Trying to Solve a Bigger Math Problem

I heard about another study that suggested removing all courses necessary for a college degree increases the chances of graduating to 100% certainty.

Number sense is the foundation for all higher-level mathematics.

When students fail algebra it is often because they don’t have number sense.

If this test is any indication of the mathematics in the remedial classes, no wonder students fail, drop out, hate mathematics.

When students work on rich mathematics problems, they develop number sense and they also learn and can remember math facts. When students focus on memorizing times tables they often memorize facts without number sense, which means they are very limited in what they can do and are prone to making errors. Math facts are a very small part of mathematics.

In order to learn to be a good English student, to read and understand novels, or poetry, students need to have learned the meanings of many words. But no English student would say or think that learning about English is about the fast memorization and fast recall of words.

In Engage NY the site links the memorization of number facts to students’ understanding of more complex functions, which is not supported by plenty of research evidence. The highest achievers in mathematics focus on ‘big ideas’ in mathematics and the relationships and connections between those ‘big ideas.’

Basic arithmetic needs to be taught by rote, period. If people graduated knowing how to do addition, subtraction, multiplication & long division using a pencil & paper, they would be prepared to cope with a lot of the math that comes up in daily life.

Learning the "abstract" way of looking at numbers is a luxury for some people. If someone can successfully answer - with pen & paper - "what's 377 minus 298" or "what's 1.3 times 78", they have a useful skill.

But rote learning is shunned because it is hard, even though the way we now teach math makes it EVEN harder to understand than rote learning would be! Let children learn to do "grocery store" math and see where they go from there. Not everyone needs to be a math whiz, just as not everyone who can write a coherent sentence needs to be an author.

george w. bush referred to this as soft bigotry. dumb down the subjects and push the kids through. when it comes time to get a job and the interviewee can't do the math or science, they'll give the job to a foreigner who can do the math or science because his/her country didn't dumb down the subjects

I just did the practice test and while I don't think it's necessary for every student to master differential equations, I don't think that anybody who can't solve these very simple problems should receive a high school diploma, never mind a college degree. We aren't talking triple integrals here -- we're talking about simple percentages and factoring equations, skills that any first year algebra student should have mastered.

Sure, we can grant degrees to students who are underprepared, but all that will accomplish is to further reduce the value of a college degree. And all you're doing then is playing a mean trick on students who will find themselves with a lot of debt and no real employment prospects as employers are forced to move the credentials bar ever higher to get the qualified workers they need.

The math curriculum in U.S. elementary and middle schools has been dumbed-down. Then, by high school, it's too late to inculcate the patience -- and joy -- for abstract thinking in all but a select few 'math natural' students.
Example 1: 7th grade math textbook, chapter on percentages: first 10 pages are full of blah blah about % of pure gold in X-carat gold, about the % grade of a Grecian arch, about white/black/male/female (must have one of each) mathematicians' life stories and nothing about why 25 cents is 25% of a $ and that it's the same as 1/4 of a $, and why 150% of something is a logical and useful concept -- the blah blah being considered essential to a math education and the actual little calculations being considered irrelevant in the most advanced country in the world.
Example 2: A third-grader's math test consisting of 4 very wordy pointless problems (most of them asked, "list strategies for answering this problem" and one of the named strategies had to be "guess an answer"). One question was, "Describe to a first-grader how to do 3-digit subtraction, but don't do a 3-digit subtraction."

Human potential is being wasted as we insist on variations of "Children should not be made to do [fill vilified math process here -- solving equations seems be a favorite], they should be writing apps to do it." Why should everything they do in math and science be directly linked to jobs of the future? We don't expect the same of reading or literature or art or sport.

As expected, we have comments from all the geniuses who are extremely proud that they managed to acquire the ability to memorize and perform algorithms in conditioned response to a set of stimuli (a small set of memorized "problem" presentations). This makes them feel superior, and they think: "I'm doing Mathematics!" . "I'm thinking abstractly!"

They are proud of this, despite the fact that any primitive computer can do the same thing. They even say: "Look, kids in other countries learn this in sixth grade.", without recognizing how this undercuts their claim that it is a great accomplishment.

High school algebra is not mathematics. Mathematics is what some of the timid efforts of Common Core, which sends the genius parents into a rage because neither they nor their genius kids can handle actual abstract concepts, are about.

Kids who are actually smart in sixth grade should be writing apps to "solve" quadratic equations as a fun exercise, not having their creativity crushed by prepping for timed tests of rote mechanics.

But hey, carry on with trying to *keep* the curriculum dumbed down while claiming you care about US competitiveness. Your kids will be well qualified to operate the sewing machines when all the factory jobs return.

Students need to take more responsibility for ensuring they are at the required level on entering college. For those who have just graduated from high school, there's no excuse not to know basic Algebra. For mature students who are going back to education and long ago forgot their equations, it's not that hard to catch yourself back up. Take a free course online (like this one: https://alison.com/courses/Algebra) or get a tutor. Google is your friend.

Anyone that has the ability to teach algebra in middle/high school can make whole lot more money selling real estate or drilling oil wells or just about anything else. Teachers are grossly under paid.

I agree with some of the comments saying how it is unacceptable the high school students in America are learning algebra when in other countries, 6th or 7th graders are just beginning to learn it as well. In my opinion, this is why so many college students end up on remedial math classes in college, and then later drop out all together because they do not feel good enough, they think, "A 6th grader could do this and I'm already confused!" They don't have the motivation to continue at this point. In my opinion, this goes back to the entire education system in America being at fault. Perhaps if we upped out education game a little bit at a time, we could have our 7th graders learning algebra instead of high school graduates.

How many otherwise gifted and talented people have been penalized and held back from promising academic careers by low math grades and low math scores on the SATs? The math curriculum needs to be completely overhauled and brought into the 21st century. There must be a track for the mathematically gifted and an equally valued track for the mathematically challenged.

As a teacher of remedial community college math and undergraduate engineering math, I was continually amazed that my students seemed incapable of showing their work and evaluating their own logic process used to arrive at their answer. If you can’t demonstrate the logic of your work, how can you repeat or build upon the process to get the next answer?

At least part of the problem is that high school teachers do not evaluate one or more significant, shown-work homework assignments or more each week for each student, that is, at least one significant, multi problem homework student per student, per week. This is a significant investment in time and is especially critical for remedial students.

As a teacher both of remedial math and undergraduate engineering math, I was continually amazed that my students were incapable of showing their work and evaluating their own thinking. If you can't demonstrate the logic of your work, how can you repeat the process?
At least part of the problem is that high school teachers do not evaluate 150+ significant shown-work homework assignments or more per week, that is, at least one assignment of a multiple problem homework set per student per week. If you are working with remedial students in particular, this exercise in evaluating one's students thinking (self-critical thinking) is VITAL.

We are moving from High School diploma as an entitlement to the College Degree as an entitlement. We have seen time and again in this country that someone having a credential does not mean they are qualified because there is always pressure that they put in the time and/or spent the money so they should have something to show for this. By dumbing down education we hurt everyone. Algebra is typically taught in most countries to 6th or 7th graders, it is just unacceptable somebody graduated high school without learning it.

The bigger question is why we care.
We'd be better off teaching financial math, how to balance a checkbook, understand debt and build a budget. They are real life issues that algebra isn't needed for, but our high schools are ignoring. My college age teens lament that , while competent in calculus, they've been taught no real world skills.
I'm an engineer and I've forgotten more math than you need in the real world.
I fall back rarely, and only in the context of my work.

We're looking in the wrong place and asking the wrong questions.
Math is only useful as math for mathematicians. Real world students need context. Math is tedious, boring and hard work, you need to be interested in it to succeed.

When was the last time a nurse, doctor, or even engineer had to factor a quadratic. Its a complete waste of time in the real world. Let's rethink what we need to know, financial literacy for example.

Success in math means having a a strong foundation. The current standardize testings allow students to move on to the next level of mathematics simply because they hit the required score not because they fully understand the materials being taught and capable of applying them in real life situations. For example, many lessons and placement testing books focus on developing students' testing strategies, neglecting the fact that materials are not being transfer to the students, or students simply memorize enough to pass and forget. Students who developed testing skills move on in their math career with uncertainty which limit them in their more advanced education. The current system of teaching based on standardize testing is proven to be lacking as other nations surpass us and the number of students who struggle as they enter college. This alone should be enough for us to question and revisit the system.

Algebra is mindful arithmetic. Critical thinking in arithmetic, if you like. And because it is tied to the practical arithmetic that everyone uses in everyday life, it is the easiest form of abstract reasoning to master.

Mindfulness and critical thinking are not needed for a person to lead a successful life as a consumer, especially those who can flaunt some mild rebelliousness in dress or food preference as evidence of "creativity". Yet there are few successful artists that work at the level of dropping paint on paper, any more than successful engineers work at the level of the rivet gun or method call. At some point in their development they had to reason about their practice, and test the chains of their reasoning through introspection and debate. It is the purpose of algebra and geometry to introduce the child to abstraction at the earliest possible point. And the purpose of proofs to demonstrate their mastery to themselves and others.

It might be reasonable to forego the teaching of algebra to students that might, just might, acquire mindfulness and critical thinking skills in other ways. We could also promise to give every child a pony.

As someone who has taught many undergraduates, it seems like more need to take remedial or basic algebra classes (in addition to English composition classes). An unbelievable number of college students are woefully prepared to do simple math or write a simple paper. As someone who has a graduate degree in Statistics, I am baffled at the assertion that you don't need to understand basic math and algebra in order to do statistics. Yes, intro to statistics probably offers vastly different material, enough that you do not need to have a good grasp of algebra, to pass it but once you get past that first course, you need to understand how basic math functions and how to do algebra. If you can't solve a quadratic equation, how are you going to be able to solve conditional probabilities?

Recently a study evaluated likelyhood of graduation among nursing students by early curriculum coursework. Far and away the greatest predictor of graduation was performance in basic math - not biology, not anatomy, not pharmacology - but math.

There is value in challenging students with a difficult task that lies outside of their comfort zone - even if they may never used the skill. Math is just that, abstraction that is challenging for many students.

Can you think of a job/career where one is faced with a difficult task that may not be a strength - thats right, all of them.

There is this urge to coddle students in this country. This article is timely given the recent expose on apprenticeship type education models recently published by the NYT. If students can't learn the basic abstraction of math (be it algebra, calculus etc.) maybe higher education is not in the student's best interest - apprenticeships may be an option. The workforce would increase, people would stop wasting money on fruitless "higher education", and the malignant exploitative college industry would be held in check.

I think when it comes to Math you have to stay on top of student performance. Math builds on itself. Once a student falls behind, math becomes difficult. Maybe our biggest problem is not aggressively monitoring student progress in High School.

Clearly identifying the problem is the first and most difficult step in solving it. The math literacy problem starts in kindergarten and that's where the solution has to start. Eliminate fuzzy math curricula and make training elementary teachers in math and how to teach it a high priority. By the time US students get to high school most of them are so deficient in comprehensive, foundational math skills it is too late.

So-called College Algebra equals High School Math.

As our over-performing Asian students have shown us - maths are simply a matter of buckling down and learning it.
This boils down precisely to the ethos of the average non-asian sets of parents not inculcating their kids in the importance of actually studying and learning a simple skill like basic algebra, trig and geometry.
There is no silver bullet by the time a student has reached post-secondary studies - if they have been poorly served by their parents - and don't simply blame the teachers - they will fail disproportionately.

Barbie summed it up nicely - math is hard. Of course , it would have been better if Ken had said it.

It is hard. Because it requires an entirely different neurology than any of the other requisites to higher learning. The median IQ in this country is somewhere around 100. That is not M.I.T level intellect.

Never mind college. How many students every year are denied a HIGH SCHOOL diploma because they can't pass algebra? Eighteen
years old and finished before they even reach the starting line.

But the righteous STEMers will have their way. Math and science for everyone - and if you're not up to it - good luck.

Not everyone can benefit from a college education. Those who are not prepared to benefit from an authentic education spend more time drinking than thinking. Their parents spend a lot of time financing their experiments with binge drinking. Deal with it.

I've told my kids that they should learn as much math as possible as it will often be the limiting subject regarding the fields that they may be interested in; the less math that they know the fewer fields they will be qualified for. I've noticed that math is also somewhat of a perishable skill. I recall asking a sizable group of design engineers for assistance in setting up an equation for a diffusion problem, and ended up doing it on my own as there were no volunteers. Looking back on my career I've actually used more math in my hobbies than at work.

I remember the 'new math' that we were introduced to in grade school. The program failed as teachers struggled with it, most parents couldn't help with homework, it was too much of an abstraction, and it displaced more practical math skills. Unfortunately that seems to describe the teaching of math in general, and ready solutions to the problem have been elusive. The UK is embracing the 'mastery approach' to math, a SE Asian style, in half of grade schools in the country. Other countries are taking notice as the Asian style of teaching appears to be the basis of such countries typically placing at the top of international comparisons on math skills.

A criticism is that good standardized test scores don’t always seem to produce the desired environment of creativity and innovation. Perhaps a mix of the German multi-tier approach and Asian style is warranted to serve the needs of our students.

While adjusting remedial classes may boost student success, dumbing down our curricula (eliminating algebra) to boost high school or college graduation rates is not the answer. Algebra, like reading and writing, remains a basic skill that any graduate should master. Even though many may not realize it, most people use algebra in their every day life. In the long run, we are doing a disservice to our students and nation.
If we would like jobs to return to America that are well paid, we must insist that students have these basic skills. Manufacturing jobs in the future will require math (with algebra as a bare minimum) and reading skills.

Perhaps the real question here is whether or not the analytical thinking skills developed with algebra are valuable. Public education across the nation says it is focusing on teaching those skills, but ignoring algebra seems a strange way to do that.

In fact, in Kentucky an education regulation actually requires competency in math through Algebra II to graduate from high school. So, it is clear the state's education leaders value this math subject. However, there also is clear evidence this legally proclaimed requirement gets only a wink and a nod from school-level educators (http://www.bipps.org/kentuckys-high-school-diploma-quality-control-probl....

Are co-requisite courses an answer? The math community in Kentucky's public universities doesn't seem to think so. There was more or less a revolt when such courses were pushed a year or so ago (http://www.bipps.org/attempt-to-dumb-down-kentucky-college-math-courses-....

Learning algebra does require an ability to focus time and attention. But, shouldn’t those characteristics be essential to real success in any higher education program?

What I can say based on a 40 year career as a mathematician and computer scientist is that no one can teach you math. YOU have to learn it. It takes effort, and a tolerance for failure, and the will to keep at it until you succeed.

Most people are stuck at the "I just don't care stage". No amount of remedial instruction will result in learning algebra. That's why the students taking the college level math courses succeed and the remedial class students fail (and drop out). Only one group has made the decision to learn, the others are still sitting there "waiting" to be taught.

In K-12 education, math should be taught only by specialists. You need real mathematical "insight" to deliver these courses, and the general education model of having teachers that don't fully understand math teach it to students is going to fail. True, STEM qualified teachers are discouraged from teaching by poor pay, but one math teacher can instruct 6 classes.

Oh, and never force kids up to the board to solve an equation. Let them volunteer; even if it's one smart kid time after time. In fact let the best kids teach a class. The enthusiasm is contagious, and the class may even have fun.

Unless an incoming student professes a strong belief that they wish
to study Maths/Sciences/Engineering it is highly doubtful they need
a full course in College Algebra.

When was the last time someone asked you - outside of work to factor
a 4th degree polynomial, to rationalise the denominator, to find the
intersection, if it exists, of three lines ?

Teach them some basic Algebra, Statistics, Business Math and Geometry.
If they wish to go on to learn more Mathematics - there are no end to
courses they can take.

The Asians are eclipsing us economically because they have been eclipsing us educationally. Too many Americans can't solve half the problems on the little quiz that accompanies this article. I'll bet the average Chinese student would whiz through them. While we dumb down our standards and sneer at the well-educated "elites," other countries are insisting that their children excel. Carl Sagan once observed that Asian students aim for a perfect score while the Americans aim for a passing score. The consequences of this attitude are being felt in our economic performance,and our trajectory is downward.

Want to make America great again? Educate our children to a higher standard.

I think basic algebra is something everyone needs to understand. It delivers practical, real world value, no matter your walk of life. Advanced algebra and other advanced mathematics? Not so much.

I have a BS/MS in Computer Science. I took many years of mathematics, in high school and college. Thirty years later, I have never used any of that advanced math. It was a total waste of time. There are disciplines and specializations that require calculus, fourier transforms, matrix algebra, etc. but most students don't go there. You think it is "dumbing down". I think it is making better use of student's time.

It would help if we leaned more towards teaching practical applications of mathematics instead of abstract math. Don't just wave your hands vaguely over what this might be used for, show me. In class.

What is this article suggesting; that most students don't really need remedial work? That algebra shouldn't be required of college graduates? It's true that the problems many students have mastering algebra will go away if the requirement is eliminated, but is that a good thing?

Most people simply lack intellectual ability and abstract reasoning skills. They cannot understand algebra, and they cannot do college-level work, at least not college-level work as it was understood before it became educational doctrine that "every child should go to college."

A sensible and efficient society provides most people with vocational training and on-the-job internships and does not attempt to provide them education they cannot master and will not enjoy. Most students receiving remediation do not belong in a scientific or liberal-arts education because they simply lack the reasoning ability.

When I was teaching, I often had these kinds of students ask me why they "needed to learn algebra."

Much to the dismay of various administrators and colleagues, I told them the truth-- it was a way to weed people out who were too creative and lacked self-discipline, a way to retain jobs for "math teachers", and a way to avoid teaching quantitative reasoning skills (even in K12) that would cause them to question advertising and propaganda.

I learned algebra the old fashioned way, I was on the math team, and I've solved science and engineering problems with pencil and paper. Now, I have to really concentrate to follow discussions online because people write out their equations in some code or other that I have to decipher.

Luddites are everywhere-- in energy policy and education as well.

"Limited academic preparation???" NYT's style keeps getting curiousier and curiousuer.. Jump to another article in today's paper about how China is ahead of us in AI. An our response is to dumb down the education. Algebra was taught at sixth grade level in the former Soviet Union. In some US public high schools, multi-variable calculus and linear algebra are being introduced in the 11th and 12th grade, but this is, unfortunately, an exception. Unless a student makes it to a magnet school in the US, she is doomed. Why is this not addressed by the NYT?

Math is a subject that requires learning basic knowledge of numbers and shapes before taking up more advanced topics: arithmetic and simple geometry before geometry and algebra. Then trigonometry, analytic geometry, calculus. It makes no sense to learn them out of sequence.

It is much easier to learn some algebra--solving simple equations with one and two unknowns and the binomial theorem--before you take up statistics.

The logic used in algebra is fundamental, its a great thinking process, more fun now than it was six decades ago, part of a great intellectual tradition passed down for centuries. It helps me to figure out basic problems such as comparing prices of items in the supermarket among other things. The older I get, the more respect I have for all the math instruction received in school so long ago, actually am sentimental about the subject if that is possible. Only wish I had learned then more advanced math such as calculus.

We have been teaching the same stuff over and over again, and it still does not work. Solving a quadratic equation is meaningless. Solving simultaneous equations has a geometric meaning.
We should follow Switzerland: teach a combination of Geometry AND Algebra together-- its called Analytic Geometry (Descartes) and the student will see visually what an equation looks like. Solving the quadratic equation... seeing the curve cut the x axis in two places now make sense.
We have created an American tragedy ... need math majors with an MS in mathematics as teachers in High Schools. Raise the salaries and they'll come

Great insight to a doorway to college. I was told by my high school counselor that my best chance was to seek work in a technical field.
My counselor had the wrong cum.
Luckily my work allowed me to build my math skills. From learning to build
a yearly operating budget to to helping develop underground utilities.
When it came time to change to a new profession, all teachers had to pass a MSAT test. I was fortunate to pass on the first try. Now 20 years later,I Iike to use hands on projects with my students from helping figure out the area of a playground to figuring out how many gallons of paint you need to paint a classroom, to being able to project the degree difference of a shadow
By doing this I believe my students get a better feel for math.