Aspects of mathematical knowledge for teaching: a qualitative study

Abstract

We present a qualitative study aiming at investigating secondary school teachers’ Mathematical Knowledge for Teaching regarding the dense ordering of rational numbers. Fifteen secondary math teachers were asked to evaluate the responses of hypothetical students, explain students’ thinking, and give feedback. The accuracy of the evaluation, the quality of the explanation, and the use of counterexamples were examined. The results showed shortcomings in various categories of Mathematical Knowledge for Teaching, such as Common Content Knowledge and Specialized Content Knowledge, Knowledge of Content and Students and Knowledge of Content and Teaching.