How to develop mathematics-for-teaching and for understanding: the case of meaningsof the equal sign

摘要

What kind of mathematical knowledge do prospective teachers need forteaching and for understanding student thinking? And how can its construction beenhanced? This article contributes to the ongoing discussion on mathematics-for-teachingby investigating the case of understanding students' perspectives on equations andequalities and on meanings of the equal sign. It is shown that diagnostic competencecomprises didactically sensitive mathematical knowledge, especially about differentmeanings of mathematical objects. The theoretical claims are substantiated by a report on ateacher education course, which draws on the analysis of student thinking as an opportunityto construct didactically sensitive mathematical knowledge for teaching for pre-servicemiddle-school mathematics teachers.