Theoretical constructs proposed by Tall for teaching derivatives
considerations on the development of an epistemological reference model
DOI:
https://doi.org/10.23925/1983-3156.2024v26i3p028-046Keywords:
Mathematics education, Teaching of calculus, Derivative concept, Epistemological reference modelAbstract
This article aims to contribute to the discussion in this issue, centered around the question “How to develop a Reference Epistemological Model (REM) for the teaching of Calculus?”, more specifically considering the teaching of derivatives. The arguments presented here advocate the inclusion of theoretical constructs, such as the ones developed by Tall for the teaching of derivatives, due to their potential to make cognitive and didactical contributions to students and teachers, respectively. The constructs that we refer to in this text were called generic organizer and cognitive root of local straightness by Tall. The authors of this text consider that adding these constructs to an REM may foster integration between theory and practice, which is important for the development of Mathematics teaching. We organized our reflections by linking ideas related to the integration between theory and practice, the conception of an REM, the teaching of derivatives and Tall’s theoretical constructs. We concluded the article emphasizing the importance of continuously observing the prevailing epistemology of the concept of derivatives for teaching, aiming to find contributions that support the emancipation of Didactics of Mathematics and promote effective Calculus teaching.
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References
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