## How to Develop Mathematics-for-Teaching and for Understanding: The Case of Meanings of the Equal Sign

Source: *Journal of Mathematics Teacher Education, 13(1)*: 73–93. (February, 2010).

(Reviewed by the Portal Team)

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 process of defining and developing mathematics-for-teaching. The article investigates 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 proved by a report on a teacher education course. This course 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.

The author concludes that teacher courses, which aim at diagnostic competence for mathematics classrooms, cannot be held by general educators alone, since they need a mathematical focus. The chosen topic, the equal sign, is only one example among many others, which are crucial for classrooms that aim to facilitate understanding instead of pure routines.

The analysis of student thinking not only needs mathematics but also it is an interesting task that helps to develop mathematical knowledge.