A friend of mine teaches at the British Columbia Institute of Technology. They are building a database of applied math problems, at the 11th or 12th-grade level. Their goal is to give students a better idea of "why do we need to learn this?", which is the bane of all math teachers.
They're not asking for calculus problems. But I've taught calculus and I often had the sense, while teaching the "applied" problems, that they were just straight-up asking the students to do derivatives or integrals, with some words added purely as a red herring to confuse the students. I mean, really, if a ladder leaning against a wall falls down, is there any situation in which one cares how quickly the area underneath the ladder is changing? My memory of pre-calculus classes is hazy, because I haven't taught at that level, but I do remember having a pervasive sense that the applications were contrived.
02 February 2011
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For good discussion of contrived math questions, see the "pseudocontext"-tagged posts on Dan Meyer's blog.
Heh, word travels fast - my department just convened for snacks, and one colleague asked, "Which one of you knows Michael Lugo?"
If I may be permitted to promote this project, we're especially interested in industry related questions and are soliciting donations. We're also willing to create problems mentioning various companies, in exchange for donations from said companies. eg, "TechCorp is a multinational corporation employing 40,000 people that designs state of the art gadgets. The design process follows [mathematical statement...]"
We might eventually extend the database to include calculus problems as well, and I'm also interested in what we end up with. It's no accident that at BCIT, at which every course offered is designed with a particular career path in mind, very few of the math courses we offer are calculus classes. (Other institutions seem to teach virtually nothing besides calculus to non-math/physics majors.)
Yeah, I'm always surprised how small the world is. You'd think I wouldn't be, after the amount of time I've spent in math, but intellectual knowledge of "small world" phenomena doesn't translate into lack of surprise at moments like this.
Yup. Humans have terrible intuition for probabilities, and this seems to be no less true for probabilists ;-)
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