Analysis of Didactical Trajectories in Teaching and Learning Mathematics: Overcoming Extreme Objectivist and Constructivist Positions
Juan D. Godino 1, Hernán Rivas 2, María Burgos 1, Miguel R. Wilhelmi 3 *
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1 University of Granada, SPAIN2 Pontificia Universidad Católica de Chile, CHILE3 Public University of Navarra, SPAIN* Corresponding Author


There is currently a consensus in mathematics education that favors constructivist instructional models, which are based on the inquiry of knowledge by students. There are, however, different views that consider objectivist models, based on knowledge transmission (direct or explicit teaching) more effective in the teaching of scientific disciplines. In this article we analyze an instructional process on elementary probability directed to prospective primary education teachers, which was designed under constructivist principles and is based on data analysis projects. A systematic analysis of the study process reveals that the optimization of the learning process involves implementing frequent moments that require explicit transmission of knowledge by the teacher. This analysis is based on some theoretical tools from the onto-semiotic approach to mathematical knowledge and instruction, which allow identifying significant didactical facts that support a mixed instructional model. The relevance for mathematics education to contemplate the use of mixed instructional models that articulate constructivists and objectivist approaches to promote mathematical learning is concluded.


This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 14, Issue 1, January 2019, 147-161

Publication date: 21 Dec 2018

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