How to develop mathematics for teaching and understanding

Susanne Prediger has written an article about How to develop mathematics-for-teaching and for understanding: the case of meanings of the equal sign. The article was published online in Journal of Mathematics Teacher Education on Thursday last week. Point of departure in her article is the very important question about what mathematical (content) knowledge prospective teachers need. A main claim which is raised already in the introduction is: "Listen to your students!" In the theoretical background, Prediger takes Shulman's classic conceptualization of three main categories of content knowledge in teaching as point of departure:

1. Subject-matter knowledge
2. Pedagogical-content knowledge
3. Curricular knowledge

She continues to build heavily on the work done by Hyman Bass and Deborah Ball (e.g. Ball & Bass, 2004), and she goes on to place her own study in relation to the work of Bass and Ball:

Whereas Bass and Ball (2004) concentrate on the first part of their program, namely, identifying important competences, this article deals with both parts, the analytical study of identifying, and the developmental study of constructing a sequence for teacher education, exemplified by a sequence in the course entitled school algebra and its teaching and learning for second-year, prospective middle-school teachers.

Here is the abstract of Prediger's article:

What kind of mathematical knowledge do prospective teachers need for teaching and for understanding student thinking? And how can its construction be enhanced? This article contributes to the ongoing discussion on mathematics-for-teaching by investigating the case of understanding students’ perspectives on equations and equalities and on meanings of the equal sign. It is shown that diagnostic competence comprises didactically sensitive mathematical knowledge, especially about different meanings of mathematical objects. The theoretical claims are substantiated by a report on a teacher education course, which draws on the analysis of student thinking as an opportunity to construct didactically sensitive mathematical knowledge for teaching for pre-service middle-school mathematics teachers.

References:
Bass, H., & Ball, D. L. (2004). A practice-based theory of mathematical knowledge for teaching: The case of mathematical reasoning. In W. Jianpan & X. Binyan (Eds.), Trends and challenges in mathematics education (pp. 107–123). Shanghai: East China Normal University Press.