Thought Stimulated By The 30th Anniversary of the Release of the Report "A Nation At Risk"
Apparently, the Bill & Melinda Gates Foundation is in the midst of a program whose stated purpose is to enhance the quality of teaching in the United States. One of the implications of their program is that insufficient teaching at a high quality level is an important...
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The math textbook of a student that I'm working with posed the following problem:
Solve e^x=x^5
The student told me that she couldn't do the problem and so, with an air of authority, I started to show her how to solve it...until I realized that I couldn't solve it, either! I believe that there is no closed-form analytical solution to such an equation, and that the best that one can do...
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Something that I've just started doing is enhancing my answer to a student's question by sometimes formulating (when possible, of course) a theorem and proof that are directly related to the question. For example, when one of my students asked me to describe the symmetry of an odd function, i.e., a function for which f(x)= -f(-x), the theorem I cooked up was:
For an odd function:
a) The...
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