 3/4 is much more valuable than being able to follow an algorithm to convert 75% to 3/4. Understanding the meaning of the integral of a function is much more valuable than being able to integrate by parts.
2. Doing math is like playing the guitar.
What most mathematicians do is much more like composing music than playing music. I suspect that this is also true for scientists and engineers. A guitar can be a handy tool for composing music, but there are many others that don't require rote skills to use.
3. PISA scores are a reliable and meaningful indicator of math skills.
Do an internet search for "validity of PISA testing" to see that this is a highly contested assumption.
4. "Fun" math is easy and less valuable than rote learning of skills, which is difficult and not fun.
Higher level thinking skills like applying and analyzing are more difficult than rote memorization, but more meaningful, and therefore often more fun for students.
Encourage kids to spend their time solving meaningful problems, not practicing meaningless drills.
Math and science education are hugely important in teaching our children how to think rigorously and navigate the complex world we live in. We desperately need to do a better job getting people to understand how important they are.
From what I saw when my sons were in the school system, most teachers tasked with teaching math had little real knowledge of the subject, and even at the high school level there was little emphasis on geometry and proof. Although my eldest son is now pursuing a doctorate in applied math, it took three years of college for him to grasp that memorizing algorithms is not the point, At the advanced level, you not only need “fluency” in the techniques of mathematical argument, but you also have to explain to others how “truth” in the symbolic realm can be related to “truth” in the external world, which is one of the reasons why manipulatives (when used by a skilled teacher), are not quite so foolish as they first appear.
This isn’t to diminish the importance of the earlier stages. You can’t run the marathon unless you know how to tie your shoes. However...
Most of the teachers of mathematics in elementary and middle school are, unfortunately, profoundly ignorant women who are really bad at math. The girls in the class can see this. The boys see it too, but they have the escape that “girls are bad at math”.
It’s not enough to “teach math to girls”. Unless the quality of instruction is raised, we’ll simply be repeating ourselves and magically expecting things to change.
Why does this article have to be about daughters? Does anything written here fail to broadly apply to men as well? (I.e. Yes, maybe girls suffer more from wrongly thinking they're bad at math, but that messed me up for years and I'm a man in a math PhD program!)
Amusing. It seems everyone has a firm theory about how to learn math, not excepting those who never really learned it but are convinced that somehow their child may have. I'd humbly suggest that those who don't really know what it is to inhabit the mathematical imagination, to relish its "desirable difficulties," ought to take a deep breath and stop themselves from promulgating a curriculum. Disagreeing mathematicians have the pedagogical confusion pretty well covered all by themselves, but at least they have a clue what they are arguing about.
On a general note, we'd probably do well to inculcate, as teachers and parents, enthusiasm for the challenge of "desirable difficulties" regardless the subject matter. The ills attributed to our educational system may not be so much a matter of right or wrong curricula, good teachers versus bad teachers. At bottom, it may be no more mysterious than the pervasive commercial culture of instant gratification we all inhabit.
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The problem for women in math is more cultural than genetic. As someone who had math genes and somehow ended up with an Ivy League Ph.D. in physics I look back on my finest undergraduate teacher in physics who candidly admitted to lying about her major in social situations. One of the dumbest declarations some years ago was when Larry Summers then president of Harvard claimed that women don't have an "aptitude" for math. Tell you daughters that math people are special people and forget the drill and kill.
I was a foreign language teacher for many years and I strove to avoid "boring" drills. Students loved my class, but when it came time to site for the International Baccalaureate tests, students in the nearby Chinese class--who were always complaining about their memorization-focused teacher--did great and my students did mediocrely.
Girls, on average mature earlier than boys. That gives girls an academic advantage throughout childhood. Eliminate anti-female bias, but also age bias.
An editorial quibble: "Of course, it’s hard to know what’s taking place in the minds of babes" sounds like a line I might have heard in my teenage years. I doubt a double-entendre was intended, and maybe it is a typo. So maybe "babies" instead of the more freighted term "babes"?
"Math is the language of science, engineering and technology." Absolutely right, but the key thing is that it is an INTERNATIONAL language, no English Math or Japanese Math.
In the author's conclusion she exhorts us to make our daughters practice extra math and our boys too so what is her point? I am infuriated by this author perpetuating the idea that biology is destiny. Does she have children? let's stop differentiating between our children, deciding beforehand what they are good at and work at developing better learning environments for all our children.
I think the question here is not whether learning is "fun" or not--the question is how does one "teach" motivation? With appropriate motivation, no task is too hard--without it--everything is impossible.
"Some learning just plain requires effortful practice, especially in the initial stages. Practice and, yes, even some memorization are what allow the neural patterns of learning to take form." This is one of the most important things people never realize about learning in the early grades. Memorization is vital. The same thing applies to any new activity whether it's a sport, a hobby, an academic subject or a job. Repetition builds knowledge and understanding. Fancy words don't.
Another thing all parents need to do but especially parents of girls is to encourage children to try things that are difficult. The grades or results they receive at the start are not as important as the understanding they have at the end. Our achievement oriented praise doesn't tell children what they've done correctly or what they need to improve. I don't know how schools handle questions or incorrect or even correct answers today but I do recall a distinct lack of explanations in my day. It was as if, in math, we were expected to absorb the answers from the air. That lack of explanation started in grade school and continued throughout college.
Tests are useless if all they are for is grading. If they are used to help us understand what we did right and where we went wrong rather than merely as tools to assign grades, they would make student lives less miserable. Getting the right answer without understanding why it's right isn't a sign of intelligence at anything.
Yes! I've said this for decades, and my training in physiological psychology validated it. My friends gave a daughter 3 pages of math drills every night to supplement their homework. She became a director of the World Bank at a very young age. (Neither parent was in a STEM field.) My father drilled me in math when I was little, because I made careless errors that lowered my grades, and in high school I scored so high on a national test that they put me on the math team. The math curriculum out here was so bad that I volunteered to drill the children in their times tables, which we used to learn in third grade. When I earned a teaching credential in my 50's, many of my 20-something classmates could not tell you 9 x 7=63! Needless to say, my own children excelled at math - I gave them no choice - and I ended up with a doctor, a CPA-financial investor, and a DOD intelligence analyst. All the math-oriented boys I knew of my generation became engineers, but, sadly, engineering was often considered drudgery and not rewarding by American Gen x and millenials.
Excellent!! Finally!!!
A large part of the educational problem with mastery is that the teachers who are instructing the children haven't yet mastered the content/concepts themselves. Because of the teachers' lack of mastery, they try to disguise their own shortcomings by making "learning fun." I lament that most of my children's teachers can't diagram a sentence or identify verb tenses except for past/present/future. God forbid present progressive or past perfect tenses need to be identified. A teacher can't teach something that s/he doesn't know or hasn't mastered.
Loved the last couple of sentences. This is NOT a battle!
I guess it's more than ok to state girls have superior ability to boys in reading but the same in math. But not ok to say boys have superior ability in math. Maybe it's subtle - this disparaging of boys - under a guise of equality for girls and PCness - but not ok.
If someone had told me about mirror symmetry, fractals, and other cool math concepts when I was young, I probably would have been a lot more enthusiastic.
Instead we were taught to memorize tables, or algebraic equations, and when asked why, was told 'Because I say so'.
Why don't we teach math like we teach science? When we speak of science we talk of black holes! Stars! Planets! Natural wonders!
Students get excited to learn.
With math....we get memorization.
Creative, visual minds are needed in this world-- not just those who memorize well.
I feel that girls are born perfectionists. They get frustrated by subjects that cause them to trip and make mistakes and are quick to drop them and gravitate towards things that come easy to them. Their natural gift for the languages is an easy fall back. As parents, we should encourage tenacity, perseverance and patience in girls. We should encourage them to fret over their mistakes in math and learn how to figure them out. Teach them math mistakes are cool.
More importantly having a parent spend time daily on math, with their child, girl or boy, in elementary school, paves the way for a child unafraid to confront numbers anywhere. And stop outsourcing their minds by sending them to a million classes, both academic and non academic. They just get used to others thinking for them and giving them instructions. Let them stumble, let them draw in weird ways, let them sing like children. Then we will have a world of thinkers and innovators, where every second person is a boy or a GIRL.
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I homeschool my three kids and they are lucky enough to attend Russian School of Math in the afternoons. They attend math class year around because I believe sincerely that math is the most important thing one can learn. I have a hopelessly inadequate background in math and I am utterly determined my children will not suffer the way I did from the crappy American math and science approach. Nothing makes me happier than to have my children come home with math problems that I cannot understand and they work out themselves.
People are differently gifted. I have learned 5 languages, and am fairly confident that I could learn any new one in a relatively short time.
Math, however, has always been the bane of my existence. Higher mathematics, I mean. I can compute just fine. Anything beyond that is torture.
WHY must those who hate math and never intend to use it for more than check balancing and recipes be forced to endure it?
I love language and would like to speak every one that exists, but I don't expect others to share my passion. Why must they force me to share theirs? So long as I can function competently in the world, take your math elsewhere. I don't want it.
Here is a story. Some years ago a philosopher at Ohio State found an error in the work of one of our top philosophy departments. He was invited to give a talk and while the erring philoopher was not present, some of his colleagues (yes, "his" colleagues).
I was present at the talk and it soon became obvious that hardly any of the philosophers in the defending program knew what on earth the visitor was talking about. And these were, for the most part, men.
I find this phenomenon particularly disheartening because philosophers are the ones who often talk about our social problems,. And these problems cannot be REPRESENTED without knowing the appropriate language.
So why confine math learning to girls? I know that is PC, but ALL Americans, especially university faculty need to know math better, especially logic, probability, and basic statistics.
Another example is the book Delusions of Gender by Cordelia Fine. Sheis a full professor of philosophy but Her book contains NO statistics whatever. How on earth can you discuss differences between men and women, which are not absolute but statistical if you yourself do not understand statistics? You cannot. But that, alas, did not prevent her from having an audience.
Do your child a favor - enroll her/him in the PACT camp taught by Dr. Gandhi at Princeton every summer and on Saturdays during the year. Kids come in from across the country and as far as from South Korea. My 15 yo completed it this summer and her feedback was "He taught me to think"(she is enrolled in Calc and AP CS starting this fall). Her interest in coding rose exponentialy after this program. Girls amounted to 50% of the class, but mine was one of the handful of non-Asian kids.
Dr. Gandhi has a program at Rutgers where he works with disadvantaged students who go on to successful careers upon graduation. He is not an easy teacher - far from it, but he challenges students and encourages them not to give up on trying to solve a problem (a critical skill for advanced math). Most importantly, he knows how to teach (advanced) math.
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One of the reasons we score so poorly on the PISA tests is that even our good math students aren't very good. Our HS math, even at the AP level is way too simple. Which is why many schools if engineering do not accept AP calc credit. Want to learn what is wrong with math education? Talk to some remedial algebra math teachers at your local community college.
To the point though, I work with women who are in the STEM field (they are almost all Indian, they have a different approach to math instruction that makes much more sense, of course they invented it so...) so even though there are more men in STEM I have long since disabused myself if any notion that there is much of an inherent difference in cognitive ability between men and women. So, any time I hear someone start a sentence with men are better at x or women are better at y (unless x equals urinating standing up and y equals bearing children) I simply say 'no that isn't true'. You always have to be aware of self serving biases which are pervasive in studying sex based differences in people.
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When I was in sixth grade my mother drilled me on the multiplication table (up to twelves). I remember it; when one goes over it and over it one doesn't forget it, any more than I'll ever forget my army service number, which I was also made to repeat. It's useful.
Some months ago I bought a case of cat food, two layers of cans, each layer consisting of three rows of four cans. The case didn't have a bar code, so the young cashier had to scan one can and enter a quantity; she began counting "one, two, three..." I pointed out that there were three rows of four; she said "Oh yes" and went to borrow a calculator. Considering this country's education system, I don't have much hope for us.
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Oakley’s really talking about arithmetic, which is wildly unpopular with US schools.
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I know a young mother who was one teacher away from a perfect 4.0 in high school & took summa cum laude as a math major in college. Math will make you a better thinker and the most organized person that you can become.
However, being good at math will disqualify you from becoming a progressive True Believer because when the Left comes up with tens of trillions in new spending ideas, you will invariably ask how they plan to pay for all of their dreams.
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Oakley's own life strikes me as a perfect counter-argument to the very points she makes here. Is she blind to the implications?
Oakley was trained in languages and then learned advanced math as an adult--with a strong background in the concepts of language.
That path makes sense to me: concepts first, practice and fluency later. Oh, and also: do what you love, and do it well, and you'll find you can learn something else, and do it well also.
Without her strong conceptual grasp of languages in the abstract, would she have been able to pick up calculus at age 26?
http://nautil.us/issue/40/learning/how-i-rewired-my-brain-to-become-flue...
To me, it's about keeping all your options open as long as possible. Maybe they won't need it for their chosen career, but if they don't have it their career choices are limited. Why establish those limitations any sooner than necessary? Full disclosure- I was a math major.
A while back – had cause to tutor several HS young women athletes in math...
The author is – almost – spot on...
The “aha” moment for them (not me) arrived almost like clockwork – when they realized that their innate reasoning capabilities were just as valid and useful as their innate rote-recall capabilities...
Could see it from the look on their faces...
Math is pure reasoning – though many of its foundational mechanics can be memorized...
Other STEM disciplines are a blend of reasoning and rote-recall...
Math and poetry are the bookends...
The comments and the article make me think we're talking about arithmetic, but that really has very little at all to do with math as a subject of study. I'm not saying arithmetic isn't important, but it's misleading to equate them.
I suppose you could correlate it somewhat as if you're good at times tables in the third grade, then you see yourself as good at math, therefore keep with it even when you realize math has nothing to do with multiplying two numbers.
Thank you MS. Oakley you are right. I write this as one who loved math all his life and is good at it.
To Danny: Your post is as Isaac Perlman teaching how to play the violin. I shall never forget his lecture PBS on " it is the space between the notes that count"
Most of us not so gifted violin players have troubles to hit the notes. To achieve the level of playing with the space between the notes. that is creative and fun, you need to practice to hit the notes . First.
As the mother of 2 STEM focused daughters, including one with a double engineering degree from one of this country’s top math and science focused universities, I know that while the rote practice was helpful it would have been disastrous if the push was coming from me. This was not the parent child relationship I wanted. A good school or enrichment curriculum is the ideal and what every parent who has the privilege to push for it should do so not just for their child but for all kids.
I also am skeptical of experts like the who told me that I should never tell my girls that I was terrible at math. The fact was that as a discalculate I was. They took great pleasure in being so much better than mommy in math!
The "fun" way of teaching math is not only useless but damaging - even to parents trying to help their children. I remember thirty years ago how often , as a father of young children, I was frustrated by the presentation of math problems in textbooks. A lot of distracting colors and shapes were more often than not transposing simple questions into "user friendly" puzzles which I had a hard time even understanding, despite - or maybe because of - the fact that I had a solid high school and college math background, which by the way I still find useful in many other areas, like detecting nonsense and bias in news coverage - for example of the type that brainwashed tens of millions of Americans into electing precisely the worst human being for the job. It turns out that "user-friendly" is not really good for you - unless you desperately need to stay dumb.
I have to laugh at some of the negative comments. Let’s face it: the author is absolutely right and it is quite elementary, my dear Watson. Do be good at something, you need to work at it and practice. Each afternoon, I sit down with my 7-year old granddaughter and we work on a math textbook and each day she gets better. In high school, at Lincoln School for Girls in Providence, RI, I would skip French class (which I loathed) and go to trigonometry instead. However, when I was a freshman at Tufts and taking calculus, the assistant professor would become outraged (yes, right in the class) when I would score 100 on exams. Apparently, as an attractive young co-ed, I didn’t fit his image of a mathematician. At 18, this was devastating and the end of my math classes. I will not let this happen to my granddaughter. But, as they say, all is well that ends well: I have been a successful corporate attorney for almost 50 years and work with numbers all the time. I just love numbers and I will pass that love on to my granddaughter. Now, when Tufts calls for a donation, I always say sure, just not to Tufts. My educational donations always go to Lincoln which recently opened a wonderful new STEM wing for all its budding female scientists.
The author writes "The foundational patterns must be ingrained before you can begin to be creative" with regards to music. I have studied music all my life, and I can't think of a faster way to discourage people from playing music then to turn it into nothing but drills and scales.
Even from the beginning, musicians progress from simple compositions to more advanced, and good curricula have thoughtful progressions. Math can and should be the same. Yes, students need to know their multiplication facts, but the idea that students need to first spend years mastering the boring part of math before they can move on to the fun stuff is pedagogically lazy and will fail the majority of kids, both in music and math.
"This is because many girls can have a special advantage over boys — an advantage that can steer them away from this all-important building block.
A large body of research has revealed that boys and girls have, on average, similar abilities in math."
That's drivel and the claim is based on cherry picking. Yes girls show superior abilities in reading/writing when tested, but no they don't have similar abilities in math.
There is learning to do math on paper or even with a computer/calculator. Yes this is an important skill, but learning to do approximate math in your head is a very valuable skill. I can see when numbers are off. We trust our computer/calculator but we need to think to see if it is accurate. Being male does not make you better at math being persistent does.
I truly hated math, was quite mediocre at it and did the bare minimum required to get into college. I suspect that I had an undiagnosed learning disability and some poor teachers. I was an exceptionally good writer and naturally gravitated towards English, history and the humanities. I think those fields are underrated and deserve more respect. Too many kids can’t write to save their lives. I taught a few of them. Sometimes I do wish I’d been better at math, which would have offered more lucrative career options. On the other hand, I would still have hated math even if I’d been better at it.
Thanks, NY Times, for including this. Ms. Oakley makes several important points. The most important is the central role of math. Math is the foundation of any STEM field. Many years of math are required, each class depending on the prior one. Once you get off track in math, it is very difficult to ever get on track again.
We have run a STEM program here for 10 years, for public elementary school students. This has given us a lot to reflect on.
The utter failure of what we Americans have done so far to address the STEM fields, including female participation, cannot be stressed enough. With the exception of the life sciences (biology, medicine, and the like), female participation in STEM is no better than it was 35 years ago. Especially in Ms. Oakley's engineering.
Every simple quick fix (e.g., practice) has failed. Based on our data, the problem looks to be about as complicated as society at large. In math as in society at large, the rich grow ever richer while the poor get even poorer.
Every student is unique but we have built a model based on several parameters which at least tells us how to direct our efforts. We think of each student in terms of the following (which are not independent of one another), and then modify our efforts accordingly: (a) ability, (b) interest, (c) confidence, and (d) plans (for future study or careers).
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Anyone else look too closely at that Getty image? Top left, second equation down. The artist who created the image neglected to square the first "x" in the numerator. And then...what exactly is the work on the blackboard achieving? It's a bunch of random scribblings related to derivatives. The artist could use some more education in math.
For years I paid for tutoring and tried to support my daughter's attempts at improving in math. They simply do not take to it and have continued to struggle and hate it. They excel in humanities and social sciences. I'm tired of our society telling kids that the only way to be successful is to be good at math. Surely, excelling in other subjects still has some merit. Are we content to live in a world that values only the quantifiable?
It is not just in math that little girls need encouragement. Especially in Trump country, little girls constantly face discrimination, although often subtle, in all of school. It is critical that parents don’t let their girls give up.
In Asia 90% of elementary math instruction is verbal. In the US it is considered harmful to students self esteem to ask them to recite times tables. Any wonder we are behind.
Math is beautiful. It is sublime. My father tutored me in math. I realized, very quickly, that I would never be another Ada Lovelace (a pioneering genius who wrote the first computer program; incidentally, Lord Byron’s daughter). My talents lay elsewhere. But I spent hours in my own reading advanced math books and figuring out their underlying logic. I was pretty good at set theory, not good at calculus, and eventually I chose a different academic major. But knowing math has enriched my life in ways I can’t even count. Math is not just the language of science- it is the language of God. And I say it as an atheist.
I'm a male who more fits the female archetype: quite good with reading and writing, decent at math. But from the time I was 13 I knew I wanted to be an economist, a rather math-intensive occupation. I studied hard and drilled, as you suggest. I got decent grades in math, nothing great. But that was enough to get me a BA and then a PhD. Persistence was the key. Even today I still drill, still challenge myself to prove theorems. I could never have been a theoretical physicist, but I am competent in my field. It's a life-long endeavor, but for me, worth it.
On another note, I don't know how today's children are taught, but in my day (I'm 40) math education lacked a healthy component of do-it-yourself experimentation. I recently read wonderful book called A History of Pi. The author begins by imagining how man first estimated pi, using a two sticks and a string to draw a circle in the mud. That seemed like a great way to teach it, much better than brutally telling kids that it's approximately 3.14.
This op-ed and comment section suffer from the delusion that we're all the same "blank slate" on which can be imposed the same cookie-cutter, corporate-friendly abilities, talents, skills, propensities and interests. No. Some of us are left-brain predominant, some are right. Some are better with qualitative, some better with quantitative. No matter how much you shove math down the throats of every child, there will be some more naturally gifted for it than others. You virtually gaurantee frustration and failure forcing a fish to be a bird. A healthy society is like an ecosystem.....each member contributing their unique talents, skills and interests. Things have changed in the last 50 years, let me tell you, having gone from "do your own thing", "be who you are" and "follow your bliss" to the increasingly narrow options sanctioned by corporate capitalism. No wonder so many are desperately unhappy.
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I am SHOCKED (no lesser word will do) to read that the author writes "UNFORTUNATELY (my emphasis), the way math is generally taught in the United States — which often downplays practice in favor of emphasizing conceptual understanding ..."
Conceptual understanding is the basis of EVERY intellectual field. Of course students need practice, but practice without understanding cannot get them very far. Emphasizing conceptual understanding is EXACTLY RIGHT.
We need to also note and understand that math is not a monolith.
You can be lousy at algebra, but brilliant in geometry.
I didn't really get plugged into math until I arrived at statistics and probability.
Suddenly, the world-wide probabilistic model made sense.
Just sayin'.
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Nobody learns math without practicing. Even those for who math seems logical, until they can work the problems accurately and quickly, they have not learned enough to be competent.
Learning is never fun until the subject is mastered, already learned. Anyone who plays with the subject to make it fun is not teaching it. Once a subject is understood then reinforcing and extending what one knows is fun. While one is learning a subject it is annoying and makes no sense, it seems impossible to ever grasp at all.
The great thing about math is that it can be proved accurate with explicit logical proofs. Once one knows a subject in mathematics, one knows that subject without any doubt, at least the mathematics most engineers and scientists and social scientists need to know.
Verbal knowledge involves so many aspects of human cognition and experience that one always seems to find more to understand, even what one has thought one has mastered.
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Like chess, crossword puzzles and the puzzler, doing math in your head is gratifying in ways you cannot imagine at first.
Start with making change at the checkout line, and move on to multiplying fractions, factoring square roots, solving for X...
We treat math as drudgery, but math is really magic. Amaze your friends and scare your spouse when you calc the volume of a sphere in your head...
Girls, boys, whatever, it applies across the board. Back in the Dim Times, I recall the best students in any class were the girls. I don't recall that they did any worse than boys in math. Maybe it's that teaching math has become too gimicky and not enough of a discipline as it once was. I don't believe females are any less skilled at basic learning.
Whose is more likely to graduate high school and college boys or girls? Who is more likely to commit suicide boys or girls? Who has higher gpa boys or girls? Who is medicated for scholastic achievement more often boys or girls? Based on these facts who needs more help boys or girls
I've always hated learning. But I do enjoy knowing.
Drills can involve many elements...physical mechanism & origination, trust, comprehension & analysis, emotional journeys & juxtapositions, organizing & coping techniques. Powerful drills integrate multiple skills; additionally, they deliver quality rewards at strategic junctures. When drills focus on cognitive skills alone, we leave students without the tools to apply those skills in the real world.
The problem is cultural, I think. Girls in other countries do not have trouble in math or think they can't do it. It's up to parents and teachers in the US to prioritize a well rounded education for girls. Has to be part of the culture
I don't get this argument. Without a conceptual foundation, where do you think this extra practice is going to lead?
As a kid I aced math and loved practicing it. I was as good as anyone at it.
Then things shifted in pre-calculus: I still got an A, but I didn't "get it". Then I went into calculus, linear algebra, complex theory and differential equations, and things fell apart. I went from As to Cs then failed outright. I studied and practiced like mad, hours every day, and could not understand anything.
I decided to not give up. I took community college classes in the summer and then took a full year off of school to study all the math topics full time all over again.
Here's what I learned: it was all about the concepts. All the practice I had done all my life was worse than useless: it reinforced my flawed conceptual models.
It took me two years to throw out my old concepts and develop the right concepts, and then I could do the math again. The process almost destroyed me emotionally.
I was proud of my grit at the time, but looking back it was a bad decision. Even though I gained a conceptual grasp and finally could do the work, I was never as good at it as my peers who received more comprehensive, more conceptual training at a much younger age. I would have been better off going into an area where the concepts came naturally, like computer science.
I strongly support those who say that a conceptual approach is better.
The demonization of "rote learning" i.e. memorizing, has done American students a great disservice. While ADULTS may find memorizing boring, elementary and middle age kids love it and do it easily. We stopped demanding that kids memorize poetry, dates, arithmetic, and for a while (the "Whole Language" fad), even spelling rules.
Despite the anti-memorization movement in schools, my own children spent their free time in the elementary years memorizing Sports stats and Beanie Baby birthdays.
The psychologist Piaget pointed out that kids about 7-12 are "concrete operational" - they are very good at learning facts and not yet very good at abstract reasoning. Previous generations of teachers seemed to recognize these stages of development through experience and common sense.
As a retired math Instructor, I know that a generation of college students may understand very well what 7 times 8 means, but they don't know the product is 56 because they have never memorized their multiplication facts. They are so calculator dependent, that I have seen a student pick up a calculator to divide by one.
For once, a really true and honest assessment of the subject and its dilution via educational system.
I am a science teacher (chemistry and physics) and I couldn’t agree more with the underlying premise of this article. I just wish the emphasis had been less gender-centric. Boys and girls would both benefit from a math curriculum that emphasizes foundational math skills – yes, memorizing multiplication tables, addition and subtraction facts, squares, doubles and halves, decimal equivalents of common fraction, measuring units, etc. The over-reliance on calculators at too young and age has done more harm than good, a mental math skills are appalling. The problems in math education described here have been exacerbated by the adoption of Common Core math with its empty promise of in-depth understanding combined with the omission of foundational facts. This emphasis on abstract, conceptual math was a fool’s errand for children who remain as concrete learners right up to until high school. Not only did CC math take a now disproved approach but the companion testing required by the USDOE has convinced a generation of students that they truly “suck at math”.
The fundamental problem with math education is that getting the correct numeric answers to problems is treated as an end rather than a means (i.e. the applications in science and engineering and real life as well).
I love math. Both my parents were high school math teachers. My dad bought me a TRS 80 to learn to write code. I was sent to summer camps to learn BASIC and perl. But yes, I was better in reading and writing. I enjoyed it so much more. I make less than I probably would as a computer coder. But I guess I was never discouraged as a girl from going that way. And I would never consider myself bad at math. I just did what I enjoyed more. Why is that bad again?
I like the exhortation simply to practice. That simple wisdom seems missing from much of math education. Maybe it comes from the pretense that it something more than symbolic logic and pattern recognition? When we stop exalting math, and relegate it to its proper place alongside skills like keyboarding and riding a bike, maybe we'll stop shutting people out of it, and more can access its more interesting features.
I was in high school back in the early 1970s. I was pretty shy. Yet one day, I timidly raised my hand in algebra class to ask for help. The male teacher came over to my desk, rapidly explained how to do the problem, and then said loudly, “You get it? You get it? You get it?” I most certainly did not but said I did just to get him to go away and stop drawing attention to me.
In raising my own two daughters I told them don’t say you understand something if you don’t. Keep working on it until that light bulb goes off in your head, even if you need help from someone else. I’m happy to say both did well in math. My youngest even became a math teacher and went on to get her master’s degree in the subject.
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In addition to all the wonderful points you make, I would add two. Females are still generally socialized away from mathematics. Second, computers, smart phones, etc. mean less availability for practicing technique. But in the end, you can't be great or even very good at mathematics without understanding its concepts very well. You have picked a very complicated subject to discuss.
Math practice does NOT have to be painful. My family was 3 boys and 2 girls, and our parents constantly played math games with us. My sisters always liked math as well as me and my brothers. We were very lucky. Then I did the same with my 2 daughters, and they always liked math because I made it a game. What's 13 times 15? Then you can have dinner. If you can tell me 18 times 6 minus 42 fast, you get the biggest dessert.
In middle school my son complained that math was boring. He always had a head for it, and loved science--especially physics--but he just didn't find the coursework engaging. I told him that he wasn't learning math, he was learning arithmetic. What's math? he asked. Proofs, I replied. Can you give me an example? Sure. Prove that the square root of two is not a rational number.
I explained what a rational number was. And I told him that one common way to prove a claim is by contradiction. A month later, all on his own, he came up with the proof. And as far as I can tell, it is an original proof (i.e. it is not a replication of existing proofs).
In high school he developed a graphic proof of the fundamental theorem of calculus, which was published. He also developed a much simpler proof for a theorem in group theory, also in high school. He's just graduated with majors in math and physics.
But ask him to multiply or add? Forget it.
Math is about power. We use advanced math to make decisions in science, medicine, finance, and even politics. Ask any business executive or medical researcher. Yes, I agree with the author that it is important to master the basics - we all use arithmetic and simple geometry for many simple tasks (cooking, measuring, building, driving, and balancing our checkbook). But we still need to learn more if we want to get the most out of our life. We shouldn't stop caring about math at age 12 because the most powerful math is what we learn after arithmetic - especially statistics and probability.
Many if not most elementary school teachers chose to teach those grade levels for fear of math. Many if not most have had poor training in teaching math and more importantly they are not comfortable with basic numeracy themselves. Try imagining a teacher with little training or ability to think conceptually and relationally, being able to teach that type of understanding to her/his students. But it's eminently possible and even enjoyable given the right training and opportunity to learn! I've seen lightbulbs go off for teachers and their students. Memorizing takes anyone only so far. If you don't have a general idea or understanding of the quantities you are dealing with, your errors will likely elude you. For example, if you have a good understanding of what the quantity, 6x8, means or refers to, then you have a better chance of self-correcting when your memory serves you wrong and you come up with something like 56 or 84 - both common errors for 3rd or 4th graders. It troubles me when I hear anyone and especially women, say they are just not good at math. My answer is that they didn't have the right teacher. We need to do better. I was an elementary classroom teacher for 9 years and a K-8 math coach for 11 years.
I can't overestimate how important it is to have this skill. Looking back I knew that I had the potential for understanding math on all levels however, I grew up in the 60's and this was not part of the plan for women. I now find myself catching up on basic skills that I wish I had been taught earlier in life. My job involves statistical analysis for process improvement and I yearn to have a deeper understanding.
I had one effective math teacher in grades 1-12. He gave us algebra problems to solve for homework, then asked 4 random 9th graders in the class to put their solutions on the board. Because of the kind of problems he gave us, there was more than one way to get at the answer. The class looked at the answers for minutes, then each board student explained how he/she thought through their procedure and answer.
He made this an interesting, problem-solving, group activity as his "opening exercise" each class. After that, he taught us math as problem solving and welcomed alternative ways. He would give us trick problems to solve so we learned to pay close attention to how a problem was described.
Then I had the worst geometry teacher in the universe, who sat at his desk and had us work on problems at the end of the chapter, while he studied for his masters degree. 90% of the class was lost, and he could not grasp why we were so stupid.
I was trained as an elementary school teacher, so one reason girls and/or boys may not like math is because teacher colleges and education courses in math were taught by experts in math who could not communicate. It was grim.
My first course in grad school was a stat course in social science. The professor (a woman) was great. She would show us the procedure, then she gave us data to process and analyze. It was decision making with lots of discussion of pitfalls. Another stat. prof. derived formulas & many had no idea what stat was good for
I think it's more our dumb girl culture where the average teen spends more hours on social media and taking selfies than actually sleeping, eating and studying.
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Started early with entertaining her with pennies, nickels, dimes etc. at restaurants. Bought workbooks with stickers. Had silly math songs on in the car. Sometimes rote learning which lasts forever is so much better than the way they teach now. In case you might think she had a grim childhood, it wasn't to excess, she had other self-directed activities as well. She showed other students in her class what a times table was because they didn't teach it in her school and they thought it was cool! Not sure how the teacher felt.
I've been reading about these issues for years, but I am not understanding the author's bias that teaching conceptual skills turns off girls.
I was born in 1955 and got interested in math for the first time when I was in sixth grade and "new math" was introduced in NC elementary schools.
I learned about "base 10" and that numbers are "ideas" and "numerals" are the symbols we use for them. I learned about "base 2" and how 10 means something very different in base 2, when the 1 means 2, than in base 10, where the 1 means 1 ten.
I was sadly discouraged in high school when I loved algebra and the concept of imaginary numbers, and I wanted to understand much, much more. In eight grade I was told that the reason two negative numbers are multiplied equal a positive number is "because the mailman doesn't bring you the bill in the delivery (one negative) and the bill was a credit (another negative), so it's a positive you don't owe anything".
I asked many questions about these simplified concepts and asked how they apply in real life and was told repeatedly "you'll learn that next year or the year after that. For now, just learn the formula and use it."
I wanted more conceptual understanding and never got it. I lost that window of opportunity before I was 16. It's sad.
Instead, I got a PhD in art history, and I learned about writing and research and philosophy and visual knowledge.
The organization I founded (Helicon, Inc., the Mathematics Resource and Support Center for Females) is currently conducting an SHSAT Prep for African-American and Latina Girls” in NYC. Because the SHSAT is a test that assesses how much one knows and how broadly, deeply, and quickly one can reason with that knowledge, first thing every morning the students take timed quizzes; and at some point during the afternoon the interns (two rising sophomores from Stuyvesant High School, lovely young ladies) conduct a “Math Facts Tournament” that a team of girls wins by answering the most math-fact-question correctly and quickly. Our purpose is to get these facts firmly embedded in, and yet effortlessly retrievable from, their long-term memories. It's working; the girls are solving college-level problems with considerable enjoyment and satisfaction. “If I didn’t know the times tables, metric prefixes, properties of exponents, and conversion factors when we started Dimensional Analysis, I wouldn’t have been able to do all the problems I did!” one of the students said—and the others concur. The interns want their say, too: “We chose to work here at Helicon, Inc. because facts, which serve as the basis for knowledge, establish a foundation necessary to all, yet from what we’ve seen lacking specifically in girls.”
For “Learning Should Be Fun!” believers I say: Learning is not fun; it is often excruciatingly painful. Having knowledge is what’s fun.
This article understands math from an engineer's perspective, as a tool to be used for other problems, but it's important to realize that the math used in engineering is very, very different than the math encountered in the pure mathematics departments of universities. I took university level math courses in both departments, and there is a giant difference in the approach to math.
I would highly recommend the book, "The Mathematician's Lament," written by a mathematician, for an alternative viewpoint. As that book argues, everyone does need to memorize 'math facts' at some point, but making rote learning the central focus of math teaching drains the topic of all interest. Like he says, it's as if elementary art classes focused only on how to hold a brush or how to mix colors, but never actually were allowed to paint. Mathematics is a beautiful and complex language, full of fascinating puzzles and concepts. To get children really interested in the true beauty of math, you need to focus more on these concepts and less on how many multiplication questions you can answer in one minute.
As a lad,I was great in math, langauges and writing,but in addition to my Hollywood leading man good looks-at age 65,no less !!!-I had a 150-160 IQ .Being black,I was thought a bit much by some other students and a few teachers,but since I made no effort to fit in, because my high school was in a working-class area of Windsor,Ont.,across the Detroit River from Detroit, I realized that I was unlike all but a handful of the other lads and lasses from the standpoint of brains and beauty,so kept myself aloof from them,even the other black kids.That's what high-achieving girls must do,as difficult as the pressure must be to become the hot-popular chick.
My experience with most of my math teachers from junior high through college was this: Those who "get" math intuitively are often, not all the time, the WORST teachers. It's like they have mind blindness of some sort when you the student ask them to explain a concept. One particularly bad teacher used to have a tone of derision when you asked a question about material just covered. Eventually, one shuts down because it's not worth dealing with the person and being made to feel dumb because you didn't intuit the logic behind the steps or the solution. Teaching is a skill and an art that few have the patience or talent for in the US. And why should we get the best and brightest if the pay and conditions are abysmal compared to jobs with the same educational requirements?
Regarding drilling and the need for children not to have fun 24/7: that's going to be a tall order with this generation of instant gratification and rampant hedonism Good luck with that!
After three years of tutoring high school students in math and science I concluded that they need A LOT MORE drill and practice. I routinely encountered high school students whose arithmetic skills were at the third grade level. They were unable to add a simple column of one-digit numbers. They did not know how to multiply. Their electronic calculators enabled them to pull through to high school algebra and there they got stuck. Calculators can tell us what 9 x 8 is but cannot go backwards and tell us what the factors of 72 are. And it's just this latter knowledge that's needed to factor quadratic equations. Why haven't educators figured this out?
The lack of emphasis on simple memorization has produced a society in which only 36% of the population can find North Korea on the map (source: NYT https://www.nytimes.com/interactive/2017/05/14/upshot/if-americans-can-f....
If the girl in the cover art, who looks to be in late grade school, is really learning the math that's on the board before her, she's a genius. Most students don't see differential calculus until their senior year of high school. Or college.
"Unfortunately, the way math is generally taught in the United States — which often downplays practice in favor of emphasizing conceptual understanding — can make this vicious circle even worse for girls." You must live in a very different school system than the one I spent a career in.
The problem with how we teach math is that all of our applied math examples target traditional boy interests: transportation, sports, space. Rarely do we apply math to social, demographic, or justice issues. And we could. Then see if girls don't find it much more interesting than "two trains leave Minneapolis at..."
An example. Years ago I read a statistic comparing life expectancy for all Americans vs. life expectancy after reaching age 40. The numbers were startling -- not exactly these, but something like 75 and 90. It got me wondering: how many people die before the age of 40? An entirely legitimate algebra problem.
I taught fifth or sixth grade for over 23 years in Massachusetts where the state curriculum and testing requires students to master computation as well as conceptual thinking. My students had to have an extensive math vocabulary for calculation, basic statistics, beginning algebra, geometry and problem solving. Students had to answer math "essay" questions by writing explanations and showing the solution to problems with equations, graph paper or drawings. This requires multiple teaching strategies which enable students with varying learning styles to succeed! And, of course, I gave extensive homework and figured out how to make drills tolerable and even "fun." Has this author spent time in classrooms? Does she realize how hard teachers work to make math accessible to everyone regardless of gender, race, and economic background?
Thanks for your article. I agree with the
"rote" premise. For years I thought I was
bad at math. When I engaged in a consistent
and daily work pattern in math I was amazed
to see that the answers or process to solve
the problems "came" to me upon analysis.
With consistent work the brain new where
to find that place where the mind understood.
If every piece of this article (as the very last sentence admits) also applies to boys, why are we completely ignoring them and focusing on girls? Because they lose confidence in themselves faster than boys? Why don't we fix that instead of ignoring boys?
Yeah, great. But, why do we force ridiculous amounts of math down our students throats like it's some sort of elixir to an enlightened existence?
Seriously, the amount of math requirements for ALL students, like they're all going to need it (please!) or wanna be math majors, who thought of this and why do we blindly sign on to it like it's from the Dead Sea scrolls?
Why do we torment kids with this crazy amount of math regardless of their individual skill set or talents? I have four kids in my house and they all despise math now because of the" force feeding for all" approach. What are doing????
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@trigoe Funny, I rather think that too many people in our country are innumerate.
They despise math because you do and they know it.
@trigoe
Everyone does need math. And going up to algebra is hardly a 'math major' level of understanding. We are paid in dollars, multiplied by the number of hours we work, being able to know how that works is important. Division, fractions - and figuring out how many hours to work to get enough money (algebra - solve for X) - all needed for everyday life.
"It’s important to realize that math is, to some extent, like playing a musical instrument. But the instrument you play is your own internal neural apparatus."
Some people will never competently play any musical instrument. Forcing them to practice will make them hate music.
Sons people will never be good at sports, no matter how hard they try. Forcing them to play sports will make them hate sports.
The old method of math instruction left a lot of people of both sexes who weren't just bad at math, they were afraid of math.
Being bad at math is not a character flaw, just like being bad at sports or piano are not character flaws.
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@Liz
But many girls who MIGHT be good at math never get to find that out because of how math is currently taught. And sorry but competence in math is very different than competence in sports or music. The stakes are much much higher for the first.
@Liz
Math is knowledge that anyone can master and use throughout their lives. It's much easier to master mathematics than it is to master verbal skills or human behaviors. The reason that math seems so difficult is because it is expressed in a language that is made up of symbols unlike those which represent words and narratives. But once one is familiar with the symbols the ability to prove the accuracy of the sums is very logical.
Being bad at math is not a character flaw, it's simply a failure to have bothered to try.
I see it more like a bicycle. Without practice you will never learn how to ride. I guess there are few people who managed not learn how to ride even after practice, but majority learnt.
As a former boy, I can testify that the relationship between thinking you're bad at something and having a hard time learning it is not a sex-based trait. It applies to all kids, and especially to kids in the agonizingly self-conscious junior-high school years. Now, if the teacher communicates the attitude that girls can't be expected to do well, that's a completely different issue.
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I am amazed that in this day and age the New York Times will publish such a blatantly sexist essay, that asserts that boys are inferior than girls. Worse than girls in language ability, and about the same as girls in math ability.
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@kleontiades
It's not sexist. Girls are out performing boys in academics across all groups of children throughout all grades. Remember that nature wires the brains of boys and girls differently. This leads to habits of thought and perceptions which show up in academic outcomes.
@kleontiades
Yes, the article clearly makes the claim that girls are equal to boys in math, and better than them in language. And the author also claims that, on average both are equal.
More political correctness: girls are just as good as boys because girls are REALLY better.
No consideration given to the possibility that the distribution of abilities may be different by sex, with boys on extended tails and girls grouped more centrally.
In other words, what Larry Summers said that got him fired as Harvard’s president.
The truth isn't sexist.
This girl still remembers my Mother drilling me with math flash cards while in grade school every day during lunch. Yes I did well in math. Ended up an accountant. The basics in education matter.
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Oh my, YES! As a first born female, I strongly support this.
I can remember, as a kid, being locked in a room with my Mother, the math multiplication flash cards, and not being let out till I could do them backwards and forwards.
Okay....maybe it wasn't that bad. But, I went to engineering school, spent 30 years in the business and retired as a V.P. of Engineering.
And I am damned good at math.
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I taught psychology in a master's program. Consistently, I had female graduate students say: "I'm not good at stats/math."
I told them to simply never say this about themselves. That was a phrase that only female students uttered, never male students, and the female students were just as capable at math/stats as were the male students.
What was interesting, and this happened over many years, is that when I said that, the female students got it and stopped saying it. It was sort of like "yeah!, you're right, I do it just fine."
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Well, time to train professors not to assume their female students are uncomfortable and unskilled in math. When I proposed taking an economics class in grad school, one professor suggested (from nowhere) that I could take a tutoring class to get up to speed on algebra, ironically run by female students. I had to inform him that that would not be necessary as I already had a math degree and was very comfortable with algebra. So I recommend studying math because people stop underestimating your intelligence when they find out you were a math major.
I suggest there is a need for more research needed in how to best teach math -- repeat teach -- because the need for math is integral to defining and understanding anything that may significantly affect our quality of life, our survival, and the survival of our species.
Math allows us to predict how our environment will impact our lives and how our behavior and the behavior of other species can affect nature.
I don't know, but I do NOT believe that HOW we learn to use math is an attribute of gender. I have both male and female grandchildren and gender is not a determinant.
After 81 years of being involved in the application of math in the development of various conceptual designs for several technology applications, my experience tells me that it is nice and may be essential to have a sense of spatial relationships, some call it spatial reasoning. I believe that spatial reasoning can become part of our nature by playing with various shapes, very early say age 1.5 years, experiencing music, and observing movement of things, so the fundamental principles of nature/physics are integral to our understanding.
Some things are invisible to our senses & we must observe the effect of what we see and feel from heat, electrons, magnetism & gravity and they have been measured in history and how its behavior has been used to predict or forecast behavior.
So biographies of scientists including their experience in math would seem to be useful in developing math proficiency.
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I think the solution is more that the child has to have a person in the family who is familiar with math. I have exposed my grandson to math principles since he was pre-school. Now when the teacher introduces a new math concept to the class, he has seen it before and is not afraid of the prospect of learning the concept because he has seen the basic concept and he is not scared of failure.
@james jordan
There is voluminous research on how to teach K-12 math. In Japanese elementary schools they implement the researchers' recommendations, with well-trained and supported teachers, keep the recommedations that work and toss the duds, and get great results. In US elementary schools they ignore the recommendations and often treat the teachers horribly, and get lousy results.
Professor Oakley,
I feel obligated to share with you the story of Drs. James Powell and Gordon Danby, the co-inventors of superconducting Maglev. They are both brilliant engineers and retired scientists at Brookhaven National Lab.
I have seen James Powell in a room full of well schooled engineers and scientists and observed that they were amazed at Dr. Powell's facility with math.
They shared their schooling with me, Powell, the first doctorate in Nuclear Engineering from M.I.T. Interestingly, both men were educated in multiple grade one room rural schools, Powell in Pennsylvania and Danby in Canada. They both felt that they learned from the older children.
These two men were exceptionally innovative and extremely facile at using math to analyze and model processes.
That's why, I suggested more research in how the brain can develop a facility in Math. In my elementary school the smartest person in math was a girl classmate and she was also the best in music. Later in high school in the more advanced classes there were not many girls. One of the girls was in my drafting class and she, like you, went to engineering school.
Powell continues to work on complex problems and has developed concepts for a maglev network, see www.magneticglide.com to complement our highways, and he has developed a concept for Maglev Launch https://www.youtube.com/watch?v=N0-npDJlxCA that will generate very inexpensive electricity from solar satellites to beam energy to Earth.
Thank you for this essay. I taught second grade for a number of years in parochial schools. I followed a traditional, “old school”
math curriculum, which I believe helped students. Math is not unlike reading and writing. We provide students with the tools they use to practice and improve their skills. If a child only reads in the classroom and does not practice reading at home, she or he will never be a competent reader. The same goes with math rules, fact families, times tables, etc. I always taught concepts along with the drills and required memorization. Kids can be taught to solve word problems. There are formulas that can be learned. I myself disliked math as a child. I had no problem memorizing but had great difficulty with word problems. Ironically, I was a gifted reader and writer as a little girl. Many math concepts I did not appreciate until I reached high school. Geometry was the math I loved. It was visual. I ended up enjoying math in high school. I was not a natural but worked hard at it and did well. I also attended an all girls high school where we were encouraged to excel. Great article!
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@Mary Ellen
Power be to you. Impressive.
Second line down on the left (in the limit), that first x should be x^2.
A female English teacher in high school told me it was right that the PSAT doubled the verbal score and then added the math, because verbal skills are most important. I never thought to ask how her math teachers had treated her, but being good at math myself (as a male), I was appalled. Why would someone say such a thing?
I eventually became a scientist and thought about this from time to time. I realized there is truth there: written and oral communications are absolute keys to success. But much of the math I learned was crucial as well. Understanding math taught me how to think clearly and logically and in doing so helped me with my communication skills.
Most of us are forced to study math for years and never wind up using it. It is a relic of the Cold War, sacrificing many to try to find the gifted ones who will continue in STEM fields to advance science and technology.
Math really becomes a series of games, hoops to jump through. We’re constantly tested on it, and if we can struggle through and pass the IQ tests, rewards await us. So it is an important game to master.
Math fosters perseverance. The TIMSS test shows that country ranks correlate directly with how many students simply complete the 20-page questionnaire at the beginning (see Malcolm Gladwell).
Math is pivotal for STEM fields and much of life in general. It is simply abusive not to keep girls and boys on an equal footing.
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@Blue Moon yes! I noticed the missing ^2 as well. I think the artist just copied a bunch of random stuff out of a solution set for differentiation.
@Blue Moon As a girl who scored 13 points higher on the math part of the PSAT, I resented that doubling of the verbal score!
I took two math classes in my first year of college. In one class, the professor lectured during class and assigned 100-200 practice problems per week. I could tell I was learning and aced every test.
In the second class, the professor used the Socratic method to teach math, and assigned 5-10 practice problems per week. When I asked for help with problems I had trouble with, he dismissed them and said I didn't really need to know how to solve that particular problem anyway. I floundered and barely passed. This article makes me feel better about that, haha.
22
As a senior citizen, although, yes, math was my worst subject (languages and English best) I still recall a well-reasoned step-by-step accumulation of math knowledge: adding, subtracting, fractions, decimals, long division ,etc. Gradually, we absorbed the basics.
BUT why in heaven's name was it mandatory to learn calculus, logarithms, etc. in college? It was SO difficult for those of us without any aptitude for it and for whom it was mental torture that I have never forgotten it! WHAT purpose did it serve? WHEN have I ever had to use these skills?
Surely there must be a sane, reasonable limit.
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There are so many fun, and socially useful, subjects to learn. Forcing students to take "required courses" could be a misguided practice in college education. STEM should be one of several combinations, not the only one.
Why learn calculus? Beyond utility, it is one of he intellectual triumphs of humanity. The first rigorously thought through approach to infinity — not the infinitely large but the infinitely small and its connection to finite magnitudes.
I still know my times tables and other mathematical things that I learned "by rote". I also learned to play guitar. My teacher told me to focus on learning chords first rather than playing note scales. He said that would make it much more enjoyable and that I could start playing and singing songs quickly. He was right. It was a pleasant change from my piano lessons. In school, I enjoyed arithmetic and geometry but struggled though algebra and advanced algebra. I hated trying to solve quadratic equations, probably because I did not understand the concept. More often I came up with the wrong answers. How satisfying was that?
At about this time (8th grade) I began studying Latin and then French. I found that I had a greater ability to learn these languages which presented students with many variables to memorize and had grammars that were not completely logical (unless one learned the "logic" in them). I liked the challenge and became a foreign language student, eventually learning German, Russian, Farsi, and Polish. With each new language acquisition I was able to see links between languages I already knew. Learning to read different alphabets (Farsi, Russian) was not difficult. Learning to speak and read languages was more fun than working with equations because I could actually talk to people in their own languages and be understood. How wonderful is that?
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@bkbyers Math notation is just a form of language. It is highly compressed which is probably what makes it hard. You could write out a quadratic equation all in words. I bet if you looked at qaudratic equations again, linguistically, you would understand them better.
@bkbyers
People who know math can "speak" to other math speakers around the world and through the centuries. It is a lingua franca.
I love math but also love languages, and glad that you were able to find your way through them, but you sadly discount what math can give you.
I struggled with math in high school, my parents were of no help at all, and I dropped it as soon as I could to concentrate on arts and letters. That decision shaped every higher study and career decision thereafter. I’m 60 now and I’d love to take math again, just to prove I could do it, and also to figure out WHY I found it so hard.
20
Please do not dismiss what the author is saying without having any evidence. Anecdotes and personal observations do not count – we suffer from confirmation bias.
"Discovering geometry" was partly responsible for my daughters not going into STEM fields. Do not fret; they ended up in the jobs they love.
The teacher would sit there and hardly help as she was not allowed to by the standards of the quasi-experiment the district was conducting. You had to learn from your peers. I found that the peers who were “teaching” my kids were not discovering geometry but had been tutored the week before in the covered topics. Eventually, every parent, that could afford it, hired tutors for their kids.
The school district was happy with the results of their experiment but did not account for the tutoring. They continued this method of teaching for a while.
18
I disagree so vehemently with this piece, I had to weigh in.
I am the only daughter of two engineers. I joke that in my family, math was spoken of the way some families speak of God. And yet--I dropped math classes as soon as NYS would let me (after the 10th grade) in order to take electives in the arts and humanities, simply because I found them to be more relevant and enjoyable.
I went on to study fine arts, and later architecture. There was a calculus requirement and a physics requirement taught by profs from the illustrious local engineering school who happened to be professional mathematicians.
Something strange happened--a student who had forgotten the basic rules of algebra discovered math--as it existed in the world, and as it actually mattered.
The "drill-and-kill," "practice, practice, practice" approach of elementary math education at my strict, Catholic school was precisely what killed my interest and my curiosity.
Let children (boys and girls) in on the secret that math is the way we make sense of our world, that math is everywhere, and that not only is it fun, it is beautiful.
And as someone trained in the arts, I can vouch for the fact that the rigor-and-technique-before-ideas approach is a terrible way to teach the arts, too.
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@Amv
Math should be taught with both, as should any subject.
I don't think that the drill killed your interest, after all you chose architecture that required math. I think the drill made you comfortable enough with math that allowed you find eventually joy in it.
I tend to think that sometimes, parents are the ones that need to be educated in math. Once that happens, kids tend to pick up math easier because they see their parents doing it. And the kids don't have to have PHd parents; they just need to see why math is critical in daily lives. And they'll pick up on it.
19
Homeschooling mom here. To combine the learning without too much rote, supplement your standard math curriculum with math competition materials.
Elementary: MOEMS
Middle School: MathCounts + AMC 8
High School: AMC 10/12 + ARML
Instead of doing 100 problems that are exactly the same with different numbers, these exams force students to draw on their mathematical toolkit they've been developing for years.
Also, take a look at the Art of Problem Solving math curriculum. Far and away, it's the best math curriculum available, and nearly all of the top math students in the country study with it (in addition to what they learn at school).
20
"Do your daughter a favor — give her a little extra math practice each day, even if she finds it painful."
What? "even if she finds it painful"
I wouldn't let anyone near my grandchildren with that philosophy.
No, to encourage learning any subject, make it fun and interesting!
PS. I am a retired mathematician and my daughter is also a mathematician.
39
There is a difference between being a mathematician and being a math teacher. I can easily say that the reason our students score so low on international tests (just because it is stated in the article) is because they do not practice (drill) math any more. Teachers like me are expected to make math “fun” but not everything you have to accomplish in life is fun. And all that fun and conceptual understanding resulted in 8th graders who don’t even know their multiplication facts. Well, guess what, if you don’t know your multiplication facts you don’t understand division, GCF, fractions and the list goes on... so I am sorry but kids don’t always benefit from “fun.”
I don't think that anything is fun and interesting in beginning when you don't know anything. More you study, more interesting stuff you discover, and if you don't discover, at least you made an effort to discover, and could honestly say I tried it didn't work.
This sounds so true and mirrors my own development. I never understood algebra until I had to do it over and over again for trig and analytic geometry, same for those and calculus. And how did I study and finally receive an A on my final in calc after a year of Bs and Cs? Rewriting problems, doing new ones, ad nauseum for several weeks. When I got to college I was actually able to tutor some of the freshman engineers in calc because I finally, finally, learned it after refusing to be beaten by math even though I honestly believed I wasn't that good at it. (And yeah, despite this, I ended up with an advanced degree in the humanities.)
11
So what was the point of learning it? You could have spent the time learning a language.
I do wish NY Times style would permit them to list the author as "Dr. Oakley" and not "Ms. Oakley." Same would go for a man. She's a professor with a doctorate.
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@gpridge Agreed, "Ms." in this case is inappropriate.
A better line would have been "Professor Oakley teaches engineering and has authored a book on learning."
I was fortunate to be able to stay home with our daughter through her elementary and high school years. We would sit at our kitchen table most afternoons working on homework. I never let her say, " I'm just not good at math, mom". I also made sure that if she did not understand how I explained a problem, she had to ask her teacher for additional help. I forgot all my calculus so this became imperative in high school since I could no longer help her. We engaged in more than a few shouting matches with me always saying, " you are not stupid, you just don't understand a concept or application." My daughter is now an engineering major entering her junior year of college. She has overcome that sense that she is just not smart enough and she realizes that perseverance, practice, patience, and asking for help can lead to success.
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@CMB I'd love to know what staying home has to do with it. With two working parents who also helped with homework, my daughter never got less than an A in math and scored 5s on both AP Calculus exams.
16
@CMB. My daughter learned from piano lessons that practice helps you get better at something ( and even like it)!
@CMB My brother and I have similar issues with our girls (who is telling them these things?!?). Frustrating, but for kids that otherwise love Science it brought a little tear to my eye. You should be proud of the results.
And learn how to play golf...well!
8
One could easily write the same essay about BOYS and ELA (or grammar/writing/English Language Arts, whatever you call it)
11
Exactly. We have fetishized advanced STEM for the past 15-20 yrs. Fields based in humanities and creative thinkkng are deeply important tbour economy. And you need MATH in any management or business field, but generally not calculus.
One Saturday when I was in third grade my dad made me memorize my times tables, from zero to 12. Dad quizzed me 13 times to make certain I knew each of them perfectly. That day I was hurt and angry because missing out on Saturday fun felt like an exceedingly unfair punishment. However, after becoming an adult and then all throughout my life I have been very thankful Dad made me learn my times tables. Fifty years later and I still recall them perfectly.
As a teenager Dad tried to convince me to learn to type because as he explained, "you'll always be able to get a job if you need one." He expected I would marry and become a housewife, but wanted a backup for me in case my husband died or divorced me (lol, how quaint that assumption now seems). I consistently refused telling Dad I did not want to learn to type because I did not want to be a secretary (this was back before computers). Dad was upset with me then and likely thought I was very stupid, but later he was very proud of me when I earned my Ph.D.
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@MyOwnWoman As I boy I steadfastly refused to learnt to type. I'm not going to be a secretary! I said.
That's probably why it has taken me five minutes to write this post! Sheesh! If I'd only known...
1
@MyOwnWoman
When I was 9 and struggling with the times tables my father (who would soon abandon his wife and three sons) drilled me for days after dinner on the times tables. To this day I can still do the 17s without an error.
Learning the rudiments of math is not easy, it is not fun, it is hard work. But once learned a world opens to you with a language all its own.
PS...My wife is a PhD Chemist and was drilled by her father. She's almost as good at the times tables as I. I'm better at binary math! :-)
PPS...In our graduate department women outnumber men.
2
@MyOwnWoman Agree. (Not just times tables but all the other operations, too.) I think they establish neural pathways in the brain that persist - practice makes permanent, and all that. I have been able to process basic mathematical calculation faster than someone with a calculator, as I'm sure you can.
But "rote" learning like this has been attacked from all sides, to the detriment, I believe, of everyone - boys, girls, women, men, employers. Cutesy demonstrations and colorful computer games are all well and good, but education has become too much like entertainment and not enough like a discipline. Rote learning has a history of success. It isn't necessary that kids like it. So this article is welcome.
1
After studying sci/engineering then teaching math to Year 12 for 10 years, I made a shocking discovery. I had never found an answer to a math question that I wanted to know. I just wanted to get the answer right and move on.
Even real world math questions are often stupid. As math teachers we have to stop asking them to calculate the cost of buying 64 water melons? Who cares?
So for the love of it, I started a math blog that has the type of math question for middle school students that is so interesting they might want to know the answer. How many blocks of chocolate can kill you? Can you out run a bushfire? How far does a car traveling at 25mph move in 1 sec? Can you get out of the way?
I'm Mathspig. I love REAL math.
https://mathspig.wordpress.com
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@Kerry Cue "Even real world math questions are often stupid. As math teachers we have to stop asking them to calculate the cost of buying 64 water melons? Who cares?"
A caterer planning a barbecue for 300. The owner of a restaurant. A commercial chef who plans to make sorbet and pickled watermelon rinds.
My oldest daughter is an Actuary and my youngest son is graduating as an Engineer (Computer and Systems) next year. My other son received academic achievement awards throughout school for his Math skills.
But my youngest daughter, who has a successful career in I.T., and is a summa cum laude graduate in Life Sciences from a great Canadian university, cannot fathom more than the basics of math. No amount of encouragement, studying and tutors were able to get around this. Same upbringing, same school systems, but completely different outcome.
It has to be recognized that some of us are hard wired to excel at math, and some are not.
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@Abruptly Biff Exactly! I did OK, but not great, in math. I - and all my writer/editor friends - have built our careers on skills quite unrelated to math. True, most of the "good" jobs are in the STEM fields, but I'm getting tired of it being emphasized all the time. If I'm OK in math, but I don't really enjoy it, I have no interest in making gobs of money in a tech job if I'm happier earning a little less in another field.
@Abruptly Biff
There is a difference between expecting everyone to get a Ph.d. in math and expecting everyone to have basic competence, which is what the author was writing about.
There are math geniuses, just as there are poets and Mozarts and sports naturals. But the fact that most of us will never be Olympic contenders does not mean we should never pick up a tennis racket, and fact most of us will not be Yehudi Menuhin or Shakespeare likewise does not mean that we should not ever learn to play an instrument or write English.
@Abruptly Biff
No, the "hard wired" argument is faulty at the high school level.
Please give me a break. What are you implying, that there is no difference between boys brains and girls brains. I know for sure that there is. I had a little girl who was truly gifted in language skills, but really not very good at math. The reason we are all pulling for math skills is because it is language neutral. Why are we doing that? Because language is about culture. And the educationalists in the USA are educating against that. So, they want to pretend that girls should be as good as boys are at math. My daughter could speak both Greek and English fluently. But for the life of me, I could not get her to understand mathematical concepts. Talk about sexism, this is the ultimate example. Making little girls feel they are stupid because they are not as good at math as boys are.
14
@CBH The author wrote: "A large body of research has revealed that boys and girls have, on average, similar abilities in math." She didn't say there is no difference between their brains -- there is also research showing that boys are more likely to place at the extremes, i.e., very very high math skills, and very, very poor. But she's talking about the average student, and not about the extremes or about your specific daughter, for that matter. I'm surprised your superior language skills didn't process that for you. ;-)
Ha! I am a female and was a math major in college, my sister studied accounting and my brother.... English! My language skills definitely lag behind my math skills. Maybe i should get my girl brain checked out.
"In today's high tech world"---- but, tomorrow is going to be, high thought. Say hi, to the department of Thought, coming to the USA University, in the near Future. And, say hi, to The Brilliant IQ All Academic Track. Coming to K-12 Schools in the USA too. This is a new paradigm for USA Education. ---- Example: The equals sign must be understood. =. Equality. The concept of equality must be demonstrated. If they do not show that they understand equality then they cannot qualify for upper level management positions, certainly. Or any professional level position. Perhaps any workplace position, at all. Maybe even get a High School diploma. Diplomas can be taken away.
So many men do not understand Equality, yet are CEO's and MDs and Lawyers and Presidents and Vice Presidents of the USA. Barbara Oakley gives them too much credit. And, since a Female has the Highest IQ, has done the best in School, and is ranked #1, she doesn't give Girls enough credit either.
1
As a public school teacher I’m surprised to find that there are teachers out there who are not practicing “rote” mathematical problems with their students, though this may be the author’s lack of understanding about what’s currently being taught in schools. We don’t call the drilling and practice of mathematical strategies “rote” learning anymore—it is called fluency. And in fact, in most major math curriculums taught in the US, mathematical fluency is as important as ever. What has changed between the old math and the new math is simply the false and rather rudimentary notion that math problems can a)be solved in one way and b) that math is simply the learning of formulas and plugging them in. In fact, what is happening across math curriculum in the US is that most math curriculum is trying to up the rigor of its mathematicians through a balance of conceptual understanding, discussion of mathematical ideas, developing habits of mind that makes one successful in thinking about math, and of course, fluency in all important algorithms. The curriculum is hardly a hodgepodge. Because of the Common Core standards, math curriculum was developed with these important principles in mind. The only roadblock has been parents and adults ignorant of the curriculum. I would highly suggest checking out engage ny mathematics as an example of current math curriculum. If it’s hard for you—maybe you weren’t taught math as well as you thought you were in school.
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@Nell Becker
Beautiful explaination. Thanks for helping demystify math curriculum and what happens in classrooms.
2
@Nell Becker I'll let you know in a few years if the changes works. What's been being done over the last decade or so has resulted in students coming into my basic college stats class with appalling math skills. I certainly look at them and assume that they needed more practice going along. They certainly aren't memorizing even basic formulas. It would be nice if they did.
8
Great! When will we see some of these wonderfully trained prodigies you are turning out actually showing signs of numeracy in daily life? Because I work with people who have finished such curricula, both before and after they attend colleges and universities, and I'm failing to see such deep understanding.
I see instead deep divisions between what is a place where mathematics is perceived and what is seen as other 'life'. I see plenty of people who didn't do mathematics K-12, and it shows, and I see publications that people encounter in the course of daily life that shy away from any mathematics beyond grades 1-3 skills of rudimentary arithmetic, while holding to high standards for reading at at least the high school level. And don't worry, engage ny mathematics isn't hard for me.
1
I doubt they'll ever thank you, but you can still do it anyways.
3
This is all so true. My daughter got a perfect score on the math portion of the SAT, and graduated soma cum laude in physics. She naturally took after her papa, and she took my advice when I told her to always use actual fractions and never decimals unless specifically required to, and to never use a calculator unless specifically required to. She learned to do the calculations in her head like we did in the old days so she could more easily maintain concentration on the actual complex problems that come later, undistracted by mundane arithmetic or calculators.
In one way she is quite different from her papa. She's also an excellent writer and loves literature. Like quite a few guys, I focused exclusively on math and science. Some guys were great math students and indifferent or worse at everything else. I'm sure there are some girls like that too, but I'll bet it's far fewer than boys.
As it turns out, being able to write is a great help in STEM too, but math is the essential.
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@roseberry "graduated soma cum laude"
Aldous Huxley would be proud.
So what do we do about the ridiculous math curricula that emphasizes drawing number lines and little circles until, oh, about middle school? My husband an ME, enraged my child's public school math teacher by teaching her and drilling her on the standard algorithms and problem solving formats and insisting she do them instead of the little pictures that bored her to tears. Although we escaped to a school that teaches old school math and has a program that accelerates middle schoolers into Algebra, Geometry and Algebra 2 - our girl was bored by and hated math in the beginning. Sure others are experiencing this.
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@ROK
Those "little pictures" are merely abstract representations of concepts.
You know what else are abstract representations of concepts? Numbers.
@ROK Yes, and it is not just girls. The curriculum is designed for the borderline "developmentally delayed" (the current euphemism), not for the normal, much less the above-average, child. No one must fail, no child be left behind, so everyone is forced to stay at the starting line. No wonder they cannot compete with foreigners and immigrants.
@ROK You are confusing math and arithmatic. Drilling the "standard algorithms" is aritmatic, not math. It promotes no mathematical understanding. Learning to mimic a $1 calculator is not an achievement.
"Pie in the Sky."
What came first, the pastry or the Pythagorean?
I run a sewer plant! We depend on math... nothing complicated.. when I was taking my EPA mandated classes for my license (I was 55 at the time) I ran into young people who had no basic idea that 2 2 is 4!
Our math is not all that complicated.. actually mostly Geometry... volume of tanks, pipes, etc... they just have no clue...
By the way have your daughters get wastewater plant licenses.. trained operators can make $75,000 and up and do not need a college degree!
11
I am an elementary mathematics teacher and I object to the condescension and tone of this writer. Where was your voice Ms. Oakley when teachers were be pilloried and clobbered by everyone in the supposed "Educational Reform Movement"? That we are illiterate low-lifes that should be replaced by computers and Common Core.
Any teacher that has any classroom experience understands the essential need for practice - we used to model, facilitate guided practice and cooperative learning practice, independent practice and assessment. But not now. Vygotsky's zone of proximal development is thrown out the window and we are asked to steam through stem.
Teaching algorithms used to go-hand-in-hand with problem solving - but not now. I suggest you read up on Marilyn Burns and her essential book : Teaching Mathematics. You might learn that you are redundant and your valuable voice is too little too late.
12
Every 10–15 years the education pendulum seems to switch directions,, I fully expect in a decade we will be reading op-eds about how math drills are hurting young girls.
10
I work as a teacher in the infamously dysfunctional Los Angeles Unified School District, and from where I hunker down in the trenches, this column is deadly accurate.
I started teaching elementary grades, and was admonished in writing for having my children memorize their times tables. I was told to use manipulatives so that my students could "discover" multiplication. When that didn't work, I was able to teach them the times tables by having them dance to a CD called "The Multiplication Rap".
Believe it or not, I was then written up for teaching them the times tables up to twelve when the curriculum only called for teaching up to the "ten" table. According to the administrator, I had "failed to teach to the standard" by exceeding the standard.
I now teach seventh-graders, and many of them don't know their times tables either.
My sincere thanks to Barbara Oakley for this column.
500
Thanks for your candor. This makes me so angry. My child has always struggled in match and would've benefited enormously from consistent drilling. Instead, we were advised to have her use Cheerios as manipulatives at home. Really? I don't blame the teachers at all as I know a rote approach has fallen out of favor.
3
I saved a letter from my daughter’s 4th grade teacher to parents telling us not to teach our kids multiplication tables but instead let them “discover” math my counting window panes or beverage cartons. Alas, it was too late for my kid. She had memorized them in third grade. She went to Stuyvesant High School. She wouldn’t have gotten in by counting window panes.
2
@Vesuviano
Thanks for being a teacher that cared!
1
Playing with tools, trucks, and Tinker Toys helps too.
5
Yes, many boys are better at 3D visualization because they have had years of model building and playing with building toys. Encourage boys and girls to do these sorts of fun activities.
Nature tends to compensate. Animals weaker in one respect , are stronger in another. Human females( most females) are usually smaller and less strong than males. Ergo they should have better brains. Indeed there have been several great female mathematicians in spite of discouragements. of course have your daughter study math
Meanwhile, post secondary, where are the boys? Other than Asians the classrooms are bereft of boys. No incentive to be there? No one seems to care. Why no despair? Like denying climate change, this will not end well.
5
I agree, practice is what makes perfect, along with application. As a child I was "good at math" until multiplication came on the scene. At that time, rote was out of favor and "understanding" was in. I couldn't understand and felt dumb. Then mom bought me a record of "Multiplication Rock" songs--the multiplications tables sung to music (with videos shown on Saturday morning tv!)
I hold a Bachelors and a Masters in science, a law degree, and I still sing my multiplication tables in my head, as needed!
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"Who doesn’t want to help a child learn to read and write? Is there the same thrill in teaching them basic numbers and arithmetic?"
Yes there is. It is precisely this attitude that leads to people bragging about their lack of math skills when they would never brag about being unable to read (and many who can't read are - sadly - deeply ashamed of the fact).
Math is abstract reasoning made visible. I feel for those who may have neurological obstacles to fully accessing mathematics, but I have no patience for those who deprecate what they do not personally enjoy. Imagine if I expressed the same opinion about Jane Austen.
5
My best recollections of having our daughter like maths was when even as a five year old, going to kindergarten, my husband, who would drive her to school, would play the math game.
Either basic multiplication or simple additions! Just quizzes! The short ride was always maths! And she seemed to love it!
Short answer— girls are as smart or smarter!
Let our daughters soar!
70
@sita57 my husband does the same thing with my 5 year old!
@sita57, The reason your husband had to do this is because the fools in charge of American education think memorization is child abuse.
1
Rather than differentiating mathematical from verbal skills, we should instead look to how they are analogous, namely, as languages that can be learned universally and fluently, but only through early and frequent practice. If we observe the thousands of hours of practice (hearing, speaking, reading, and writing) involved in learning our native tongue, we might see that mathematics, being far simpler, can actually be learned with far less exposure and practice.
For this reason, I introduced mathematical concepts to my daughter from the beginning, knowing that practice and frequent use of numbers and operations, in a way that was fun, would make math easy for her in school, and hence, much more appealing. Though this early math practice never amounted to anywhere near as much of her day as she devoted to learning English--chattering or reading non-stop, 14 hours a day-- it was much more than in most American households. I have been doing something similar with my five year old son. He is fascinated by numbers and is constantly working out addition and multiplication problems out loud. Why we should worry about girls' math skills, which are on par with boys, is unclear from the article. The only problem demonstrated is that boys lag far behind girls in language skills. However, drilling is no solution. In my experience, boys and girls can learn both skills equally well from varied, engaging practice (reading, puzzles, stories) from an early age. Drilling kills interest.
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This is bunk.There is no "large body of research" showing girls are any better than boys at language arts. The author cleverly, or deceptively, juxtaposes the real research that says girls and boys are equally able, with the claim that some studies show girls are better at language arts. But the only large body is that which shows equality. There are no well controlled and designed, randomly conducted studies that show either gender is superior in language arts. The entire article is like PT Barnum's observation about the frequency of certain births.
This entire area of research started with a well justified effort to explain why boys seem to outperform girls in math. It turned out that was simply not true and mostly if not entirely due to socialization. How this useful revelation became twisted into a mistaken belief that girls somehow were more able in language arts is mysterious if not suspicious. There is no solid support for this. It simply doesn't exist. No large body of research. Jeesh
23
Not only is there a large body of research showing that girls are stronger in language arts in K through 5 education, any primary school or middle school humanities teacher you talk to will attest to the same through personal experience.
The author's point is that if a student feels more successful in humanities than math many will tend to focus on their comfort zone. We have to counter that until students are old enough and mature enough to make their own choices about where to focus their efforts.
i think you're dead wrong. i always loved playing soccer and learning languages, even the hard parts. i loved writing, even though it was hard. not only was math hard, but i hated it, and no one had to tell me that. i knew it for myself. why spend so much of my time in K-12 banging my head against a wall?
5
"girls have a consistent advantage in reading and writing" and are as good as boys at math
Hmmm, this could be very discouraging news to the parents of boys and boys themselves- apparently boys arrive to the world mentally handicapped compared to their female competition.
Perhaps the issue here is that boys mature later than girls, which is also a fairly well established fact.
By adolescence and probably much sooner, boys and girls are cognitively affected by different hormones which also must effect the manner in which they use their intelligence.
That said, American culture obviously does a very poor job in inspiring our girls to pursue careers in science and that hurts us all because it represents under-utilization of our human capital.
Most of the rest of the world does a better job of recruiting females into science related careers- so there is obviously more going on here than girls misinterpreting their relative natural talent.
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Great article. Thank you for this!
1
Barbara Oakley is a rock star.
Two years ago I interviewed for a math teaching position at a new charter high school. The school emphasized teaching vocational skills. The school's young barrel-chested, flannel shirted, director expected the math teacher to instruct several grades simultaneously, using a real-life construction or similar projects as the basis for the 'multi-grade-level problem set for the day.' No textbook. No drill. No remediation. No computer-based learning to shore up weak skills. I told the director that math is sequential: If a student is not grounded in his or her multiplication tables et cetera, then he or she will not get a handle on fractions, and so on. Same idea as not knowing one's ABCs and struggling with reading. The director would not budge. I told the director he had the wrong person and left. I went home and googled on the subject of "drill and kill" in the teaching of mathematics. From years of teaching, I was firm in my belief, but I wanted more backup. I found this: http://nautil.us/issue/40/learning/how-i-rewired-my-brain-to-become-flue...
I sent Professor Oakley a short email. In so many words, she said, "right on." You are doing parents, students and teachers in the United States a great service.
9
Love this!!! Thank you for reinforcing what I've been telling my daughter all along!
1
My freshman college German professor taught us there were three rules to learning German:
1. Review
2. Review
3. Review
The American public school system has been a disaster for teaching American children (witness PISA). It is a disaster because the architects of American public school education were avowed Socialists (aka "Progressives") who wanted to dumb down American children. Oh, and they also greatly admired the Soviet Union. Research John Dewey, the foremost Progressive who architected the education of teachers to educate our students along the lines of the "nanny-state".
Until public school education is abolished, and the free market of American education - which we used to have - returns, you can expect only abysmally horrid results. Which is what we have now.
Until then, parents must do the best for their children. Including being the teachers they thought their taxes had already paid for.
2
@KarlosTJ
How is it then that all the countries doing far better than we are with their children (eg. Finland) are educating their children through public education?
My public education was superb, BTW.
The author makes such an important point about the contribution of "rote learning" to the development of skills in mathematics.
Is there any chance she could be persuaded to rewrite this very useful article as "How to Make Your Child As Fluent in Math as in English." That's right, forget the gender stuff (it's as inappropriate as racist stuff) and instead lets focus on the generic problem of making ALL our kids more fluent in math.
6
"All learning isn't - and shouldn't be - fun" AMEN!! Can we find a way to convince K-12 professionals of this.
5
Yes! We need more articles on STEM education for girls! Our nation needs the push and the understanding that 50% of our population is being left out of this important means of education and professions.
Encourage the daughters and Grand-daughters of the USA.
"A large body of research has revealed that boys and girls have, on average, similar abilities in math."
It was hard for me to read past that. Why not discuss some of this "large body of research"? I've also read a large body of research. The only problem is that it says exactly the opposite what Ms. Oakley is trying to portray.
15
The Khan's Academy youtube presentations are an amazing way to learn Mathematics.
11
Perpetuating a myth as usual! Girls are thriving more than ever! This applies to math, as well as the other disciplines! Fifty years ago, maybe this article could have been applied! It's the boys, in many cases, who are struggling today!!!
8
Math is fun for everyone. Stop acting like girls need special treatment.
If Mathematics isn't fun, blame the teacher, not the student.
4
I’m going to take this article in the spirit in which I believe it was written. Contrary to what some of the commenters seem to believe, I don’t think the “”a”uthor is advocating exclusively rote learning. To my mind she is promoting the good idea that students master subjects by working with the various concepts until they get it intellectually and can use them (almost) effortlessly. Repetition or practice can be part of this.
10
I always gave my daughters extra math by giving them math workbooks to do the same way one would do crossword puzzles, for instance. They grew up being proficient in math and not shying away from math and science. It was sexual stereotyping in the past that kept girls from STEM subjects. I hope those times are over.
128
My daughter has a terrific grasp of applied mathematics and my son is an aeronautical engineer.
At early ages, by kindergarten, my children handled money--cash to make grocery purchases. I didn't worry about perfect calculations, instead I wanted them to have a shot at real math nearly every day.
In grade school, I paid the kids small amounts to add and subtract daily household expenses, for example: groceries, meals out, treats, snacks, and toys. (Word spread and their friends landed at my kitchen table eager to play 'Accountant' -- and I paid them, too.)
By the fourth grade, I taught the kids how to write and balance checks for larger purchases: new bikes, summer camp, Back-to-school purchases and so forth. When a sale was announced for sports gear, I helped the kids set up a quick equation to determine if the sale was a good deal.
During rush hour traffic, we played 'Car Casino' for instance, the probability of a sighting a particular automobile, the frequency of red lights vs green lights; the kids invented games-- and we used real money and real dice. Our carpool was sought by other kids who wanted in on the action.
When Algebra II spread torment, I hired a student from the community college who tutored. Together, they tackled quadratics and logarithims until the kids chewed 'em up like popcorn. Eventually, the kids broke through and embraced higher-level math. I wanted to encourage an appreciation of mathematics, and we had fun!
13
There is a skill that is the subject of rote learning that often begins at home, and continues through kindergarten: it is called mastering the alphabet and it is a basic skill that needs to be acquired before learning to read. Why there is so much opposition to the rote learning needed to master basic multiplication facts? I agree with Barbara Oakley's observation that practice is not emphasized enough. However, I see the problem as a gender neutral affliction.
20
How about we encourage children to try new things and challenge themselves while we adults challenge ourselves to end gender, class, and racial biases before we inculcate them in our children?
While we're at that, why don't we also talk to children about their interests and ideas rather than sit them down for - and I'm quoting here - "drills"?
I am an award-winning teacher with almost two decade's experience in primary classrooms. My students do well academically and enjoy mathematics - which they practice in many subjects and in play, all on their own. Given support to identify the learning they're doing, they begin to see themselves as mathematicians.
This work - which, again, is evident in their academic success - is fun. Increasingly, persons not actively engaged in primary education like the author propose that teachers provide drill work and unpleasant practice in the name of rigor or developing "grit". These demands have not improved PISA results. They haven't challenged institutional bias. And they fail to appreciate the vital work of childhood: cooperation, collaboration, and knowledge-building. What they have done is encouraged successful teachers to leave the profession because they refuse to preside over joyless children.
6
Make sure your daughters [and sons] learn ARITHMETIC.
Make sure they learn their addition and multiplication tables.
A student who has not learned ARITHMETIC will have trouble learning algebra.
A student who can not combine 2/3 + 3/4 by hand will not know how to combine a /b + c /d.
Knowledge of simple algebra is essential for the study of more advanced topics like geometry, trigonometry, calculus and even in the quantitative social sciences where mathematical concepts are used.
Forget all this irrelevant nonsense {thrown into the curriculum by geniuses in the education schools } like different bases, and sets and rotational symmetry.
Do not allow students to substitute mastering basic ARITHMETIC for learning about the nonsense I listed above.
I taught math and physics for many years at an elite NYC private school. In my experience weak students had never learned ARITHMETIC.
47
More than 60 years ago, my fifth grade math teacher told our class, “I know you can do these problems; so you will do them 50 or 100 times. Then you will do them always.” To this day I can answer most arithmetic problems without conscious calculation. Prior to that I spent hours at home with Mom doing my multiplication and addition tables. My down fall was the lack of interest in understanding 3Rd and 4th year calculus, and thus not appreciating thermodynamics and enzyme mechanics in graduate school. Still, molecular genetics beckoned and provided a creative and scientific outlet.
6
"Memorizing vocabulary" is NOT helpful to learning a foreign language. As an experienced teacher of English as a second language and a student five foreign languages, I know this to be true. Using the vocabulary repeatedly in meaningful sentences is what creates learning. Language learning (like music learning) is a matter of repetition, which is why children learn so amazingly well. For them, repetition is fun. For us old people, not so much. Memorizing vocabulary is unpleasant and more often than not turns students of to foreign language learning altogether. When I first studied French, I would do the assigned written translations and then repeat the French version 10 times aloud. The results speak (literally) for themselves.
6
I loved math and eventually became an engineer. I loved math partly because it was graded objectively. The answer was right or wrong unlike writing and literature exams/projects where grades were influenced by how much the teacher liked/disliked you. So I disagree with Ms Oakley's interpretation of male/female liberal arts skills.
Personally, I felt that we males were discriminated against in liberal arts classes because young male opinions and voices were shunned - all of my high school liberal arts teachers were female. Too often, students were asked to tell a story about how we feel; men of all ages have trouble with "feelings".
Another issue is that many of the books students are asked to read are just not interesting to young men. Sensitivity, empowerment and diversity issues need to be taught, but should be taught in separate classes - English should be about reading comprehension and writing skills.
Another key issue is what part of math needs to be taught? Is long division of polynomials more important than non-euclidean geometry, and so on? Students can't learn all of the areas of mathematics. Some parts of high school math (long division of polynomials, the equation for a right angle cone, MacLauren series, etc.) are just not needed today and better done numerically by a computer. Much of what is asked on the national math exams is minutia. Young men and women need to be taught math that is directly applicable to real world careers.
12
@JAR Take it from someone who teaches vector calculus, math is a visceral experience for many students. It puts people through the emotional wringer.
@JAR I believe you nailed it. I would add public speaking skills to your reading and writing skills.
1
The best math students in our school district were given more math classroom time and more math homework. And, of course, those students became better at math. I have one child who was not pushed in into the "better math" section and another child who was. I paid for a weekly math center to help the child excluded from the better math club. Thank goodness I did. This isn't rocket science. If children receive more instruction in a subject, they will do better at that subject.
15
When I tried to help my own children with long division, I could not believe the brain manipulation that was required...think of groups, how many more for 100, stars everywhere. One problem would take up a page.
I could do long division in quick order because I knew the multiplication tables on which we were drilled constantly as kids. My children had to labor under such math machinations. Just do the math!
13
I am a many-times published author. In school, I won regional prizes for essays and short stories. My math was fine until 9th grade--first year algebra--a disaster. I ended the year with a 2% in the final exam. A clever tutor revealed that "x" jumps over the equals sign, and by visualizing that hop, I was finally able to do equilateral equations. In Grade 10, we did geometry, and I picked up an A. Until April, when algebra crept in. By profession, I am a graphic designer, hold an MFA from Yale. Where I met someone who'd been at Music and Art in NYC. He informed me that all the music students got As in Algebra and Ds in geometry, and the reverse was true of the visual artists, and everyone took it for granted: "Of course, you did." Maybe the new math prevents the "x" shock? Maybe when x is a number, any number is introduced along with x is a letter in the alphabet things go smoothly...
8
You need a goal. The aspiring musician wants to play music. I was awful in statics until I discovered "SPSS" Statistical Programming for the Social Sciences. That book showed me what I was looking for. Mastering the HP Business Calculator took a month, but it made passing the CFP exam on the first try possible.
Schools don't really teach to an objective. They should.
.
2
@George, DC: No George, they shouldn't. Math classes shouldn't be taught with the objective of students passing any sort of exam, much less one for a professional license. It's exactly that attitude that kills the spirit of inquiry and higher thinking.
1
Math is the language of the universe and it follows that, rather than just "practicing math," it is easy to inspire a love of it in young women by showing, with real life demonstrations in, say physics, how it describes and predicts the world around us. Math gives meaning and symmetry to nature.
I did fairly well in math but was never taught the amazing ways in which it informs us about every day life. I found that out many years later as an adult. I wish my teachers conveyed that knowledge when I was in primary and secondary school. Children are incredibly curious.
25
@Emergence
Bingo. Daughter inherited her papa's advanced-math brain but hates it as I did, A's and all. Hschooling allowed us to focus on the wonders and skip the calculations: Muderous Maths a good example.
Still, she will never go into any field req much math.
1
@Emergence
This. I am of the firm belief that, if you are teaching math within a K-12 setting, you should be able to write out EVERY equation or problem you assign as a word problem. It doesn't matter if it's multiplying fractions, figuring out time, or calculating logorithms. If you CAN'T rewrite the equation in the form of a word problem, it doesn't belong in a K-12 math class. College, possibly. But not in a primary or secondary setting.
Why? Because figuring out rote equations is all well and good, but it's important to understand how math is used OUTSIDE the classroom. As you put it, we need to know all "the amazing ways in which [math] informs us about everyday life."
Case in point: I lost all interest in math when I had to learn about hyperbolas and imaginary numbers. I couldn't understand how or why I would ever use them. (I still don't. And twenty years later, I've yet to use either one.) The only explanation I ever got was, "Some people use them in engineering."
The good professor undersells the sex difference between boys and girls - average results mean very little. To succeed in Engineering you need above average math skills - so the question is how do boys and girls in the upper math cohort perform.
The easiest way to assess this is via the million of data points in the SAT's. Results for the top performers in the math section have reliably been boys at about two-thirds and girls at one-third for decades.
Listen, I have tried to recruit young women to pursue engineering for over two decades. I have watched them match and exceed males in Law, MBA programs and Medical School. This problem with engineering is more than just getting the girls to practice math.
ERTW!
10
@SteveRR
By the time they take the SAT, they've already decided long ago that they're not as good at math as they are at language.
5
@SteveRR You may have a point, although the explanation for why girls' efforts at math fall off as they get older (there's plenty of social science research demonstrating this) has nothing to do with innate ability. Girls are socialized into femininity that is appropriate for their particular society and through this process girls pick up on the fact that ideal femininity focuses on their physical attractiveness and that girls are not supposed to be good at math.
Just look at the assumptions made about which inherent attributes are innate in females and males in our society. On average even girls who are way above the curve in math at earlier ages will start to get lower grades as they go through puberty and start focusing on being ideally (and stereotypically) feminine. This decline in math scores and interest in math is not common in all girl schools, partly because without boys in the classroom girls are much less pressured to "do ideal femininity." They have less concern with how they perform femininity and can therefore focus more on learning.
Although a good article the author fails to mention the specific social pressures that influence individual psychology and leads many girls to decide to be good at femininity rather than math. The gender system and traditional gender expectations are highly influential and unless we change gender norms all the encouragement of individual girls will not sufficiently change why girls choose not to be good at math.
5
@SteveRR don't worry about it. they are better off in law, mba and medical school.
2
Whether or not standardized tests show slight statistical differences between boys and girls is meaningless. Having raised twins, a boy and a girl I can speak from experience, although anecdotally, that parents expectations are important in their education attainment level. We let them know that we expected them to be college graduates but hoped they would get PhD or like degrees. This year that happened. Our daughter earned a PhD in Bioinformatics and Cell biology and our son, an M.D.
Our daughter had two science teachers in middle school and high school who said she’d never be a scientist. (Note to all teachers who do that stuff, STOP IT.) We knew she was smart and has an incredible work ethic. She also had a wonderful chem teacher in High School who supported her. Our son never had anyone doubt his intellectual abilities, even though he was pretty goofy as a kid. Both worked very hard to get to where they are and to our delight are employed.
17
@Carole Shortt--I can't believe any teacher nowadays would even say such a ridiculous thing like what was said to your daughter. That is outrageous. Teachers really need to get with the program. It's the 21st century. If you can't be encouraging to all students, forget about teaching.
3
Back in the day in my high school geometry class all the girls were required to sit in the back two rows of the classroom. The teacher, one Mr. Egge, would always reply to our questions from the hinterland, “ You girls will never use what I’m teaching here...it’s a waste of your time and mine.”
Needless to say, I abhorred math after that though I did continue on.
My daughters received exceptional math educations, had amazing teachers, and, one, utilizes it everyday in her tech career.
Time have changed,but they still have a long way to go!
20
@LJB Don't believe it!
1
This article has the science exactly backwards. Training by rote (aka cramming) has short term positive effects and long term negative effects. Blind algorithmic learning leads to disaffection, burnout, and anger.
I teach math at the graduate level. The students who have the hardest time adjusting to research are the ones who learned math as dogma. Math is not fixed. It is a dynamic living language with many dialects and conventions. If that were not the case, our capacity to conduct basic research in the field would be zero.
My research is the science of learning and the role that autonomy plays. I focus on math education because often children find far fewer opportunities to assert themselves in the math classroom as they find elsewhere. As a result, our students have trouble transferring math skills to problems outside of the classroom. "Where can I use this in the real world?" is far too common a refrain.
Here is the kicker...There is nothing wrong with math drills. There is everything wrong with mindless math drills.
Do yourself a favor. Let your daughter play with math. Expose her to its beauty and mystique. Tempt her with musical instruments, cooking, and maker hubs early and often. Play dice games. Play cards. Take her to museums. Let her run past the massive canvases of Salvador Dali and Georgia O'Keeffe.
Start big. Be bold. The fine details of this jeweled discipline will catch her eye and draw her in.
39
@cleverclue I think you do the author a disservice. Learning the multiplication tables by rote is not the same thing as cramming. Memorizing math facts frees up cognitive space in short-term (or immediate) memory so that you CAN play with math.
13
@cleverclue As a college student I was great at everything but algebra. I'm a critical thinker, so when my sister (a math wiz) was tutoring me in algebra I struggled greatly because everything she tried to teach me made me ask "why?" or "why not?" She finally sat me down and said "listen, right now you have to just memorize and learn the formulas so you can depend on them at any point, eventually that will enable you to learn more complex ideas and theories if you want to."
As a professor I now teach my students to not rely on memorization because most students do not understand that memorization isn't learning, because without comprehension it cannot enable application. So this is how I explain learning to my students. As a child you memorize the ABCs, and to a child they are just lines and squiggles that have random names. Then as you move into higher grades you start to conceptualize how the placement of those ABCs enable you to spell words, and you also learn that the words are not the actual objects but rather represent particular objects. You learned to spell, and the next step is learning how the words can make sentences that describe ideas...then you learn about paragraphs, and so on and so on. Each new level of learning moves one to be better able to grasp higher and higher levels of abstraction so one can fully comprehend. Memorization is a basic element of learning, but you have to move beyond it to comprehension and application to truly learn.
@cleverclue
This reflects my experience. I did math as mental drills, but never learned to "play" or "explore" with it. I was never encouraged to think about the concepts behind it. When I got to the "real" math that starts with calculus, I could not do it.
Now I have a great appreciation for math but it has done me little good. The extra time I spent trying to re-learn the concepts, which I did because everyone said math was the "gateway" to physics and science, actually kept me from doing the things I was really good at and truly loved.
I recall reading that Aristotle declared that the "roots of education are bitter, but the fruits are sweet". I do not think many students want to accept the bitterness of the beginning.
10
@FilmMD Math is only bitter when it is unfamiliar. Present it to children like you might introduce them to spinach...early and often. When they become familiar with a dish, they will be ready to try it.
https://www.nytimes.com/2016/02/16/opinion/why-poor-children-cant-be-pic...
4
At age 67, I took up the violin. I enjoyed the conceptual aspects of learning different keys and the frequencies of notes, etc. But I knew that I had to practice to ingrain the movements into the neural circuits of my brain to make that 8 ounces of beautifully carved wood sound worthy of playing in front of someone. When I became discouraged, I asked my violin teacher, Paula Su (age 25, from Taiwan, at the University of Wisconsin), how many times she practices a piece before she can perform at a recital or competition. She told me she will play it and practice it a thousand times and more. She told me one day, “you know the old adage - practice makes perfect!”
7
I blush to remember the endless hours I put into Game Boy! But I did get to the next level! Mathematics is the language of the universe itself: the Pythagorean theorem, and, just add a fourth dimension, BUT with a minus sign instead of a plus sign, and you have: ta da! Einstein's theory of Relativity - with time slowing down, and also a limit to velocity predicted.
2
Thanks for this article. Just sent it to my grown up kids. I did make them practice -- and I was at times criticized by other parents and maybe even a little bit by teachers also. Actually, it was not uncommon for people to come up to me in the supermarket and ask: Why the math practice? In my experience, people like what they're good at and this goes double for kids. If they practice math, they'll succeed at it, and then they'll love it. I would point out also that as a parent I saw firsthand that girls were less encouraged than boys in math and science, but both girls and boys will excel at what they love and when it comes to math (or basketball), success takes practice, or at least it did for my kids.
6
I made the mistake to assume that the school system was teaching at a high level. Good grades in class turned out not to mean what I expected. Get involved even with with A students!
15
Thank heavens for this article. 20 years ago I applied for a grant from the Dept of Ed to develop an online practice system for students learning programming (arguably a cousin of mathematics). The proposal was turned down because it focused too much on "drill" (i.e. practice) -- it wasn't focused on "concepts". Fortunately the NSF did understand the value of practice, just as this author does, and recognizes that like music and athletics, learning programming (and math) require practice. Not practice exclusively to be sure-- but practice is a sine qua non. Today, 50,000-60,000 students a year use the CodeLab system to help them learn programming.
23
Every parent of a daughter - and daughters old enough to read - should read the book, Broad Band by Claire Evans, watch the movie, Hidden Figures, and other inspirational - and mindset-changing - true stories about women and math/computer science, including Ada Lovelace.
The idea that girls can't do math is a cultural narrative that needs to be changed.
https://www.penguinrandomhouse.com/books/545427/broad-band-by-claire-l-e...
11
@Suzanne: I do not believe for one second that "girls cannot do math".
They certainly can. But not all HUMAN BEINGS can do math.
Many people simple cannot learn math beyond a certain point. And everyone (but a few geniuses) have a point where they will never get past -- it might be calculus for some, and basic addition for others.
A certain percentage of the population has DYSCALCULIA and can never learn math -- no matter if you beat or punish them or torture them with endless "drill & kill". They just cannot process it, their brains are not set up that way.
1
Math professor here (CUNY, John Jay College). I am very refreshed to hear someone advocate more drilling in math classes. I regularly tell my calculus students that they must practice problem types until the solutions come virtually without thought. Usually when I say this I get silence. No nodding heads. I see no recognition of drilling as a familiar route to mastery in mathematics.
I also like the emphasis on pain. Math is not a joy for some and torture for others. It is an activity that requires a lot of dolorous exertion for all takers. The joy comes in the understanding and feeling of accomplishment once the learning is complete.
65
Yes, the difference between tasks that are fun and work that is fulfilling. Excellent point.
My wife had a father that just taught her everything he liked to do. Physics and math, professionally. Engineering, aka, building stuff, in his off time. Balancing the family checkbook started as a shared father-daughter activity at age 8.
It's more than "just math". It's also Spatial reasoning that comes from building things, and that is considered a male trait, but it is also something women can do well, as my wife has a perfect aptitude for that.
If your parents are "STEM", then participating in what they do will train you in math, and it won't be work, and it won't be drills. I'm not sure what parents should do when they are not math literate. You need to understand math to teach it.
Not many people,and unfortunately most lower division teachers, do not either. Trying to learn math from people that don't understand it is painful. It's not a linear process either. I understood elementary calculus, before trig., and doing proofs in 5th grade geometry class was for some reason easy, but not a big part of math education until college and graduate mathematics.
9
When my daughter, now 34, was in grade school, her computational skills were poor, and we decided it was because she did not have enough repetitive practice of the sort I had as a student in the 1950s.
So we enrolled her in Kumon, a Japanese program that has kids do computational exercises over and over until they gain mastery before they move on to the next level.
This helped her tremendously, and, as an adult, she thanked us for having her do this.
Sure, this is not high level math, but if you can't do basic computation, you are not going to be ready to move up.
I don't get why schools don't ensure that kids have these skills.
40
@vibise I couldn't agree more. We enrolled our daughters in Kumon, and it has served them in good stead through their careers. Kumon changed them from not liking math to doing well, and appreciating math. (Our daughter who was worst at math is now doing her medical residency at Stanford.)
9
Students can be good at a variety of things. Everyone who is well educated needs to understand statistics and probably calculus as well. Now I wonder how we teach math impacts anybody, teach it as we have for decades, after all Algebra has existed for a long time as has calculus, no need for a different method of teaching it.
1
There are three levels at which math can be taught and understood, not just two: first, the conceptual level, like knowing what the real line is, how decimals are logically constructed, and why you add exponents when you multiply.
The opposite is the drill of the multiplication table, or remembering the derivative of sin(x), or the quadratic formula.
The main reason for rote or "mindless" practice is to give you quick tools for the middle level of math, the most important level: the successful manipulation of symbols and concepts to move from one mathematical truth to another.
If every time you see the derivative of sin(x) you have to look up the answer, or are forced to re-create it from first principles if you can, you will not get far. It's like knowing that the past of "is" is "was" without the use of a dictionary each time you speak.
We also fail here at the middle level of math. It is important to develop the mental skills of deduction, such as solving equations, or factoring, or conceptualizing and solving math puzzles, where you must use the combination of things remembered and some instant creativity.
I have said all my life to anyone who would listen, including my kids: math is easy, and math is fun. All you have to do is develop the mental attitude (not aptitude). The right mental attitude is acquiring, by practice, a knack for the middle level, supported by some basic "automatic" knowledge.
The confidence that you can do it lets you do it.
36
@John Xavier III. My late husband was a secondary school math teacher. His approach to teaching math was to first approach it from the conceptual level. Some faces would light up: they got it. Other faces would be blank @ they did not understand it at all.
He would then tell the “blank”students that they were going to have to know how to do this work. If they didn’t understand it, then drill, drill, drill until thecould do the work - it was okay - they would be able to do just fine that way. He said a few ended up finally getting the concept and found pleasure in this. But at least they all learned to do the work.
3
This essay correctly makes several very important points, applicable to both boys and girls. A long time ago, when I was a kid, in parochial school, the nuns taught very much along the same line as Ms. Oakley counsels. They did leave one thing out, and it was also left out in most math courses I took, through college. The teachers rarely, if ever, gave meaningful examples of the practical use of the various math functions, other than the very basic ones of making change, simple measurement of a room, etc.
My impression was that most teachers did not know the practical uses of math functions, other than the most basic. Perhaps things have changed, nowadays, particularly with the wide variety of video and other electronic aids.
7
Dr. Oakley's essay is perfectly true and, sadly, completely useless.
As human beings, we have been teaching and learning mathematics at least since the temple schools of dynastic Egypt, some 5,000 years ago. There is nothing in this essay we have not known for a very long time. Indeed, American schools used to be organized around these principle two generations ago.
Why American schools jettisoned basic principles of pedagogy, that are known work, is entirely a political matter. A matter that Dr. Oakley does not address.
15
@Haim You are correct. Possibly not the political matter that you think, though. Public education has long been taken over by people with ed degrees who don't know anything about literature, math, biology, etc. and have found ways to control and order around people that DO know subject matters, by making education about "skills" devoid of content.
I was math teachers used real time examples. I learn fractions when I became an avid baker. If someone had taught math using real world examples, we might have all been better off.
And learning can be fun...it just requires work from teachers and administrators.
3
This article is the story of my life.
I taught myself to read before kindergarten and was the best reader in my class in 1st grade.
But in math, I had to count of my fingers and it was harder so I thought I wasn’t good at it. I kept up practicing in reading and scored 770 out of 800 on the SAT verbal.
I pushed along math, taking AP call in HS, but my grades were not very good (like not straight A’s, so ‘bad’ for me. I enjoyed and understood the concepts, but I was not good at the math fundamentals to get problems right. I didn’t enjoy and didn’t practice enough.
I went to West Point though my SAT math score was only a 620. I made it through all the math and engineering, and again, enjoyed the concepts but was not good at getting things right, whereas I excelled as a history major.
Post military, I’m in marketing now - I don’t have a fancy MBA because I know I’ll be ashamed of my GMAT math score. I feel so ashamed about my average math abilities compared to men I work with. It’s possibly my greatest shame.
If I had been encouraged to do more practice at my earliest years even though I thought I wasn’t good, my life would probably be different.
My daughter is 3, she is going to be a fast reader. My husband had to remind me that we need to emphasize her learning numbers and math along with a love of reading so that the cycle doesn’t continue.
7
I think you're more talented than you give yourself credit for, Melissa of West Point.
:)
5
I agree that learning is not necessarily supposed to be fun. I partially blame the Public Broadcasting System and Sesame Street in particular for infantilizing math.
4
When I was in elementary school, we started doing "new math" and I suddenly started having a tough time.
Then we went overseas, and I went to a girls' school that taught math the old way. For example, I learned that to divide fractions, you turned the second one upside down and multiplied. No pizzas cut in X numbers of sections, coloring in squares, etc.
Just turn it upside down and multiply. I did great at math and loved it, up through trigonometry.
Then we came back here. It was only because of what I had learned overseas that I survived US math teaching.
Kids need early, ongoing success--mastery. We've turned math into a hodge podge of theory, concepts, etc that many kids simply don't get till they're older. I was one of them.
We've made math so hard that many adults have no idea how to help a kid do grade school math. It doesn't have to be that way.
59
@Talbot, I couldn't agree more! I was an elementary school teacher for 34 years. I saw students' skills acquisition drop when we began emphasizing "problem-solving" before students had mastered the basic facts. This "rigor" (eye-roll), an education buzzword right now, misses the point if students don't master addition, subtraction, multiplication, and division.
18
Actually there is a statistically significant difference between boys and girls on standardized math exams across all ethnicity, and across several generations.
This effect has been shown consistently in the SAT and ACT with huge sample sizes:
http://www.aei.org/publication/2016-sat-test-results-confirm-pattern-tha...
http://www.aei.org/publication/gender-differences-on-the-act-test-boys-s...
The converse is also true, as the article accurately reports. Girls score higher on reading comprehension and writing.
I think it's odd that the author would gloss over (or rather deny) the former difference in math, but emphasize the difference in language abilities between genders.
I also think that sounding the alarm bells for girls and math is odd at a time when the boys in general are failing, being held back, or dropping out of high school at far higher rates than the girls. By the time a cohort graduates college, there are 4 college educated women for every 3 college educated men.
Maybe we should be focusing on improving the boys language skills or asking ourselves why we're failing our boys.
134
Sachmo, the statistically significant difference between boys and girls on standardized math exams occurs after girls have beat into them that math cannot be something they are good at.
Look at the test scores for boys and girls starting at a much younger age. They will be about equal.
Boys are not going to college at the same rate as girls because the job opportunities for boys are far superior.
1
The studies you’re referring to assess math skills after many years of education (and therefore potentially all the biases to which the author refers) - they do not assess inherent mathematical potential. So I don’t think they actually contradict the author’s point. I too would be interested in seeing the studies she’s referencing, though.
4
@Sachmo You actually believe that those tests are highly accurate in measuring such things? No cultural issues, and how wide is the variance?
3
Math is no different than any other subject - a difference lies in HOW it is taught and applied. I once had a roommate in college who told me "there is no reason why I should not get an A in statistics". It was never a question of will I but rather I WILL get an A in stats. I never forgot that kind of mindset.
When my brother took geometry in high school, he started out pretty badly. But then his teacher found out how good he was at playing pool. His teacher showed many examples and comparisons of the different angles in geometry and what my brother saw on the pool table. Suddenly, he had something concrete which he loved and enjoyed as well as could relate his studies to.
I had problems with fractions when I was little. My mother helped me solve that problem in the kitchen. So many of her recipes included fractions like 1/8th tsp., 1/3 cup, etc. Fractions never were an issue from that moment on.
I think making math fun coupled with concrete examples of something the daughter or son is involved in (which they find fun and exciting) is a key to learning and remembering that subject. At least it worked for my brother and myself.
25
I am about to begin my 27th year of teaching high school math, and I am very glad to hear someone say that "All learning isn't-and shouldn't be-fun". It's actually refreshing. I should say that I totally believe that all learners create their own understanding, that the over-dependence on rote algorithms is often harmful, and that the phrase "drill and kill" contains some truth. But if a high schooler does not know their single-digit times table by heart, or cannot combine positive and negative integers, or any of several other indications of numeric fluency, they are in a deep hole from which very few teenagers will struggle enough to pull themselves out.
I must say, however, that my experience at the high school level does not bear out the claims of this author with regard to gender. I do not see girls shrinking from challenge any more than boys do, and in fact girls' generally better classroom discipline often gives them an advantage. Moreover, I do not think it is helpful or even accurate to make distinctions between language arts and mathematics. The right/left brain dichotomy is overrated. The ability to read accurately and easily, the ability to listen, the ability to form a good question, the ability to cite a reason to back up a claim, the ability to write clearly, all of which could be considered language arts skills, are hugely important to success in learning mathematics. So is lots and lots of practice, and it's not always fun.
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@KirkTaylor Your observations ring true for this HS math teacher. Learning any subject is not all about fun; practice to build fluency is essential. Suffering usually accompanies learning and practicing (to master) something difficult. Being coached to work at learning by a competent teacher in school is a gift sometimes lost on teenagers, many of whom are stressed by overly demanding course and extracurricular loads along with a focus on grades. Hence the unusually high stress levels teachers see in students nowadays -- at least in schools where students are striving to be accepted to elite or competitive colleges.
I agree with a lot of this article, but I'd add a couple of points.
1. First, it's not just STEM-bound students who should be encouraged to be good at math. As an English teacher, I know that the logic and reasoning that math helps you develop are important when you're sorting out an argument or working with music theory.
2. Second, I believe the "practice, practice, practice" mantra is core to Asian success in math, and it's why Asian girls are often just as good at math as Asian boys (in Asian countries, at least).
3. I think mental-math skills are woefully neglected in the US, and calculators are woefully overused. If you need to pull out a phone and punch in numbers to figure out that 13 13s are 169, you are never going to enjoy numbers. Kids' brains are so spongelike. Teach them the tables through 20 before they're 10 and they'll have them for life. Multiplication tables are foundational, but only the starting point of mental math agility.
4. Parents play a key role in fostering math anxiety. Parents who are bad at math themselves are likely to ask questions like "why do they need algebra anyway? I don't use any algebra I learned in school." Parents who don't know why algebra is important should just stop talking. They should send their struggling kids to Kumon, and take the time to relax with a good book.
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@MP
You are making many relevant points, including the fact that Asian girls are (in essence or as a matter of actual fact) equally as good (ven in advanced) math as Asian boys.
The same also more or less applies to many Europeans countries.
Thus the reason behind the fact that U.S. students (of both genders) consistently rank at the very bottom of developing countries in international comparisons (inc. mentioned PISA) is cultural.
Unlike Germany, Europe in general, including Russia, and China, Japan etc. we worship lawyers, bankers, marketers, etc., engineers are pathetic "nerds" who never get a girl, are not cool and certainly dont get to CEO corner office.
This sadly applies even to Silicon Valley as soon as company stops being a start-up.
Thus a culture which doesn't care much about math and hard science doesn't have people and insight to develop effective math and science teaching methods (K-12). What we actually do with say Asian quotas as top colleges, drastically downgrade importance of SAT and SAT math scores in admission as smart plus hard working Asians dominate.
& MP:
And to Point 1: I am impressed and dismayed by how often innumeracy is accompanied by near illiteracy. Innumerate people may not have the clarity to be truly articulate, despite the apologia that “I just wasn’t good at math.” Literacy in its broadest sense and numeracy both require rigor and effort, and each can reinforce the other, when present.
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@MP: I am sure algebra is important -- to someone, somewhere.
But in my real, every day life since high school....I have literally never encountered it, anywhere...ever.
I do know that LEARNING ALGEBRA....was not worth being slapped, smacked, called stupid and lazy, grounded, humiliated, lectured or made fun of by teachers and my parents.
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Where to start . .
As a long time school head and author, I find there is some to like and lots to question in Ms. Oakley's rather traditional opinion.
Yes, repetition is helpful in strengthening the dendrites that constitute learning. But repetition and memorization also have the counterintuitive effective of become a "default" mechanism that can crimp the apprehension of novel solutions to problems or the ability to solve a problem never seen before. Here, a constructivist understanding is far more important.
Good teaching blends both approaches. Critics of progressive or constructivist methodology always draw a silly caricature of what it really means, because they don't know what it really means.
Key to it all, in direct opposition to Ms. Oakley's somewhat pessimistic view, is making math fun. Even repetition (best done at varying intervals) can be fun. Amazing math can be constructed around things kids love and love to do. I've seen 3rd and 4th graders begin to understand algebra through these more creative means. And they also learn their multiplication tables. Girls in my school who were taught this way took multivariable calculus by 11th grade and many went on to major in science, math or engineering in college.
Also, using PISA scores to prove anything is a useless exercise. But that's a whole different comment (or column, if the Times would only ask!)
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@Barking Doggerel Thank you. Yes, there is this unhealthy obsession to mimicking how Asian countries drum math into their children's minds, and how they do better on some standardized tests. I believe it ends up crushing truly innovative thinking. Look at where the Fields medals come from: Majority from the USA, where, at least for now, students have more freedom and less regimentation.
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Whether you were ever a school head is unknown, but what is clear is that you didn't teach math and that you didn't carefully read the article.
Math students who don't practice and don't memorize may enjoy their constructivist projects, and some will indeed master and love the material because they had the chance to construct their own understanding, but the majority will never develop facility with math.
A much better approach is significant practice leavened with open ended math problems and occasional projects. Save the constructivist learning for humanities, where it fits best.
Children pick up parental cues as well. If the parent actually likes math and sees it as interesting and fun, the child may, too. However if the parent fears math or sees it as boring or difficult, the child will be less likely to be interested in it. My dad enjoyed solving math problems and puzzles. I learned from him that math can be fun. Seeing that the same problem can be solved several ways was intriguing. Thanks, Dad. And I hope as a mom I have shone my enthusiasm to my sons.
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@Lynn Rivera: my dad was a brilliant engineer, with dozens of patents. He worked for a Fortune 500 defense contractor and he did math all day long and carried a slide rule in a pocket protector!
He loved math and science, and they were like breathing to him -- fun, easy and fascinating.
My mom was above average in math, and got As in it in school.
I was incapable of doing even simple "computational" math -- I could add a little, but something like long division may as well have been Ancient Sanskrit.
WHY is it so hard to understand we are all INDIVIDUALS? and not the same? we have our own strengths and weaknesses! There are lots of things I am very good at, but math is not one of those things. I'd love to be good at it -- it would have made my life SOOO much easier. But I wasn't, and I can't. Laziness has literally NOTHING to do with it!
I was OK in math, in an all boys high school, where there was a lot of competition. But I never felt that I excelled in math.
If I had to do it all over again, I would focus on the aesthetics of math and science and the power of proofs.
I also think that the greatest learning motivator is helping others to understand and appreciate key ideas. I call it the "Golden Rule for Schools.", learn in order to teach other students, something.
It is often very hard to explain and motivate a concept, but it can also be very motivating to unselfishly, help others to learn...
www.SavingSchools.org
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I forgot to add that both my nieces have gotten straight A's in math and science, kindergarten though 12th grade and throughout their college careers (both will graduate in the next two years). Both are going into STEM, one wants to be an emergency room doctor and the other wants to be an orthodontist.
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In high school, I had a teacher who was a brilliant mathematician. The problem was--she wasn't a very good teacher. She could not understand that her students didn't "get it." She fell into the trap that snares most teachers. She understood her subject matter so well that it was automatic to her, as simple as breathing and requiring about as much thought. To her students (myself included), pre-calc was like falling off a cliff.
When my classmates and I told her that we didn't understand a particular skill or idea, she responded with "Why don't you understand?" She had missed the whole point. "We don't understand" WAS the problem. "Why" was immaterial. We told her we had trouble grasping a concept. She took it as a challenge to her authority and got defensive about it. Any true communication between students and teacher was lost. My classmates and I survived the course...barely.
If you think I'm exaggerating, then I ask you to recall how you taught your children to drive a car. Not so easy, was it? There are so many things we do AUTOMATICALLY when driving, from buckling a seat-belt to merging onto a highway to making a left turn at an intersection. When teaching someone to drive, we have to slow down and THINK about every action we take behind the wheel. And THEN we see it from the student's point-of-view.
I never got over my math phobia, and I regret it. Today, I teach high school English, and I constantly remind myself, "They don't get it. SHOW them."
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@Jack, I hear you. But I am a professor myself, and I am going to defend "your teacher" (by which I mean a lot of teachers who exhibit this behavior, not literally your teacher who I clearly do not know) a little here.
My point is, your teacher was very likely not asking "why" you did not understand in an antagonistic way but in the sense of figuring out which part of the background was missing.
It is different from driving where a teacher teaches you from scratch. Your teacher did not have that luxury, in all probability s/he was trying to figure out what was missing in your background. The math s/he taught you builds on foundations built by your elementary/middle school teachers. It is likely s/he asked this why at points that should have been axiomatic by then---when students don't get it, it means that they were missing something in the background.
Just showing doesn't help since students then memorize then new thing, the prior gaps are just there, and will hit you harder in the future. It is likely that this was the one teacher who did not want to take a shortcut at your expense.
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Looking at the US BLS statistics on employment for math graduates, it's pretty grim. The "job market" for math majors is pretty small. The career path is mostly teaching in graduate school, or finding another STEM field that needs those skills. It can leave math graduates disillusioned.
The UC Berkeley graduate math department is filled with people like you describe. Brilliant, and not interested in people below their level of skill. On the other hand the motto of most of my professors there was. "I cannot teach you math".
I learned, painfully, that this was true. Math education, in a way, is unlearning the way you think, taught to you by everyone around you. Math is not itself hard, it's that our society prioritizes "certainty" and conformity over the capability to engage in real thought.
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At some level math education is a very 1-1 experience. Similar to having a personal music teacher. At that level of attention and focus, learning becomes accelerated.
That's not what public schools can support, and math is as much about "unlearning" ideas that students have, before they can learn the math concepts being taught. At least in music education you can spot the bad note when it happens
I remember getting a D in algebra as a sophomore in high school and my dad was completely enraged with me. He told me I had to sit down for an hour every day at the kitchen table when I got home from school, study my algebra book and redo all my algebra homework a couple of times until it was perfect. Well, I ended up with the highest grade in the class the next quarter (an A+) and my algebra teacher flipped out. My dad said I didn't have to sit at the kitchen table anymore during the third and final quarter of the year long class, and I ended up with a C.
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I was a math major, my mom was a math major, and any future kids I have, regardless of their gender, will be mathematically literate through extra math practice.
I'm currently a Biostatistics PhD student in a Statistics department. I teach introductory statistics courses to undergraduates, and the lack of basic mathematics proficiency in some of my students has made me wonder: How did you make it to college without being able to do basic math? How did your parents allow this to happen? (Just to be clear, the classes I teach are not calculus based.)
Yes, I agree with the author that proficiency in math is the foundation for all of the STEM fields. I was never particularly talented at math, and I was never going to become a mathematician because graduate level math is beyond me, but I knew that if I did a math major in undergrad, I would have so many career opportunities and graduate studies options.
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The tricky part is that most parents don't have jobs that involve much math. I have a lot of confidence in matters of language, but almost none in math. Sadly, I may have transmitted that discomfort to my kids. They have superb vocabularies, but middling math skills.
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@Cousy, a really good program is that of Kumon or, more recently, the online Smartick. Even if you aren't a math maven yourself, Kumon has a very nice system of gradual mastery that helps you walk your child through plenty of practice with math basics. I had our daughters in Kumon when they were growing up, and it was really helpful in changing them from "I can't do math," to becoming more confident in their skills. Our older daughter, for example--who never found math to be obvious or necessarily easy--is now completing her medical school residency at Stanford. What I love about Kumon or Smartick is that you don't have to be a math whiz yourself to have your child get a lot of value from the program.
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Hi Cousy, the author of this Op-Ed also started out as someone with a proficiency in languages. She worked as a translator for many years. See http://nautil.us/issue/40/learning/how-i-rewired-my-brain-to-become-flue...
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My daughter got 800 on her math SAT and 5 on her AP Calculus.
I did NOT make her practice, nor did her schools. Over practice is a turnoff.
I started with numbered blocks of different sizes. Both I and her schools made math fun. We did not use the "new math" methods of specifying every step. We taught THEORY and let her figure out the steps.
Try it this way.
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Did you know one of the best predictors of a child's academic success is how much education her or his parents have? For any kid from a family of humble means and backgrounds, practice and more practice, and a culture of same in the household, may be the best way out of poverty.
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@dr. c.c. Congrats but if it was oh that simple. Your daughter is lucky to have an engaged parent and, among other identifiable benefits, a natural propensity for numbers, most aren't so fortunate. As with this article, any research, suggestions, or additional tools are good for those not similarly situated.
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@dr. c.c.
I learned exactly the same way and always found math to be easy and fun.
I practiced only enough to confirm I understood how to implement the concepts.
In college, math started to get slippery and I had to spend more time thinking about it conceptually or else, my understanding would slip away.
Mastery was about more thinking and never about more practice.
The way to improve Americans' math skills is to treat--and pay--teachers like professionals. Neither "understanding-based" nor "rote" math instruction (there is really a need for both!) works when the teacher doesn't understand what's supposed to be taught. We know what's needed; what's missing is the political courage to adequately fund our schools. (p.s. I'm a math professor, an active researcher, and the mother of two school-age children.)
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@Tamar R.
We also need to look at teacher training.
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@Tamar R."We know what's needed; what's missing is the political courage to adequately fund our schools. "
Sorry but that's one of those liberal urban myths. The U.S. actually funds its schools to a very high degree. Some of the best funded, like Detroit and Washington DC, have the lowest test scores.
@ Tamar R:
Bingo! The most germane post in this threat. Far too many teachers attempting to teach math, or even just manipulations, do not know the subject well enough to convey its substance, utility, or beauty. Most of those who do are making much more money elsewhere. That fact alone makes the rest of this well-intentioned discussion vain.
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Now let's read a comment from a mathematician writing about math. That would be me.
The author of this opinion seems to equate "math skills" with manipulation skills -- manipulation of numbers, rapidity of calculation, a thorough mastery of the mechanical skills we associate with doing mathematics when we don't know much about it beyond long division and other impenetrable and incomprehensible algorithms. Not very human, not very empathic, much not communication with other people going on, no feelings involved. The stereotypical view of men and boys.
The author also seems to attribute higher native "language skills" with girls and women. The art of communication, empathy, understanding, sensitivity, the higher human values.
Mathematics requires both. The separation posed above is artificial. Mathematics is a very austere and rigorous art form, for those two reasons leading to profound vision, clarity, and understanding when practiced as it it ought to be. To detect patterns in nature, and in numbers, requires sensitivity. To express them in the form of a conjecture requires language skills. To dig them out of raw material, and to prove the results rigorously, requires manipulation skills.
No, we don't want to train research mathematicians in grade school. Moreover, they tend to be self-made, not created or taught.
What we do want is a proper understanding of what mathematics is, and how even children can be taught to appreciate and develop these abilities.
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@Danny Thanks, Danny. Read my comment too. We have a similar view.
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@Danny
I would love suggestions on resources to teach this for parents. My kid is almost 7, and I would love to practice math skills, just don't know how to start.
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Thanks @Danny
and as another math teacher, I find many of Barbara's assumptions are build on thin foundations.
Certainly the teaching of math can be improved, beginning with a definition of what it is…. But I resent making Math a part of the 'gender wars'.
The best teachers see gender free, race free, identify free classroom. Teachers need to, as best they can, get to know and address the individuals strengths and weaknesses.
Can we please stop differentiating my bias....
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Thank you so much for the insight on _why_ girls may lean away from math. Both of my daughters (4 and 6) have been very early readers, and I am now realizing that the stream of affirmation they get for that (from teachers, us, etc) could be accidentally discouraging them from a similar interest in math. Definitely something interesting to think about.
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@NS
Not only as a parent of daughters (besides parent of boys) all competitive college students or graduates, some of then nationwide in top 0.1% on PSAT scores, I would suggest that you resist (statistically significant) temptation and tendency in our society, communities, families, "culture' and K-12 schools to feed in girls fantasies that they will be yet another in unbelievably numerous armies of "creative writers", and those who hope or occasionally "get published" or have a column in any newspaper or media.
Words are indeed cheap, especially in this internet era.
The greatest thing you can do for your child (at a very young age) is tell them that: '' No, you did not do very good. ''
I know this is against the grain against positive reinforcement at all costs and that every child should be congratulated just for participating, but start them off with honesty and then they will accept that positive reinforcement/compliment when it is genuinely applicable. (I have experienced this first hand when all of my children's teachers were aghast that I would actually tell the truth)
As far as math, there are no calculators in our house. If they cannot do the basics inclusive of long division, multiplication of any large numbers, square roots and the like, then they are simply not trying. We started at a very young age doing verbal quizzing and I always tried to make it fun. - another key to learning.
Better to solve the problems when they are young and they are small, rather when they are older and they can be too large.
Good luck.
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@FunkyIrishman How about just being honest and congratulating people when it's deserved and criticizing when appropriate? No special strategy required.
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@FunkyIrishman I agree with your point but I might tell my kids "I know you can do better, and I expect you to." My son, for example, just wails that he is not good at math, so telling him he did not do well would be a dead end.
@FunkyIrishman - Since I'd like my children to learn grammar as well as math, I would say, "No, you did not do very well." Actually, if they didn't do well I would find out why. If there was something they didn't understand I would go over it with them. If it was simply that they didn't study enough I would tell them they have to study more.
The things that we adults pursue with vigor are rarely the most "fun." I'm talking about home maintenance, reading the news, writing to a sick relative, chauffeuring our children, or moderating our vices. They are interesting, important, satisfying, and fulfilling. In math, the thrill of accomplishment *is* enjoyable, and it is long-lasting.
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@Eric
Thank you so much for this comment!
This emphasis on "fun" in school has been a disaster for learning.
Much which is worthy and interesting is not "fun."
From the step-father of an 11-year old daughter who is good at math and enjoys it (at least in school):
My daughter reads constantly, and loves reading. I try to get her to do as much math as possible, but it is a little bit of an uphill fight. I don't think she is challenged enough by the math curriculum in NYC public schools, which, in 5th grade, was mainly aimed at the state-wide test.
btw, the state-wide tests are a huge waste of energy, both for the teachers and the students. this "testing regimen" is reason enough to vote for Cynthia Nixon for Governor. The Cuomo administration's emphasis on these tests is simply political grandstanding and borders on abuse of the students and teachers.
I have given my daughter Ken-Ken puzzles, and at various times she does them and enjoys them, but she will go periods of time with no interest. She can't yet do the very hard ones, but she can do medium-hard puzzles, and they require a good deal of math-style logic.
i would appreciate any further suggestions.
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I have two daughters still in school, one at least and probably both excellent in math and English. There is no magic key. Just keep buying them books. Do math homework WITH them and have fun with it. The older girl is in Stuyvesant and loving it, at the top of her class. No magic. Just be genuinely excited about learning. I don't think there is anything more you can do but I suspect it is more than enough. At 73 I am getting ready to learn calculus at last because I blew it off for other pleasures in college (the 60s of course). If you love it so will they.
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@bruce bernstein
Would she mind watching cartoons? There's a show on PBS called CyberChase (on the website if not on tv anymore) which, while teaching younger kids concepts, puts that concept into a real life situation, making math relevant. I think that's half the problem: it appears useless but if we see how it is applied all the time in our daily lives, it starts being interesting. I wish I could think of a source that's for pre-teens. We tend to stop after baking, and shopping when trying to apply it. Also, if she likes languages and reading, noting math is another type of language could make it more interesting to her. Good luck!
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@bruce bernstein I suggest you pick up a text book by Mary P. Dolciani titled PreAlgebra: An Accelerated Course and work through it with her, at her pace.
Then hop over to artofproblemsolving.com and enjoy yourselves.
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Fascinating. I avoided math my whole life, because I believed I was bad at it, until I was forced to master it for the purposes of the LSAT exam. How did I do that? Practice, practice, practice, for days on end, over a period of weeks. By the time I took the exam, I was better at the "math" portion than the other parts. A good lesson for my daughters.
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@CN I took the LSAT exam and don't remember any math at all. Mostly reading skills and logic, but not math.
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The “math” portion of the LSAT exam? Basic elementary skills only needed.
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@CN
I certainly do not want to pour a rain on your parade (i.e. how you at last mastered "math" as part of your preparation for LSAT) but as I recall (when taking LSAT) and checking even now ... there are no math problems or math section in LSAT.
What is there are advanced logical thinking requiring questions, the Logical Games.
Actual math, even in basic math, algebra, calculus classes at a high school teaches mastery of many other skills and concepts besides that.
Logical Games @ LSAT isn’t math, but it requires a system of thinking that is at times rather linear and hierarchical in nature, and students with a math background tend to to well on this section.
I've been a math and science educator in a variety of settings, and I see a bothersome commonality in them all: females tend to be more likely to accept that their struggles in math are insurmountable and, worse, worthy of capitulation. I worry that a generational trend exists; mothers will unhelpfully tell their daughters "I wasn't good at math, either!" as if a lethal academic gene was passed, unaltered.
There exist few careers now that don't demand skills like database manipulation, statistical analysis, and basic financial literacy, so I hope more young women are told that not only can they improve at math, they'd better.
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I encounter way too much "I'm terrible at math" sentiment among adult women and believe it is a negative influence on young women and girls. As the mother of two daughters we used to do gentle math problems we found in everyday situations and I also told them how much I liked math. Both girls did well in math and have no fear of it. But I do find it interesting that being better in reading and communication can make it seem like math is 'harder'. We need to encourage appreciating a challenge!
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@Brian I think parents would do well to hold high expectations for their children whether it is mathematical or verbal skills. Growing up Asian-American, I and my same-ethnic-background peers were never told, as girls, we could not do math: it was understood if you didn't understand it, you just studied harder, same as the boys. Being female was no excuse.
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@Brian
With all due respect, being intimately familiar with educational systems in Europe and here and even in Far East, I think that in general, American student - of BOTH genders - permanently very low ranking in PISA and other international comparisons is a cultural phenomena.
Our culture values lawyers, bankers, marketers, etc. etc., not engineers or scientists (in "hard" sciences).
TV shows, Hollywood, popular "culture" has math wix and engineering/science oriented kids as a nerd, symbol of pathetic lack of social skills.
Also, with exception of Silicon Valley startups, American corporate culture overwhelmingly prefers CEOs and "top dogs" with background in business (MBAs), sales, marketing, not engineering.
In successful, export oriented economies (Germany, Japan, Finland, etc. now also China), engineers are much, much often in CEO office.
Typical American CEO know how to slash workforce, shut down plant, move it to Mexico, etc.
So, again, it is mostly cultural.
I agree with the sentiment, and find the contrast with language arts skills insightful, but it’s not the inherent duty of parents to assign additional math practice to their children.
Early in life, parents are more likely to read with their daughters and encourage them to read. It’s an activity that keeps the child well behaved and quiet - things we like in our daughters especially.
Parents, read to your children, both male and female.
In the early years of formal schooling, preschool and elementary school teachers are more likely to be enthusiastic about language arts. Who doesn’t want to help a child learn to read and write? Is there the same thrill in teaching them basic numbers and arithmetic?
Teachers, take the time to teach children math, employing the same focus, enthusiasm, and practice applied to reading.
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@MH
Given that children are not , by and large, are not developing the level of understanding needed to succeed in the world of the future whose responsiblity is it to make sure you children compete effectively in the modern world. Do parents have any responsiblity for the education of their children?
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@MH
> Is there the same thrill in teaching them basic numbers and arithmetic?
Absolutely!
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Practicing math can be good family fun. We challenged our children with real world word math problems to pass the time in the car. If a truck had 3 axles and there are two tires on each axle on each side....how many tires does the truck have? A splendid time was had by all.
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