In this essay, I explain why math education matters from a slightly different point of view than the one in my previous essay, by closely following the preface of a math book titled “Burn Math Class: And Reinvent Mathematics for Yourself.”
Many people think that mathematics education beyond simple arithmetics is useless unless you become a mathematician, scientist, or engineer who uses mathematics for their job. They point out that you will never have occasions to use mathematics you learned in high school if you get the other “ordinary” jobs as an adult. They argue that mathematics education must be left alone for those who really need it.
However, strangely, nobody says that music education is useless if you don’t become a musician. Nobody argues that we should teach music only to the students who will later become musicians. Why? Because not only students but also adults enjoy music. Music enriches our lives. Then, why should not mathematics enrich our lives? Why can’t we teach mathematics to our students so that they can enjoy it?
That’s what makes Jason Wilkes angry. In the preface of his book “Burn Math Class: And Reinvent Mathematics for Yourself,” he wrote
“We should all be angry. Something beautiful has been stolen from us, but we’ve never felt its absence because the theft happened long before we were born. Imagine that by some massive historical accident, we had all been convinced that music was a dull, tedious, rigid enterprise to be avoided except when absolutely necessary. Suppose that we had all attended music classes for more than a decade during our youth, and that through some feat of brilliant sadism among the instructors, we all left these classes with a firm belief that music is at most a means to an end. We might agree that everyone should have a basic level of familiarity with the subject, but only for reasons of practicality: you need music because it might – rarely – help you with other things. But the consensus view would hold that music more closely resembles plumbing than an art form.”
As he explains in his book, so did Jason Wilkes think that math was “a dull, tedious, rigid enterprise.” He got a C in algebra and a C in trigonometry. He wrote, “mathematics had never been anything but memorization, boredom, and arbitrary authority.” By his senior year of high school, he finished all the required math courses. He was relieved that he would never ever have to deal with math again. But, one night during his senior year, he came upon a calculus book in a bookstore. He had always heard that calculus was difficult. As he had no obligation to study it, the book seemed more appealing; he just wanted to take a look at the book for few seconds. He had expected to see some “scary symbols” and that he would put down the book immediately and “be done with it forever.” However, contrary to his expectation, he was able to understand the calculus book. Jason Wilkes wrote that the author was saying something like,
“Straight things are easier to deal with than curvy things, but if you zoom in far enough, then each tiny piece of a curvy thing almost looks like a straight thing. So whenever you have a curvy problem, just imagine zooming in until things look straight, solve the problem down there at the microscopic level where it’s easy, and then zoom out. You’ve solved the problem. You’re done.”
Struck by the elegance and the necessity he had never felt in his math class, Jason Wilkes flipped through the book more and found out a section in which the author criticized how math is taught. As Jason Wilkes could relate to it, he bought this book and studied it without any pressure or obligation. It gave him “an odd sense of justification” to have hated mathematics. As he didn’t really remember the prerequisites to study calculus, he didn’t understand how to solve the “easy problems” at the microscopic level. Thus began his “strange journey of learning calculus” before knowing the prerequisites to it, such as algebra, trigonometry, and logarithms. What he found out was that calculus was the easiest part, while its prerequisites were harder. From time to time, he couldn’t follow the book because he didn’t remember the basics, such as addition of fractions. In cases such as this, he figured out the steps by staring at them, but in others, he couldn’t.
When he entered college, he took calculus 1 for fun, an “unthinkable” decision, according to him. Then, he took calculus 2. The professor, who taught him calculus 2, suggested taking a graduate math course for the sophomore year. He replied that he didn’t know anything, and the professor was insane, but he took it anyway and ended up getting the highest grade. By his senior year, the math department gave him a plaque saying something like “Congrats on being the best math major we have.” After graduation, he got a Master’s degree in mathematical physics, and wrote the book “Burn Math Class: And Reinvent Mathematics for Yourself.”
He was lucky because he found out late that mathematics can be beautiful and joyful. However, most teenagers graduate high school without realizing that something beautiful has been stolen. It’s time to give it back to them.