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.
(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.