On advanced mathematical methods and more elementary ideas met (or not) before
Résumé
Some mathematical problems, which could be solved by a general approach, also have different and often original solutions that appeal to less advanced mathematics. For example, drawing a tangent line to a parabola can be done by methods of differential calculus, and by exclusively using methods of Euclidean geometry. A project that I conducted with students who recently completed a Bachelor degree focusing in mathematics revealed that they were familiar with advanced methods but lacked more elementary views. I argue that unfamiliarity with alternative elementary solutions hinders for students the opportunities both to build mathematical connections and to appreciate the groundwork of related advanced methods.
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