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Knowing More than I Teach

I have been reviewing how to do some programming in Mathematica. I use Mathematica, a mathematical computing environment, intensely in one of my Spring classes---Multivariable Calculus.  The class focuses on techniques from a more qualitative perspective---many real examples can't be done by hand and so we use the technology to extend what problems we can discuss.

Very little of my knowledge of Mathematica programming is discussed explicitly in class. This is pretty common---my comfort level as well as my knowledge base in teaching relies on having a firm foundation that is rarely relevant in a direct fashion. I am reminded of working with an adjunct once who knew that (-1)(-1) = 1 but was a bit shaky on why. The why is a fact from abstract algebra that does not need to be discussed explicitly with students but can easily be used to motivate an explanation that helps them to build intuition.

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