Detecting strengths and weaknesses in learning mathematics through a model classifying mathematical skills

Abstract

Through a review of the literature on mathematical learning disabilities (MLD) and low achievement in mathematics (LA) we have proposed a model classifying mathematical skills involved in learning mathematics into four domains (Core number, Memory, Reasoning, and Visual-spatial). In this paper we present a new experimental computer-based battery of mathematical tasks designed to elicit abilities from each domain, that was administered to a sample of 165 typical population 5th and 6th grade students (MLD = 9 and LA = 17). Explanatory and confirmatory factor analysis were conducted on the data obtained, together with K-means cluster analysis. Results indicated strong evidence for supporting the solidity of the model, and clustered the population into six distinguishable performance groups with the MLD and LA students distributed within five of the clusters. These findings support the hypothesis that difficulties in learning mathematics can have multiple origins and provide a means for sketching students’ mathematical learning profiles.

Acknowledgements

This study was part of the doctoral research of the first author of this paper, thanks to support from the Research Center for Psychophysiology and Education of the National and Kapodistrian University of Athens. We are also deeply endowed to Dr Alexandros Dimopoulos for his fundamental contribution in programming the tasks of the experimental battery. We are deeply grateful to Professor Joanne Mulligan and to Professor Marie-Pascal Nöel for her insightful comments and suggestions during the writing of this paper.

Notes

1. The domains are not considered, a priori, to be hierarchical in any way.

2. In particular, many complex mathematical skills such as counting, recognizing patterns, base ten structure, multiplicative reasoning, etc., are not included, since they critically involve more than one domain. Moreover, we see their connection with a particular domain to be heavily based on how they are assessed.

3. Or possibly of other nationalities once the tool has been calibrated on other populations.

4. See http://titiagebuis.eu/Materials_files/comp_dots_version180112.m

5. In this a priori classification we were actually uncertain about the relationship of these 3 tasks with the four proposed domains. In fact, in the classification of skills in the theoretical model we included number lines tasks both in the visual-spatial domain and in the core number domain.

6. For a more complete discussion see volume 42(4) of the Journal of Cross-Cultural Psychology.

7. Since both the tasks that loaded on this component elicit fact retrieval, in the rest of the paper we will refer to this component as facts retrieval domain.