Abstract
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.
Highlights
Learning in general, and in particular mathematics learning depends on many factors
A variety of models and theories of instructional design have been developed in the field of Mathematics Education and for specific areas
In this article we argue that a mixed instructional model favours the acquisition of mathematical knowledge and the teacher’s management of the student’s emerging knowledge
Summary
The selection of situations – problems which contextualize and give meaning to curricular contents, the way to interact and the resources used are determining factors in the students’ learning. This complexity explains that there are different instructional theories supported by different epistemological, psychological and pedagogical assumptions. A variety of models and theories of instructional design have been developed in the field of Mathematics Education and for specific areas. “The constructivist learning framework is a foundation for today’s K-12 mathematics reform. This preference can be observed in the curricular orientations of different countries, which are supported by the adoption of constructivist or socioconstructivist theoretical frameworks. When challenged with appropriately chosen tasks, students become confident in their ability to tackle difficult problems, eager to figure things out on their own, flexible when exploring mathematical ideas and trying alternative solution paths, and willing to persevere” (NCTM, 2000, p. 20)
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