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College Calculus versus HS AP Calculus
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Teaching
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By jvano
Posted Sat Nov 13, 2004 at 03:29:05 PM PDT
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When I teach Calculus I often find 90% of my students have had some form of calculus before. However many still struggle with topics beyond mechanical questions of computing derivatives or integrals. I often use 'anarchist' or 'skeptical' friend type questions in which I ask my students to help out their confused friend by presenting an argument to justify various key results and theorems that we have studied (e.g. the product rule, the 1st Fundamental Theorem of Calculus, etc.), basically give an informal proof.
Not surprisingly, many students struggle with these types of questions and some even feel these theoretical questions are not mathematics!
In an effort to explain to my students the importance of getting some understanding the proofs of the theorems we study, I use the analogy of a car - knowing the gas pedal makes the car go is not enough, we have to look under the hood and, while I'm not expecting everyone to become ASE certified mechanics, I do expect them to get a sense that there is this thing called an engine that has chambers in which vaporised gas explodes and pushes pistons that turn cogs that ultimately make the car go when you step on the gas.
So, in this context you can understand my glee when my wife pointed out this segment entitled Colleges Reevaluate AP Math Credits from All Things Considered which talked about how 'Colleges are making it more difficult for incoming students to get credit for advanced placement calculus, and some high schools are changing the way they teach calculus as a result.'
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