Calculus teaching ideas

[recovering_fan]

Hi Earl,

Your wife and daughters might like this idea. I tell it to everyone I know who knows Calculus -- Republicans and Democrats alike:

CALCULUS IDEA: â??CONCENTRATION GAMEâ?

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(This game can be played as soon as you start differentiation.  The more they play it, the easier a time they'll have when they get to integration.  So even as they're still learning derivatives, they're actually learning to integrate.)

You could play a game like ordinary concentration, except instead of matching identical tiles you'd be matching a function (in green) and its derivative (in red).

The beauty of this game is it forces kids' minds to work in both directions, prompting them to perform differentiation at one moment and integration the next.

FUNCTION                            DERIVATIVE

5                                              0
4x + 7                                      4
â??positionâ?                                 â??velocityâ?
â??velocityâ?                                  â??accelerationâ?
â??temperatureâ?                           â??rate of heatingâ?
 
â??voltageâ?                                  â??electric fieldâ? (gradient)
â??potential energyâ?                     â??forceâ? (gradient)
â??populationâ?                             â??birth rateâ?
â??bank balanceâ?                         â??rate of depositâ?
â??reactant presentâ?                     â??reaction rateâ?

â??total costâ?                               â??marginal costâ?
â??debtâ?                                      â??deficitâ?
x^n                                           n*x^(n-1)
ln x                                           1/x
e^x                                           e^x

a^x                                           (ln a) * a^x
sin x                                         cos x
cos x                                        - sin x
tan x                                         (sec x)(sec x)
sec x                                        (sec x)(tan x)

ln |sec(x)|                                  tan x
sinh x                                        cosh x
cosh x                                      sinh x
arctan x                                    1 / (x^2 + 1)
arcsin x                                    1 / sqrt (1 â?? x^2)

f(g(x))                                       f `(g(x))*g`(x)
normal dist. function                  e^(-x^2) / sqrt (pi)

[Earl]

Hey, thank you very much, recovering_fan! I shall pass this suggestion to my daughter who has been working as a high-school math teacher for several years now. I'm wondering if my wife has heard of this game. As it's now way past midnight here, I'll be sure to tell her about it tomorrow. Again, thanks; and have a great weekend!

[Mrs. Earl]

Thank you, recovering_fan! This sounds like a really good game. I would have responded sooner but Earl forgot to tell me. He says he is really sorry.

You might be interested in this song: http://www.youtube.com/watch?v=uqwC41RDPyg It made me and both my daughters laugh. I especially like the line about the relationship between pre-Cal and Calculus.

[recovering_fan]

Well, I don't know Mrs. Earl, the geekiness in that video was a little concentrated for me at times...

But I liked the part where they were talking about the limit not existing at x = 0 for f(x) = 1/x.

(It's too bad i_like_1981 couldn't have seen that video. He liked math, too, and I think I recall "Bohemian Rapsody" being his favorite song.)