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Monthly Archives: September 2011
Playing with the Form of an Answer – The ShadFack Transom problem
A recent article in The College Mathematics Journal entitled The ShadFack 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 handwaving 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”
Socalled “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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