# If We Actually Taught Math…

…we would get rid of course designations like Algebra I, Algebra II, Geometry, Calculus, etc.. Mostly because they convince kids that they can be finished with material when the course ends.

…we would stop teaching a linear progression of math “courses” as if every student was planning to major in math at university. That is demonstrably false.

…we would worry more about those times outside of math class when mathematical thinking would have solved a social issue. Like when my students struggle with racism and prejudice and have no context because they live in rural Iowa. Statistics, and being able to parse them, would have helped a lot there, but alas, they are not used.

…we wouldn’t be so quick to give quizzes over material that was just covered. Cramming is a pandemic issue in the learning of math.

…we would ask students to generate the “word problems” they hate so much.

…we would only give our highest marks to the students who can answer “when will we ever use this?” on their own. Hell, we’d only give them to the students who start there.

…we would ask an effing question that is actually interesting. Like, how fast do boats sink? Does the size of the gash in the hull matter? Or, How many people have there been, total? Or, is there a relationship between latitude of a country and its GDP? Or, what’s with the Hawaiian island hot spot? Or, or, or, or …

…we would teach kids to program computers as early as possible (~10 yrs). We don’t now because it would make most of the high school math curriculum redundant and esoteric, and many teachers lack the training. Example redundancy: finding areas with integrals using anything but numerical methods, or you could keep teaching the myriad “rules” about odd powers of cosine multiplied by even powers of sine…

…we would see those “art” kids taking math electives.

…we would see students connecting math skills to the limitations of those skills instead of the chapter or sub-chapter number. Like, “Oh, vertexes, that was some parabola thing from chapter 2.3.4,” when instead “Oh, a vertex of a parabola is useful when you want to reflect stuff in a coherent way” would be music to my ears.

…we would see math teachers spending as much out-of-pocket cash as science teachers.

… and finally, we would never have to have our aunts on Christmas Eve tell us that “math was just way over their heads” in front of their own children. That’s not a very good present.

This list goes on forever.

Why?

Because I once had a student ask me when she would ever have to take the derivative of:

$j(x) = sin(sqrt{x^{-19}+tanx})$

I said maybe some crazy periodic system like the eddies surround the input of a flute’s mouthpiece, but what are the chances she’d ever study that?

Really, I’m only making them do that because some professor later will make them do that for points, and I don’t set my students up to do badly in college. Honestly, finding the derivative of sin(3x+90) is probably capable enough, but enough or capable isn’t the constraint we’ve put on math class, now is it?