Learning to see distinctions through learning studies: Critical aspects as an example of pedagogical content knowledge

The purpose of this paper is to identify changes in teacher’s pedagogical content knowledge (PCK) as a result of their participation in two learning studies in mathematics.

A group of four mathematics teachers and the researcher of this paper explored two objects of learning related to division with decimal numbers and the straight-line equation in a learning study (LS) project over the course of one year. The data used consist of eight video-recorded lessons, four written student tests, eight student interviews and 14 recorded team meetings. The analysis was based on the variation theory principle about learning (Marton, 2015) and on ontological assumptions within the phenomenographic approach (Marton, 1981).

It was found that teachers’ PCK was changed and refined through the LS process in terms of differences in ways of understanding and discussing critical aspects related to each object of learning. In the paper, the terms “presumed critical aspects” and “explored critical aspects” are used to illustrate this difference. Furthermore, the concepts are viewed in relation to three subdomains of PCK: knowledge of content and curriculum (KCC), knowledge of content and students (KCS) and knowledge of content and teaching (KCT).

Bringing out the difference between “presumed critical aspect” and “explored critical aspects” advances the view that critical aspects are dynamic and emergent in practice – in the interaction between teaching and student learning. The research exposes “explored critical aspects” as a specific form of PCK in which KCC, KCS and KCT are intertwined.