Mamikon's Approach to Teaching Calculus Thesis

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Mamikon even takes this simple observation about curves to establish a new relationship between the tractrix and exponential curves (Apostol & Mamikon 2002).

Mamikon's visual understanding and explanation of calculus is not limited to two-diemnsional curves, nor does he concern himself only with new insights into mathematical relationships. In another paper, again published with Apostol, Mamikon established new proofs for Archimedes' discoveries concerning polyhedrons and their circumscribing prisms (Apostol & Mamikon 2004). Again, his explanation abounds with visual examples, clearly shaded in various tones to correlate areas and volumes for an easy understanding of the relationships Mamikon is describing. The mathematical formula are present too, of course, but they are far more easily understood for most students when accompanied with visual examples.

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In sharing these and other visual learning techniques with students, I would start (as Mamikon does) with examples familiar to their daily lives -- the curve made by two bicycle tires, or the arc described by jumping out of bed. Handouts, prepared in advance, would illustrate these activities along with more diagrammatic illustrations. Once the relationship of the tangent to the area of a curve is established (for example), its applications in more strictly mathematical settings (e.g. measuring the area of a graphed curve) can be examined. For less visual thinkers, mathematical formulas could be included on each page. This will help to establish and reaffirm the relationship between illustration and formula for all students......

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