As a math major who has loved math in all of its elegant beauty for years, there is nothing more depressing and frustrating than this country’s sorry excuse for mathematical education in its public schools. Everyone knows there’s a problem with the way math is taught, but not many people seem to know exactly what that problem is.
Politicians say it’s a problem with standardized tests. Schools and teachers say it’s a problem with funding and resources. These complaints are all well and good, but they are general problems that plague all aspects of public education; however, there seems to be something uniquely twisted about math education specifically. People just don’t complain about English or art class the same way they do about math.
The people who best understand the math education mess are the ones subject to its torture: the students. Odds are if you took a high school math class in the United States, you’d describe the experience using some combination of the following words: boring, useless, and stupid. The simple observation that most people had bad experiences with high school mathematics is proof enough that there is something deeply wrong.
People don’t brag about being bad at writing or reading, so why is it normal to brag about sucking at math? This really shouldn’t be the case. Mathematics, as it should be — as it is in the real mathematical world — is an exercise of imagination and creativity. It’s an art. Unlike students in precalculus, modern mathematicians don’t spend hours each day doing mindless calculations; that’s the job of computers.
Mathematics is all about discovery. Mathematicians like to think about imaginary objects and see what logical steps they can take to learn more about those objects. A number theorist might think about prime numbers and ask themself whether or not it’s possible to write down every prime number, and if they can if there is some formula for them.
These questions are not at all obvious and take a significant amount of thinking, trial and error, and creativity to answer. It’s thinking for thinking’s sake. Sometimes, the thinking even leads to real-world applications, like in mathematical neuroscience or theoretical physics: applications that would never exist without the freedom to think.
When asked to plug numbers into a formula, however, a precalculus student has nothing left to discover. There’s no room for creativity or questions, only blind obedience. The student is never allowed the glorious struggle and satisfaction of actually deriving these formulas on their own. Instead, equations are mercilessly ripped out of their historical context and presented as cold hard facts to be memorized, verbatim. The student is never taught the deep history surrounding the derivation of these formulas. The derivations themselves are glossed over or even skipped to save time.
Precalculus, elementary algebra, and all of the other little monsters of high school math are nothing more than another way for schools to test how well their students can follow directions and memorize useless facts.
Of course, precalculus is useless! No one in the mathematical community or out of it is ever going to have to know how to solve a horrifying polynomial equation by hand or row-reduce a five-by-five matrix by hand or solve elaborate algebraic word problems or do any of the other mind-numbing, cookie-cutter exercises that precalculus poses.
No job that involves the manipulation of numbers or data is ever going to expect someone to work without the assistance of a calculator. It’s 2022, not the Stone Age! We shouldn’t be subjecting students to material that is not only mind-bogglingly boring but also completely irrelevant to their lives. When was the last time you used the quadratic formula outside of a math class or found the focus and directrix of a parabola? To make matters worse, many students struggle with high school math. Who would’ve guessed? Following directions exactly to the point is difficult and so are arithmetic and algebra. How can anyone be expected to stay engaged in a class which stomps out creativity, discourages free-thinking and sucks the fun out of everything?
If you’re even the slightest bit interested in math, education, or geometry, Paul Lockhart’s “A Mathematician’s Lament” is an incredible read. In this fiery book, Lockhart critiques mathematics education as it exists now, particularly geometry, and he argues for an alternative. He provides the perspective of a professional mathematician and an educator. It’s funny, relatable, and informative. Read it, and see what could have been. High school truly robbed you of a wonderful mathematical experience.
~ Pat Mallory `26