Perspectives on pre-service teacher knowledge for teaching early algebra

Abstract

This paper examines a pre-service teacher’s content knowledge for teaching early algebra from two perspectives, i.e. using Rowland’s Knowledge Quartet theory and Ball’s framework for Mathematical Knowledge for Teaching (MKfT). The study intends to examine the differences between the inferences using each framework and to reflect on how they may help us to better understand the knowledge needed for teaching early algebra. Both perspectives are used to interpret selected episodes from a videoed Grade 3 patterns lesson. The findings show that the two perspectives are simultaneously complementary and distinct in both purpose and outcomes. The Knowledge Quartet identifies and describes ways in which the teacher’s content knowledge for teaching is enacted in the classroom including those aspects that need reinforcement. The MKfT scheme identifies situations and tasks in teaching where content knowledge emerges including instances where a broader base of knowledge for teaching is required. The results of the analysis show how each perspective emphasises different aspects of teacher content knowledge and, together, provide a more holistic account of what happens in developing knowledge for teaching patterns. They highlight the difficulty for teachers in helping learners to shift from focusing solely on number pattern to a simultaneous focus on function, a transition central to the teaching of early algebra.