Godino, Juan D.Rivas, HernánBurgos, MaríaWilhelmi, Miguel R.2022-09-302022-09-302019Godino, J.D.; Rivas, H.; Burgos, M.; Wilhelmi, M.R.. (2019). Analysis of Didactical Trajectories in Teaching and Learning Mathematics: Overcoming Extreme Objectivist and Constructivist Positions. International electronic journal of mathematics education. Volume 14 Issue 1, pp. 147-1611306-303010.12973/iejme/3983https://academica-e.unavarra.es/handle/2454/44130There 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.application/pdfeng© 2019 by the authors; licensee Modestum Ltd., UK. Open Access terms of the Creative Commons Attribution 4.0 International License apply. The license permits unrestricted use, distribution, and reproduction in any medium, on the condition that users give exact credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if they made any changes.Mathematics instructionDidactical modelsOnto-semiotic approachProbabilistic notionsTeacher traininginfo:eu-repo/semantics/article2022-09-29info:eu-repo/semantics/openAccess