Teachers’ Perceptions of Risk when Teaching Mathematics through Problem Solving: Implications for Leading Pedagogical Change

Abstract

The ability of educational leaders to improve teaching and learning through affecting teachers’ pedagogy is the primary goal of professional development (Ingvarson, Meiers, & Beavis, 2005). Teaching mathematics through problem solving is currently considered to be a highly effective approach to improving teaching and learning (National Council of Teachers of Mathematics, 2014a). Unfortunately, however, the notion of teaching as telling (speaking, explaining, demonstrating) rather than listening (hearing, seeing, interpreting) is still characteristic of most mathematics classrooms (Suurtamm & Vezina, 2010). Whether teachers embrace a change in pedagogy may depend on the risks teachers’ perceive when considering new approaches in the classroom. The purpose of this study is to explore the risks perceived by mathematics teachers at a large New Zealand secondary school when asked about teaching mathematics through problem solving, investigations and higher order thinking (HOT) tasks. Using an explanatory sequential mixed methods design (Creswell, 2014) teachers were asked to complete questionnaires that recorded their willingness to comply and perceived risk when considering statements about their mathematics teaching. A purposeful sample of teachers then participated in semi-structured interviews. Analyses of these data indicate risks associated with assessment demands and of losing control are two main reasons why teachers may not have employed as much problem solving teaching in the classroom as they may advocate. One teacher, in contrast to the majority, explicitly claimed a perceived risk in not teaching through problem solving. Findings focus on implications for leaders regarding teacher professional learning to support the implementation of a change in pedagogy to a more problem solving approach. These approaches include attending to teachers’ ‘theories of action’ (Argyris, 2002) and focusing heavily on shifting the fundamental beliefs teachers hold about how they should teach and how students learn (Ball, 1996). Teachers subject knowledge both in mathematical content and teaching pedagogy (Zehetmeier & Krainer, 2011) would have to be addressed through collaborative professional development that provided relevant resources and strong ongoing support.