A teaching experiment on periodicity: relevant factors for learning
DOI:
https://doi.org/10.5007/1981-1322.2019.e61915Abstract
In this article we discuss a teaching experiment that dealt with periodicity of trigonometric functions and was applied to sixteen first-year students of one Mathematics Graduate Course. A hypothetical learning trajectory (HLT), based on Simon and Tzur studies, was designed contemplating the cognitive mechanism centered on the relation activity-effect, from Piaget's idea of reflexive abstraction. In the qualitative research, with elements of Design Based Research, we investigate how the mathematical task promoted the students' learning. We highlight how the undergraduate students developed tasks using applets in GeoGebra software and how they used the analytical and geometric languages in order to characterize the functions under study and their periods. The results indicated that the records were coordinated while modifying the parameters of the algebraic expressions of the functions and related them to the periods of the functions. We identified relevant factors for learning provided by the teaching experiment, which explained the relationship between conceptual learning and mathematical tasks proposed in the HLT. We conclude that the cognitive mechanism provided a framework for undergraduate students thinking and advancing in conceptual learning.References
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