Knowledge demands in teaching decimal numbers

Existing frameworks of teachers' knowledge required to teach mathematics do not adequately capture the dynamic aspects of knowledge manifested in teaching practice. In this paper, we examine the knowledge demands that arise in situ, in the course of a teacher listening and responding to students' thinking, while teaching the topic of decimal fractions. We describe how contingent classroom situations pose challenges to the teacher, through an analysis of paired episodes, i.e. episodes of classroom teaching of the same sub-topic by a teacher in two consecutive years, with significant differences in the teacher's responsiveness to student thinking. We explicate the topic-specific knowledge demands posed on the teacher as students make connections between their prior knowledge of whole numbers and fractions with their emerging understanding of decimal fractions. We argue that an abstraction of knowledge demands from a close study of practice and reflection on them can be used to unpack the complex knowledge required by the teachers to teach responsively.