#and that simply thinking critically and approaching problems with something like Polya's or the scientific method is still a math exercise

[vivalasestrellas]

Rambling Thoughts on Math Ed

The school I teach at started up a robotics program and is looking to provide more engineering-based classes. This has led to discussion of how these programs can be used in tandem with traditional content and in relation to ‘applications’ of material traditionally found in classrooms. And whenever I listen to people talking about math education, it almost always gets around to “we need to be teaching applications, not just algorithms”. I get it, I too think there needs to be more emphasis on applications, but I also firmly believe that students need to be able to work with the pure and theoretical math as much as apply it. It would be super cool to have a class that revolves around the applications of calculus, but if the focus is just on applications then there’s little value in it if students don’t understand how to take a limit, derivative, or an integral or let alone not understanding when or why they would want to do so. Applications can be used purposefully, but math class is a place to learn math; and math is more than just applications.

Really I think more advanced science and technology classes are the place to emphasize applications. Physics, for example, is literally just applied math in tandem with conceptual explanations. In physics, it’s expected that students understand quadratic equations and basic right-triangle trigonometry, but the class does not teach those concepts. The same is true for any science class that applies any kind of mathematics: it is expected of students to know the math and be able to apply it. Chemistry utilizes quite a bit of math, physics is basically all math, astronomy as well, and an understanding of mathematics and logic is crucial to anything related to programming or engineering. 

Yet because classes such as chemistry, physics, and engineering are all ‘science’ classes, it is acceptable to some people to sweep the math under the rug. It doesn’t matter that students don’t apply math when working out problems in chemistry because they still understand the periodic table and basic reactions. It doesn’t matter that students don’t apply math when working out problems in physics because they understand Newton’s laws of motion and the basic principles and relationships of motion, heat, and energy. Students can still describe general ideas and relationships, they get the ‘science’, so there’s no point applying math; it’s just more complicated detail. I understand that some classes and some teachers take this approach, but I think it’s a disservice.

I mean, the way most of the robotics coaches have led this year seems to be a philosophy of ‘build first, then test, then fix’, emphasizing the scientific method, with no regard to the idea of prototyping or planning. If one of the goals of the program is to demonstrate the value and importance of math, then they’ve failed in that goal as they’ve done no actual math.

It just seems to me that there are plenty of places that ought to naturally allow for intense mathematical applications that do not take advantage of them. Then people turn around and ask why math class isn’t like this: a place where students get to see applications in action, to give lip service to math while not actually doing any. It seems to me, in my admitted cynicism here, that people would rather remove math from the math classroom just as it has been removed in science and engineering. All in the guise of “making math mean something”, “preparing students for the workforce” (don’t get me started on that bs), and “applications”.