Development of mathematical concepts as basis for an elaborated mathematical understanding

Annemarie Agnes Fritz-Stratmann

doi:10.4102/sajce.v3i1.31

Abstract

A common theme of models of conceptual growth is to establish the hierarchical structures of abilities that can be interpreted along developmental lines. Integrating the literature on the development of mathematical concepts and skills in children, a comprehensive 6 level model for describing, explaining and predicting the development of key numerical concepts and arithmetic skills from age 4 to 8, is proposed. Two studies will be presented. In the first study, 1095 preschool children completed a mathematics test (MARKO-D0) based on a 5-level model. The test fitted with a one-dimensional Rasch model. The extension of the model to a sixth level was verified in a new study: 312 first-graders took part in a mathematics test based on the six levels (MARKO-D1). In order to check whether the data of both samples adhered to the principle of unidimensionality, the data of MARKO-0 and MARKO-1 were used in a common analysis for comparative purposes. The applicability of these findings for a qualitative diagnostics and an adaptive training will be discussed.

Highlights

The acquisition of complex cognitive skills such as reading, writing and calculating depends on a variety of ‘building block systems’ (Spelke, 2000:1233)
Studies from the past three decades indicate that the brain is equipped, from birth, with domainspecific core knowledge systems, which allow for initial representations and reasoning about particular kinds of events and entities such as objects, persons, places and numerosities (Spelke, 2000)
It is necessary to construct a developmental model with which the performance of kindergarten children can be described qualitatively and which forms the basis for the development of adaptive training programmes

Summary

Introduction

The acquisition of complex cognitive skills such as reading, writing and calculating depends on a variety of ‘building block systems’ (Spelke, 2000:1233). Developmental models of reading and writing have promoted the diagnostics and instruction methods for these skills, as well as the support of children who have difficulties with acquiring them (e.g., Ehri, 1995). There is no empirically validated model for the development of mathematical competences available, and the accompanying training of mathematical knowledge, at a pre-school age, is still in its early stages. To improve this situation, it is necessary to construct a developmental model with which the performance of kindergarten children can be described qualitatively and which forms the basis for the development of adaptive training programmes

Modelling mathematical development

Operationalisation of the mathematical levels

Level Tasks

Findings

Discussion