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Monthly Archives: September 2011
Playing with the Form of an Answer – The Shad-Fack Transom problem
A recent article in The College Mathematics Journal entitled The Shad-Fack Transom by Annalisa Crannell explores several methods of finding the radius of the small circle tucked up in the corner of a square circumscribed about another larger circle. In … Continue reading
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Completing the Square – Fast and Formal
Here is a strictly formal way to complete the square. We want to express in the form . We may want to do this for many reasons, for example, to graph a quadratic function (parabola), to solve a quadratic equation, … Continue reading
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Exaggerate to Teach
My wife was watching a Clinton Anderson video on training horses. I was fascinated. The man was training a horse at the same time he was teaching us how to train a horse and the horse was not necessarily his … Continue reading
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Real Numbers in Calculus
In my last post I alluded to the hand-waving we do discussing limits in calculus because students have a imprecise conception of real numbers. The clever article in the current The College Mathematics Journal, The Intermediate Value Theorem is NOT … Continue reading
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Calculus Counterexamples
Counterexamples are important tools in mathematical argumentation. As a math instructor I naturally gravitate to refutation by counterexample when an erroneous statement arises. My students however are less familiar with this type of argument, so first I give this example. … Continue reading
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“Stupid Mistakes”
So-called “stupid mistakes” are really failures of character. This dawned on me over 30 years ago when I was tutoring a bright teenager. I was using Birkoff and MacLane to teach beginning group theory to the boy. In exchange his … Continue reading
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