Reconstruction of the Interpretation of Geometric Diagrams of Primary School Children Based on Actions on Various Materials -&lt;br /&gt; A Semiotic Perspective on Actions

Lara Kristina Billion

doi:10.29333/iejme/11068

Abstract

This paper adopts a semiotic perspective on mathematical learning according to Peirce, in which the actions on material arrangements are considered the bases for diagrammatic work. The focus is on the learner’s actions using digital and analogue material arrangements which are the starting point for the reconstruction of the learner’s mathematical interpretations. In this paper a qualitative interpretative paradigm is adopted for the reconstruction. Specifically, a semiotic specification of the context analysis according to Mayring and an adoption of Vogel, is carried out. The reconstruction of the mathematical interpretation is presented with a focus on a geometrical problem that third graders are working on. Finally, the results of several cases are compared to identify possible differences between the analysed actions when using digital and analogue material arrangements.

Highlights

A cognitive psychological perspective largely determines the perception of actions on the learning material and the focus is on their function as means of illustration
The aim of this paper is to show which possibilities of reconstruction become available by the semiotic adaptation of context analysis for the investigation of mathematical interpretations
The paper aimed to carry out a semiotic adaptation of the context analysis and to illustrate it with an example

Summary

Introduction

A cognitive psychological perspective largely determines the perception of actions on the learning material and the focus is on their function as means of illustration Following this perspective, actions on the materials will develop action-based schemes which can be transferred to new elements in recurring situations (Aebli, 1980; Floer, 1993; Lorenz, 1993; Piaget, 1998; Radatz, 1993; Wittmann, 1981). The focus of this paper is on the actions themselves and, in a semiotic sense, on the visible actions made on the material Based on these actions, the relationships recognised by the learners will be reconstructed. The comparison of the results of the analysis will eventually lead to the formulation of implications for the use of digital and analogue materials in primary school

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