Written by Hector Osegueda.
Graphic by Quynhmai Tran.
I’ll be the first to admit that I’m bad at math. My high school report card would be straight A’s all the way down until, quite rudely, a math class reminded me of my shortcomings with a big fat C. I was always elated whenever I managed to eke out a B in algebra or geometry. I certainly would have failed all my math classes throughout the years if it wasn’t for test retakes, as well as what I suspect to be a copious amount of pity on my teacher’s side of things. I’m as good at math in the same way that monkeys aren’t.
This isn’t to say, however, that I lack an appreciation for the field of mathematics, but quite the opposite, in fact I find the subject to be fascinating; topology, number theory, linear algebra, all this and more is fundamental in truly understanding the inner workings of our reality. Many people early on make the mistake of blaming their lack of mathematical understanding on a failure on their end; they tell themselves that they must be stupid and that they’ll never understand math, that math isn’t for them. This, in turn, creates a negative-feedback loop that perpetuates their perceived mathematical inability. This is why I believe I was robbed of a robust mathematical education, along with millions of other students here in the United States.
For all you STEM-types who intuitively understand math, this article isn’t aimed at you. Concepts come easily and simply for you, and there is minimal stress associated with math tests. I envy you. Not everyone just gets math though, and you can’t blame them for it. Mathematics is full of concepts that need to be taught in specific ways or else risk losing some children behind. As Elizabeth Green from the New York Times writes,
“Most American math classes follow the same pattern, a ritualistic series of steps so ingrained that one researcher termed it a cultural script… By focusing only on procedures — “Draw a division house, put ‘242’ on the inside and ‘16’ on the outside, etc.” — and not on what the procedures mean, “I, We, You” turns school math into a sort of arbitrary process wholly divorced from the real world of numbers. Students learn not math but, in the words of one math educator, answer-geotting.”
Math teachers often present lessons as if they exist in a vacuum. They teach us to memorize formulas, and then to plug and play, without ever really explaining the underlying logic behind any problem. Teaching math as if it just exists cultivates disinterest and oftentimes, confusion. It is difficult for one to develop an appreciation for math if it is presented and taught as a self-contained field. How can a student be expected to take interest and joy in math if no meaningful connections can be made? For lack of a better word, teachers are guilty of making math boring. Dr. James Stigler from UCLA explains,
“In other countries, students are asked to work on a variety of problems. In the U.S., students work on many repetitions of, essentially, the same problem, making it unnecessary for U.S. students to think hard about each individual problem. We teach math as disconnected facts and as a series of steps or procedures — do this, and this and this — without connecting procedures with concepts, and without thinking or problem-solving.”
These disconnected facts don’t particularly inspire students to embrace the material being taught. The problem with this is that a good foundation is absolutely crucial to succeeding in math. Lessons build and expand upon previous concepts so, if a student failed in learning a critical topic, they can severely fall behind to the point where they become dismissive and/or scared to ask for help.
My fascination with math is recent. As a liberal arts student, my interests and strengths lie in history, literature, writing, and philosophy. My younger brother, on the other hand, entered UT Austin as a physics major. Curious, I would accompany him to some of his lectures. Afterwards, I would ask him to explain what exactly I just listened to, and he graciously would because he knew that math wasn’t my cup of tea. He helped explain to me how beautiful math actually is, through the discussion of the logic underlying mathematical principles. After taking an introductory philosophy course, this explanation helped me to connect math to a way of thinking that I was already familiar with. The study of logic is merely an attempt to identify formal structures of reasoning. It felt like I was learning philosophical logic, and that’s all math really is, applied logic that ascribes symbols to facilitate and condense logical propositions. These are manifested in the forms of algebra, geometry, calculus, et cetera. Unfortunately, these are now monotonously drilled into the students of today.
The inquisitive nature of the discipline is stripped away by worksheets and equation charts. It’s easy to forget that the Greeks, Babylonians, Mayans, and a myriad of other ancient civilizations approached mathematical discoveries—not as procedures to be memorized—but fundamental truths. It was an approach that I could understand, and I was so intrigued by this re-discovery that I began to frequent Khan Academy online in order to remediate my less than stellar math performance. I enrolled in a computer programming course and found the problem sets to be almost pleasurable after gaining this new perspective. The following semester, I developed a fondness for statistics, a fondness that would not have come about had I not had those earlier discussions with my brother over the philosophical nature of math.
I understand, however, the difficulties that math teachers must have in conveying essential information. There’s a breadth of curriculum content required to be taught by school districts and states that they have to get through; they can’t stop and personalize math lessons for every individual student. The status quo method of instruction—rote learning—is ineffective because it forces students to learn through sheer repetition and memorization. Jo Boaler, a professor of mathematics education at Stanford University wrote in the Scientific American,
“In every country, the memorizers turned out to be the lowest achievers…Further analysis showed that memorizers were approximately half a year behind students who used relational and self-monitoring strategies. In no country were memorizers in the highest-achieving group, and in some high-achieving economies, the differences between memorizers and other students were substantial. In France and Japan, for example, pupils who combined self-monitoring and relational strategies outscored students using memorization by more than a year’s worth of schooling.”
Class discussions, collaborative work, class games, and learning cells are all active learning alternatives that could be implemented in classrooms as an alternative to the mind-numbing, punishment-esque worksheets and problem sets that are the norm across high school math classes. It is necessary now more than ever that kids not only learn math and science in middle and high school but that they enjoy learning these subjects. As society increases in technological sophistication, more careers will require basic quantitative skills. Not everyone needs to become a programmer or a computer engineer, but we must become a society where everyone is scientifically and mathematically literate.