Rethinking High School Math Trajectories

High Schoolers get four years (at an extremely impressionable age) to learn the building blocks of what will become their passions and/or careers. That’s not a lot of time. Mathematics in high school tends to be reactionary to what has gotten students admitted to highly selective colleges. Through these reactions, many high school students will learn a lot about functions, equations, proof, and planar geometry. These topics don’t always land on students, especially since their utility isn’t immediately obvious.

This isn’t a post about how we should make all mathematics relevant to students’ lives. I don’t actually think that’s a good idea. There is real value in learning mathematics for the sake of the struggle - “because it’s there” as Sir Edmund Hillary said. Math has value to our brains and our development in much the same way as physical exercise has value to our bodies. With progressive overload, we get stronger.

But, I do think that we as math educators have held fast to a too-narrow interpretation of high school math topics. Let’s take functions as an example. Students tend to learn about how a function is like a machine - it converts inputs (typically numbers) to outputs. They then learn about these different families of functions - linear, quadratic, higher-degree polynomial, exponential, radical, logarithmic, trigonometric, rational, and perhaps more. Each of these families has defining characteristics, behaviors, and other patterns. A student who studies these is practicing their pattern recognition, higher-dimensional reasoning, and communication skills. These are good things to study and learn well.

Ask a computer scientist about functions, though, and you’ll get some serious divergence from the narrow scope of function families learned in high school. From the same origin (a machine that converts an input into an output), functions in computer science are usually about performing a specific task that accomplishes a goal. Computer scientists also must string together functions that call each other and make use of recursion - the complex notion of a function calling itself. The real universe of functions is broad, diverse, and really interesting! We shouldn’t consign an entire interpretation of functions to an elective that only some students take. The computer science interpretation of functions as helpful tools in a task is no less important than the pure math interpretation of functions as groups of graphical and analytical patterns and behaviors.

And, in the 21st century, it seems like both of these interpretations of functions are equally important. Writing code relies on algorithmic, job-performing functions. Interpreting and improving code relies on knowledge of mathematical function families and how they can affect runtime and space efficiency (big O notation, anyone?).

I could write similar arguments about many subjects in high school math. Geometric proofs utilize logic statements much like Boolean operators, which are critical for data science and programming. Equations in high school are things to be solved, whereas equations in computer science are assignments of value. Both are important! The current view of high school mathematics makes narrow definitions that students need to unlearn in order to pursue other mathematical domains, which feels really icky to me. At the very least, we should be clearer with students about how other domains expand upon the subjects they’ve learned.

I’ve written before about how Data Science and Calculus shouldn’t be seen as opposite pots of gold at the end of the high school math rainbow, but rather as complementary subjects that motivate each other. I don’t think about two distinct math trajectories - one for “calculus track” and for “applied math.” I do wonder about how much more motivated students would be to learn mathematics if there were problems they have encountered elsewhere that require some study. Maybe I’m just looking for more authentic answers to the worst question a teacher can be asked, “When am I going to use this?” Maybe we can do better at pushing some students to say, “Oh, I CAN use this!”