Mathematical competence, teaching, and learning. Reflections on 'Challenges in Mathematical Cognition' by Alcock et al. (2016)

Kerry Lee

doi:10.5964/jnc.v2i1.25

Abstract

In this commentary, I focus on the notion of competence and issues related to the distinction between knowing how mathematical problems are solved versus knowing how to teach mathematics. Although definitions of competence may necessarily be affected by value judgements and thus less amenable to factual answers, providing a defensible definition is important because it affects eligibility for intervention and treatment. One way to tackle this issue is to focus on the identification of prerequisite skills and concepts needed for particular domains of mathematics. Recent work on fraction and algebra has shown that long held assumptions may need to be re-examined. On knowledge versus application, some cautionary notes are made on the importance of not losing sight of translating our knowledge of processes involved in mathematical problem solving into better pedagogical practices. [Commentary on: Alcock, L., Ansari, D., Batchelor, S., Bisson, M.-J., De Smedt, B., Gilmore, C., . . . Weber, K. (2016). Challenges in mathematical cognition: A collaboratively-derived research agenda. Journal of Numerical Cognition, 2, 20-41. doi:10.5964/jnc.v2i1.10]

Highlights

In this commentary, I focus on the notion of competence and issues related to the distinction between knowing how mathematical problems are solved versus knowing how to teach mathematics
Laying out a research agenda is seldom an easy task; the more so when there are multiple investigators and when one is aiming at developing an agenda for the whole field
In the section on mapping predictors and processes of competence development (Alcock et al, 2016, this issue), one question that deserves some attention is how we go about defining competence. This question may fail the authors’ selection and refinement criteria on the grounds that it may not have a factual answer that does not depend on value judgements, it is important because our definition of competence affects directly whether individuals’ achievements are considered adequate

Summary

Introduction

I focus on the notion of competence and issues related to the distinction between knowing how mathematical problems are solved versus knowing how to teach mathematics. Country specific norm-referenced definition of competence, together with likely concerns that these children are performing more poorly than their peers in the same educational system, will likely direct intervention efforts to them.

Results

Conclusion