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Solution paths in solving geometry problems in a paper and pencil environment in leveling courses for engineering

Abstract:

The present article focuses on the different methods to solve a geometrical problem from the formal perspective, considering three fundamental ways present on the written discourse and that are dependent on how the problem is approached. The objective of the study is to find paths to the solution after the problem has been approached, with special interest on the method and the quality of the developed cognitive structure. From the obtained results, we differentiate three ways for the solution to the problems posed to engineering students in academic leveling courses at Escuela Politécnica Nacional. One path to solution is realized on the mental plane, where the configurational discourse is used in a heuristic manner and the language in a synoptic way. Another path to solution is one where the student assigns a great value to the initial configuration through the natural or symbolic language, and starts to structure a discourse, by granting it a heuristic role. Finally, the third solution path is achieved by the student structuring the approach phase cognitively, for it starts with previous analogies to similar problems in the past.