Abstract
AbstractAccording to the guidelines of the Didactic Engineering as a research methodology and in complementarity with the Didactic Situations Theory, we will show how Didactic Engineering and the Didactic Situations Theory can be articulated to study integer sequences. We will present two examples of applications of this articulation between Didactic Engineering and the Didactic Situations Theory to the study of numerical sequences and it is our intention to describe the main elements of two initial stages of Didactic Engineering, namely, Preliminary Analysis and Design and a priori Analysis. We will highlight the conception of didactic situations and the possible behaviors and resolution of the students before the problem situations, organized for purposes of experimentation.
Highlights
The work presented here aims to reflect on some models of generalization and extension of numerical sequences
In line with the guidelines of Didactic Engineering as a research methodology and in complementarity with the Didactic Situations Theory, which allows a thorough analysis of the phenomena related to teaching and learning the topic of sequences, we will describe the main elements that constitute the two initial stages of a classic Didactic Engineering (Didactic Engineering of 1st generation), namely, the Preliminary Analysis stage and
Many other works related to Didactic Engineering can be found in the literature, such as those by Godino, Rivas, Arteaga, Lasa and Wilhelmi (2014), where the authors analyzed the possible connections between Didactic Engineering and the approach to research in the teaching of Mathematics – “Design-based research” (DBR) – having concluded that Didactic Engineering can be seen as a particular case of DBR, linked to the Didactic Situations Theory, or that DBR is a generalization of Didactic Engineering that uses other theoretical frameworks such as foundations for planning teaching experiences
Summary
The work presented here aims to reflect on some models of generalization and extension of numerical sequences. According to Warfield (2006), Brousseau (1997) reflected on these questions/ reflections (1 – what conditions guaranteed a rigorous construction of mathematical knowledge based on a model of teaching and learning systems; 2 – determining the conditions for scientific observation of teaching activities), and formed the opinion that psychology should not be used solely and exclusively to answer them. At the time, he pointed out three main reasons that led him to take this position, namely: the fact that Piaget’s work focuses on each child in an individual way; the fact that constructivist approaches are insufficient to model the learning processes of mathematics in a satisfactory way – that is, their social and cultural dimensions are not sufficiently taken into account These three elements are part of a dynamic and complex relationship – the didactic relationship – where the interactions between teacher and students are considered, mediated by the knowledge that determines how these relationships will develop
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