Highlight of the Day:
Context: AP Calc class, talking through some multiple choice (no calculator) problems from a practice test.
Problem:
what is 
;
Me (typical first question): So....what should we do?
Student: Substitute the 2 in for t to find the answer
Me: Why would we want to do that?
Student: Well, f(x) is the integral there, which means it's really the anti-derivative of the function. We want the derivative of that anti-derivative, which basically means we want the stuff inside the integral. So if you just substitute 2 in, you'll get the answer.
Me: You basically just explained the first part of the Fundamental Theorem of Calculus that you struggled with when we first talked about it. Woohoo!
Granted, I know his explanation skips the step where t in the integrand becomes x after you take the derivative, but the conceptual understanding of the relationship between derivatives and integrals is there. Made my day.
Context: AP Calc class, talking through some multiple choice (no calculator) problems from a practice test.
Problem:
Me (typical first question): So....what should we do?
Student: Substitute the 2 in for t to find the answer
Me: Why would we want to do that?
Student: Well, f(x) is the integral there, which means it's really the anti-derivative of the function. We want the derivative of that anti-derivative, which basically means we want the stuff inside the integral. So if you just substitute 2 in, you'll get the answer.
Me: You basically just explained the first part of the Fundamental Theorem of Calculus that you struggled with when we first talked about it. Woohoo!
Granted, I know his explanation skips the step where t in the integrand becomes x after you take the derivative, but the conceptual understanding of the relationship between derivatives and integrals is there. Made my day.
Super Cool. They GET it! Nice way to ease into the weekend.
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