Do you agree with the following two statements?

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• Computers can follow a logical process (and get blue ribbon awards for doing so fast and faithfully)

• Computers can't think (at least, not yet)

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Humans have skills that were utilized to develop Logic--before we had Logic.

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Humans do the thinking that is required to put together the computer program.

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So, if you were stranded on a desert island with a friend, how would the two of you rediscover Calculus and other important themes in Math?  We're making an optimistic assumption that your safety, sleep, water and food needs are being taking care of, and you might want something to occupy your mind while you do all that agriculture work. Oh, and don't forget, when you get back to civilization, it might help to have more story to tell.  

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At Mockingbird Academy, we call the very basic, important, difficult to see ideas--Black Magic.  We use the name Dark Blue Magic for specific projects that have made use of Black Magic.  We envision a transition between the darkness where the cool stuff lies and the outside world of bright sunlight and cloudless beautiful blue skies.

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Dark Blue Magic projects have reached success for rediscovery (or even initial discovery) of several math ideas:

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• Calculus - Derivatives of Monomials

• Calculus - Derivatives of a^x

• Calculus - Product Rule

• Calculus - Quotient Rule

• Calculus - Derivative of a Composition Function

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Appendix A

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This all started at a Physics help session where another student made a mildly sarcastic joke--that had some truth to it--about someone enjoying "seeing how our thought processes work".  Sometime later, it was realized that something else had happened in tandem with the joke.  The purpose of the evening was for students to work together to study for a hard test that was coming up, and the instructor of the class was there to help.

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"What is it that you don't know?" the teacher asked students coming up up to the desk to ask for help.

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• On the one hand, you could say this was encouraging students to think hard about where the gaps were in their knowledge.

• On the other hand, you could respond with "how could someone know what it is that they don't know?"

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We're modifying the story to "what things in Magic are there that you use as tools to build Science?"

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