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

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]