Symposium: Multiplicative Thinking: Enhancing the Capacity of Teachers to Teach and Students to Learn

Abstract

Multiplicative thinking is a key aspect of primary and middle school mathematics and is considered to be a predictor of students’ capacity to progress beyond basic mathematical learning. It is characterised by a complex set of connecting ideas about which teachers need to have a broad and deep understanding. The study on which this symposium is based began in 2014 in Western Australia. It has involved over 1900 primary school students of ages 9 to 11 years, approximately 120 teachers, and 16 schools. This symposium presents an overview of the project and then focuses on the New Zealand phase of the project. Assessment of students’ multiplicative thinking in the form of a written quiz and semi-structured interviews enabled teachers and researchers to identify students’ knowledge and understanding of multiplicative concepts and led to the structuring of a targeted teaching program over several months. Parallel pre and post quizzes were used to investigate the extent of student learning that occurred. A highly significant increase in student attainment was noted. The use of manipulative materials to identify the extent of students’ multiplicative thinking was also investigated through semi-structured interviews. Teachers’ content knowledge was explored with particular emphasis on the use of student tasks targeting specific aspects of multiplicative thinking. It was found that teachers became more confident in teaching multiplicative concepts, showed a greater awareness of connections between ideas, and demonstrated a growing awareness of the importance of explicit mathematical language.