As a teacher I encounter all of the typical kinds of students. There’s one kind of student I routinely encounter, usually in a freshman calculus course, that really boils my blood: the failing student who “has always been good at math.”
Oh it’s so annoying! And it’s even worse to hear because the stuff we teach in calculus isn’t really math either. The irony is so thick in the air when a student says it I’m surprised I don’t cough. Invariably, they never actually understood the “math” they were always so good at. I don’t get angry because they don’t understand the material (indeed, that’s the point of the class!). I get mad because they have absorbed a message about what constitutes mathematics that is, at best, misguided.
Of course, the problem is deeper than a handful of students who accidentally say ironically stupid things. The problem is that American high school students are taught something named “math” for four years which is not even close to math.
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This article highlights the difference between the engineers view of mathematics and the mathematicians view. The first is interested in the application of process to solve problems and the latter is more interested in the “why” of the process, which includes pattern recognition. I never had any problem with learning calculus because it was presented in light of how it related to algebra and how to use what I learned to solve real problems. Sometimes these disconnects occur because one method of teaching is applied to the teaching of algebra an another style is applied to the teaching of calculus.
John Dickert
Mount Vernon Farms