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Generating Readable Proofs and
Step-By-Step Explanations
for Education \
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A main purpose of this talk is reach out to educators for ideas and feedback \
about how we can do better at this and how we can use these programs in new \
ways. (So feel free to interrupt)\
\>", "Subsubsection",
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"This is a multidisciplinary effort involving two very different worlds: \n\t\
",
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"\tI\[CloseCurlyQuote]ve been part of both worlds.\n\t",
StyleBox["These worlds really don\[CloseCurlyQuote]t interact much, and less \
and less. \n\tOne of the ironies here I think is that, as mathematicians, we \
mostly see the subtlety and ingenuity required when making mathematical \
discoveries, and sometimes only see the less creative side of education, \
although we know in fact their essential natures are the opposite.",
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StyleBox["A personal view of Wolfram|Alpha, homework, and CBM: \nAlthough I\
\[CloseCurlyQuote]m very pro-CBM, I don\[CloseCurlyQuote]t see giving steps \
and proofs in W|A as making the teaching of these algorithms obsolete. \
Rather, I see it as possibly allowing students to better learn these \
algorithms and/or learn more algorithms. (recall the story about von \
Neumann). \n\tBut aren\[CloseCurlyQuote]t kids gonna say \
\[OpenCurlyDoubleQuote]why should I have to learn this if my computer can not \
only DO IT, but also understand and present and explanation that even I CAN \
UNDERSTAND!??\[CloseCurlyDoubleQuote]\n\tThe answer is that it prepares you \
to understand other things ",
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"\n\t",
StyleBox["To actually make these programs, we basically \"apply\" one \
world's ideas to the other, in both ways (\[OpenCurlyDoubleQuote]pedagogical \
computation\[CloseCurlyDoubleQuote] and \[OpenCurlyDoubleQuote]computational \
pedagogy\[CloseCurlyDoubleQuote]). \n\tThe obvious direction is that we \
\"make explanations/proofs computable\", by programming the logic of existing \
methods in the pedagogy (many of which are distinct from the way computers \
actually do these computations)\n\tBut the pedagogy also informs the actual \
logic of the program, and actually necessitates the creation of novel \
algorithms, as we\[CloseCurlyQuote]ll see.\n\tFinally, we need to use some \
tricks to prevent Mathematica from evaluating too quickly",
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Examples of the divergence of theory and best educational practices\
\>", "Subsection",
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Cell["\<\
2. Geometry proving
(synthetic v. analytic, and even theoretical synthetic v. 9th grade)\
\>", "Subsubsection",
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Cell["\<\
simple physics formulas have a common function:\
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