The Case Against Math

Resolved: Math education is mostly pointless and over emphasized.

Why do we teach math? We all use arithmetic and could use some knowledge of percents and fractions, but the education system seems to push a lot of abstract math. When I ask this question of educators, I often get these answers:

  • It is beautiful
  • A basic understanding is generally useful (and advanced study is required for certain professions)
  • It is mental exercise/a sign of intelligence
  • Knowledge of math can be transferred to general critical thinking

All of these might be true however, listed below are several arguments against these reasons.

Are these reasons unique enough to math to warrant the focus that our education institution places on math?

Many disciplines, e.g. music, art, dance, cooking, and computer programming,  all meet the above requirements, yet are not taught daily to all students, do not have state adopted curricula, and are not assessed as a part of school, teacher, and student success.

Do the above reasons represent how we or why we really teach math?

My observation of math education is that we teach and test the specific math functions and abilities that have little practical application, context, or critical thinking. For example, here is an example question from the California State Standards Algebra 2 test (passing Algebra 2 is required to apply to the University of California (UC) system).

This question represents a specific and esoteric application of math, for math’s sake, without context. There might be one or two fantastic math teachers who can present this kind of problem to students in a way that emphasizes critical thinking, real world application, or the beauty of the logic. However, my belief is that most math teachers present this kind of problem as an end unto itself, ie learning how to divide polynomials is the goal. So the question is, why do children (or adults) need to learn how to divide polynomials? Definitely some people do need this kind of knowledge, but some people also need to know how to modulate from Eb min to G#dom; some people need to know the difference between Hungarian and Spanish paprika; and some people need to know how to communicate with another person in a difficult relationship. Why do we teach some knowledge “just in case” and some knowledge “just in time”?

Are the above reasons, actually all true?

I agree that math is beautiful, that a general understanding is useful, and more in-depth understanding is vital for a very small percent of people. However, I disagree that math is a sign of intelligence and transferable logic/critical thinking I disagree with. I have seen students who could very easily find the 4 roots of a complex polynomial, unable to determine the correct scale for a graph for a science lab. It has always seemed to me that students leave their math brains in math class. The concept of situated knowledge is documented, and I am not sure that the case for generalizable knowledge has ever been proven. Just because math is very abstract, does not mean that it is more generalizable. As an analogy, if our goal is for students to appreciate the beauty of an ancient Greek vase, the way we go about teaching it is to break that vase into very small, comprehensible, and abstract parts. Then we teach each of these parts as if it was very important and never reference the larger goal because students are not prepared to understand the whole. Is it any wonder that students never appreciate the vase? Maybe we should approach students with the complexity and messiness we want them to be able to deal with. Perhaps the only way to teach critical thinking in complex situations (if that is a real goal of education) is to have a critical thinking class, even if the problems we present in these classes don’t have easily grade-able answers; even if the complexity scares and frustrates our students. I think we would rather have students frustrated by general complexity, than by abstract simplicity.

Are the above reasons enough to give math the heavy focus that we give it in our education system?

If you need evidence to the heavy weight that math is given, here are the percentage weights of the API (the official rating/grade of school) for California.

Subject K-5 6-8 9-12
English–Language Arts 56.5% 51.4% 36.10%
Mathematics 37.6% 34.3% 27.10%
Science 5.9% 7.1% 22.9%
History–Social Science N/A 7.1% 13.9%

(Even though Science and History are given some weight in K-8, they are only tested in 5th and 8th grade  and predominately on the 5th and 8th grade standards). The SAT and GRE tests are essentially 1/2 to 1/3 based on math.

Does math represent a third of what we think people should know? Remember, by math, I am not talking about the ability to estimate that 37%, 34% and 27% are a third. Percents and fractions are lower-level elementary math while algebra, geometry/trigonometry, and calculus are the true goals of math education. Estimation, number sense, and practical application are not the end goals of math education. Even if math qua math is valuable for all, or at least valuable enough for future academics, and all students need to be exposed to it, is it more valuable than the languages of the people of the world, health, technology, the arts, history, and science combined?

So why math?

Math is easy to test. Math is seen as a proxy for intelligence. Math is used to sort and select, ie to determine which students are good enough for continuing studies. Math has traditionally favored male students (I would argue not due to genetic reasons, but due to socialization). Perhaps math education used to focus on deductive reasoning and logic. Cultural inertia means that we have taught math and so we will teach math.

Why are you picking on math?

Science, history, English literature, world language classes, physical education classes, all share many of the same problems that math education faces. These all represent symptoms of the same disease: teaching content over skills, compartmentalizing knowledge, focusing on academic departments of universities over the real needs of our students. However, only math seems to hold the hallowed place as the proxy for intelligence. Also, many students have a very poor experience with math, which turns them off of the entire school system since math is given such a strong emphasis.

So what to do?

If we must teach math, teach it  as if math was just one aspect of the larger concepts and questions that are the main thrust of education: critical thinking, problem solving, communication, empathy, and creativity. If we must teach math, teach it through music, art, science, technology, history, cooking, construction, engineering etc. because math as an abstract system is useful to very few of our students. If we must teach math, focus less on the answers and the algorithms for specific types of problems and focus more on the questions and the processes of problems.

Caveats/Conflicts of Interest: I love math (the Fourier transform makes me laugh with joy). I am good at math. However, I don’t feel that my personal experiences in school represent an adequate reason for determining the focus of education for all children. I love learning for learning’s sake. I believe in the well rounded, academic, humanities education in which math and science are members of the humanities. I am a science teacher and technology coach. I believe that facts are important.

Content Areas
K–5
6–8
9–12
CSTs, CMA, and CAPA
English–Language Arts
56.5%
51.4%
27.1%
Mathematics
37.6%
34.3%
18.1%
Science
5.9%
7.1%
22.9%
History–Social Science
N/A
7.1%
13.9%
CAHSEE
English–Language Arts
N/A
N/A
9.0%
Mathematics
N/A
N/A
9.0%

15 comments

  1. 0
    discriminate says:

    LOL
    Discrimination. And self worth!

    Generalizations are untactful even when well placed in my experience. Why? Because for some reason this simple way of analyzing data that affords humans most of our beliefs and encompasses identity is viewed as discrimination. Discrimination is natural. We all discriminate all the time and yet rarely acknowledge this process in ourselves. If discrimination is so bad why is there no importance placed on self evaluation? Maybe people are just bad at discriminating.

    People with educations generally think they have educations because they are smarter than those who do not. Those educated people go on to have careers and think that they are better than those who have less money. All because they are smart. This belief of intelligence is proven to be a fallacy and is common knowledge amongst those who live outside academia and especially among those who are forced out by current educational standards. For some reason those in academia have put themselves on a pedestal in America and pulled up the ladder behind themselves. Competitively this is ridiculous. In the past affording education to the masses has always been about bettering society as a whole. Modern education is about maximizing the percentage of those who will be capable of achieving higher education. This change has left America with a large uncultivated populous that is incapable of getting there children through High school yet alone higher education. In turn forcing Education to lower its standards in a plummeting dive with no end in sight. The world is laughing as we bend over backwards for those that we have disenfranchised.

    Education has always been a traditional institution. Never short of blatant public outrage and revolution has it changed. And even under those extreme circumstances it has changed very little. Why?! Because no matter how you go about changing its problems only the Educated are in a position to educate. Unless you are brilliant beyond comparison it is hard to have an effect on the ways of the world.

    Not so long ago it was common practice to beat left handed students for doing what was natural to them. There was special schools for these afflicted souls. This form of brutality is known as Victorian era education. In ancient japan it was common practice for the Samurai class to disown male children who were afflicted with this condition due to the standardized right handed martial arts systems of the time. It took the lifetime of arguably one the best martial artist of all time to change this slightly. AKA Miyamoto Musashi in case you didn’t know who achieved this was or why he is recognized as one of the most influential strategists of all time. To think these types of injustices are solely a western thing or that these types of problems don’t still face large percentages of our modern population is just another example of how the haves ignore the needs of the have nots. An estimated 30% of the population has a dyslexia spectrum mind, 20% of the population is estimated to have attention related so called dys-orders. All in all about 40% of the total population has some fundamentally different way of thinking or dealing with life. These alleged afflicted have much to contribute to the whole. For example dyslexics have an above average IQ’s by about 10 points. A lot of these so called attention deficit people do well in chaotic situations that the average person would be overwhelmed with and also have above average IQ’s. Public education does absolutely nothing for these people. Only those that fall on the extreme end of these spectrum disorders get special treatment. And then only on the grounds that they are disabled rather than gifted. Those who are not in these categories are simply viewed as having low intelligence despite the fact that there is no evidence to support this claim. Almost all of the progress in the world has come from an afflicted source. Almost every invention you see around you exists because these people think the way they do and not like the norm. Why would disenfranchising them make the world a better place. How does a society justify this action?

    If there is a such an academic equivalent of Musashi who can force change through enabling those in need and slaughtering competition. Then I welcome it but since that is not likely due to the democratic nature of modern society. We all need to check ourselves and encourage change through how we live our own lives and what we communicate to the world.

    I Believe affording people education is about those that need it. Not enabling further those who already have it.

    Better people for a better future. Not a better future for a better few.

    Maybe I am a moron.

  2. 0
    margret says:

    colin if its possible for next year going to tenth grade i really really need help on algebra 😛 PLs

  3. 0
    Colin ( User Karma: 0 ) says:

    Hi Stefan-its great to hear from a real life colleague!

    I could probably think of some great names in innovation from the later 20th century related to tech (personal computing, Human-Computer Interface, networking), space (moon, satellites), physics (sadly the fission and fusion bombs), and biology (DNA, RNA, Genome, cloning). However, I agree that these achievements and individuals aren’t as known or valued as professional athletes and pop stars.

    Sadly my cynical approach is that we can’t change the paradigm just by looking at the testing. Even if we got rid of standardized testing, most teachers would rely on 30 problems for homework and bi-weekly 100 problem tests. We still call collaboration cheating. There are a lot of teachers to convince we need to change, as well as monied interests like publishing/testing companies.

    To continue a cynical perspective: I have heard some arguments that the push for STEM is really just a push by US corporations to keep the cost of engineering down by having a higher supply of labor.

    While I agree that STEM is great and integration of subjects can promote better education. However, we also need to get school off of the competitive bandwagon, ie the only reason school needs to be good is so that we can compete with those foreigners. School needs to be good because we are responsible for school.

  4. 0
    Stefan Mayer says:

    I think the push for STEM in California is a good idea. I am hoping that it will re-direct the education system from an old model of algebraic based problem solving to one of applicable problem solving in areas like robotics, distribution of resources, and the creation of economy.

    However, publishers and STAR (California state) testing are in the way of progress. Too many politicians are relying on STAR as a way to indicate student progress, and publishers are making way too much money to support the STAR cause. Publishers and politicians are maintaining a certain status quo in state testing because of the power and money involved. Unfortunately, by doing so, the education system perpetuates the old model, creating an army of U.S. test takers, high drop out rates, and no problem solvers.

    For years, the niche of the U.S. had been creativity and innovation. When we think of U.S. influence in the evolution of global technology, we think of personalities like Thomas Edison, Henry Ford, Graham Bell, Benjamin Franklin, George Carver, George Eastman, Grace Hopper, Samuel Morse, Levi Strauss, Nicola Tesla, Eli Whitney, and the Wright Bothers. Can you think of today’s great names?

    We should support and celebrate innovation and collaboration across our great democratic nation. The U.S. should be a model of these ideas, especially during this amazing time of social networking across the globe!!

    How do we get a revolution in education going, when all we do is tweet and write about it in blogs? Will it really take a crisis to inspire action? Does that always have to be the American way?

    Here’s a video on Changing Education Paradigms:
    http://www.youtube.com/watch?v=zDZFcDGpL4U

    PEACE

  5. 0

    What an interesting article and discussion, especially now during a period in which the US continues to fall further and further behind other countries in many areas, but especially math. I agree that this subject is foundational to being able to achieve success in many disciplines, including social sciences. It’s the quality of teaching, and the backwards way so many people are taught, that makes it seem irrelevant and hard to grasp.

    I see your argument that most Americans don’t use math in everyday life beyond a certain level. But I challenge this: if we had better math education and comfort with the subject, maybe we would use it more in our everyday life. I know I do.

    Last night I was at a party where I presented a riddle that one of my students had told me. The riddle required one to think critically about calendar dates and numbers. The group was a mix of American- and European-born people. The Americans (both man and women) gave up almost immediately, while a European woman persisted and solved it after about 10-15 minutes of thinking about it (about the same amount of time it took me to solve it).

    I think we do need a revolution in math education in general in this country, and that’s why I am enthusiastic about teaching teachers about Singapore Math, as the approach is one that makes math *make sense.* And my students find it fun!

    I also think we also need training in critical thinking too; my good friend and colleague, Charles Ames Fischer, specializes in teaching this in high schools.

  6. 0
    Jane Bozarth says:

    Michael, I didn’t say I wasn’t good at it. (I have a doctorate and did great in college math and in grad school statistics, if you consider that ‘math’. I expect that still won’t change your belief that I am a moron.) I said it was useless for me and was not taught in a way that linked it to the other claims those who love it make (it’s beautiful, it teaches critical thinking, etc.) Can think of much better ways to spend my time in school then and my tax dollars now.

    Best,
    Jane

  7. 0
    Colin ( User Karma: 0 ) says:

    Hi Michael,
    I agree with you that people often complain about a subject because they find it difficult. I am actually quite good at math and have always enjoyed studying it. I do think we need scientists and engineers, however I feel our society is the one which you exhorted me to found, i.e. most people do not have a firm grasp on 4th grade math (as is proven by the high level of credit card debt people take on). I am trying to make the point that we emphasize academic math over practical math, we emphasize math over a wide variety of other valuable subjects even though the vast majority of people are not going to be scientists. Also by trying to get all freshman through Algebra 1 and all Seniors through Algebra II we end up watering down the curriculum for the advanced students who actually will become the future scientists. Thank you for sharing your point of view, but I don’t think that we actually disagree on the point you brought up. Feel free to clarify what you didn’t understand or still disagree with if you have time.

  8. 0
    Michael says:

    It’s common for those who don’t like a subject to make a case against it because you don’t like to feel stupid. Well, wake up because the world’s a technical place, and math is the language of the sciences.

    A world without math is like a world where everybody is a literary theory major or some other soft discipline. Try employing the country with that skill set, morons.

    Tell you what – why don’t you start your own country and try to build a society where nobody has math skills above the fourth grade level.

  9. 0
    Jane Bozarth says:

    Colin, I couldn’t agree more. I remember even as a high schooler doubting the ‘math is good for critical thinking’ argument. If that were true, why didn’t they use it to teach critical thinking rather than make me memorize equations?

    I once had the sublime pleasure of running into my 3rd grade teacher and telling her I’d created a very happy adult life for myself that didn’t include fractions. As a US taxpayer who, although I have no children am required to support our public schools, I wish schools spent precious time on more useful/relevant skills.

    Best,
    Jane

  10. 0

    Hi Corey,
    Always good to hear from you, even though you have returned to the Ivory Tower of Cal State University :) Thanks for pointing out that even good students like yourself can reach that frustration point when we expect high level abstract knowledge in all subjects. Your comment about jobs of the future reminded me of a conversation I had with a district administrator. She said that life/work is now much more complicated than it was 20 years ago and so students need higher level math in order to be successful in this complex world. I find that argument to be totally bogus. If we are really about job prep, then we should have actual engineering, nursing, computer science, graphic design, etc. courses as the focus of our schools.

  11. 0
    Corey says:

    Colin’s post hit me squarely in the face, pushing me back in time to my high school days many many years ago. I was the kid on that academic track. I enjoyed math and science. I took all the required classes in math until I hit the wall. It was the middle of my junior year and I had just transferred to a new school. It was a pre-calculus class. I remember how my love for learning started to take a nosedive. I just could not get it. I wasn’t as successful as I had been previously, and I couldn’t figure out how to get better. I would go up to the math teacher with my questions and he would try to explain the concepts, but it just would not work for me.

    It had struck me that I couldn’t relate to what I was doing or trying to do. The teacher couldn’t inspire me, couldn’t tell me how it all works, and how math fits. It was like studying something for something’s sake. And you know how well that works for any one of us.

    Perhaps, if I had a great instructor, one who could inspire and help me see how math makes sense to my life at that moment and in the future, I would have stuck with it. Instead, I turned to the arts and discovered new avenues to explore.

    Fast forward to today when we expect students to be good at math, to be good at science, to be good at everything. Our educational leaders imply that by being good at math, among other subjects, we’ll not only have a much better future as knowledge workers, we’ll help our country be more competitive than the billions of other really good math students around the world. We are led to believe that everyone needs a high level of math to compete at jobs that we are told have not even been created yet.

    Perhaps, the argument for advanced math, concepts beyond addition/subtraction/multiplication/division, has not been clearly explained. It shouldn’t be a secret.

    Or perhaps, as Colin suggests, we just need to be a little more practical in our approach to what kinds of math our students should know and understand.

  12. 0

    David and Colin,
    Thank you both for your comments. It is nice to hear from actual math (or maths) folks on this. I like the idea of a broad general ed focused on practical uses of knowledge for everyone and then higher more academically focused subjects (whether it is math, science, english, etc.) based on the interests of the students. I also love the idea of cross-curricular projects (so that math isn’t seen as just math, but as a way to solve problems). That might be a way to approach a more generalizable critical thinking, even though I agree that we have very little evidence of that existing.

  13. 0
    David Radcliffe says:

    The main reason to study mathematics is that it is useful in many other disciplines. I believe that mathematics is very important, and the focus on math is warranted. But I do not believe that all students should be required to take algebra. They should be allowed to follow their own interests in high school. In most cases, they discover that mathematics is useful to their interests, and they
    will be more motivated to study it.

    I am very doubtful of the existence of general critical thinking skills that are teachable and transferable between disciplines.

    Many math teachers are aware that the current math curriculum is obsolete, but change is difficult due to the cumulative nature of the subject. Polynomial long division is not an essential topic. But if I refuse to teach polynomial long division, then my students will be at a disadvantage in future classes. When I teach the subject, I carefully explain the logic behind the algorithm, and show the connections with other topics, such as polynomial multiplication and integer long division. I don’t discuss real-world applications, because it doesn’t have any important applications on its own.

    The test question you posted is terrible. It could be improved by asking the students to find just one of the coefficients. For example, if the quotient is x^3 + 7x^2 – 7x + c + 4/(2x+7), then what is the value of c? This could be answered by solving the equation 7c + 4 = 46.

  14. 0
    Colin says:

    I’m a math tutor and I largely agree with your thesis here.

    I think math education (such as it is) is a leftover from classical education that’s somehow more firmly in place than Latin was.

    Personally, I’d like to see some kind of recognition that there’s math you need for everyday life – arithmetic and a basic exposure to algebra and geometry – and there’s the math you need if you want to be a scientist/engineer/economist/mathematician.

    I’d like to see cross-curriculum projects – maybe the science, gym and math teachers could get together and discuss the physics of curve balls.

    And I’d like to see a very broad, coherent education that allows students to excel in the areas they enjoy and get the basics in areas they don’t.

    Is that too much to ask? ;o)

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