Provoking contingent moments: Knowledge for ‘powerful teaching’ at the horizon
Embargo Lift Date
MetadataShow full item record
Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content knowledge, horizon content knowledge and specialised content knowledge, have been used to describe aspects of such knowledge. Purpose: This paper proposes a model for teacher knowledge in mathematics that embraces and develops aspects of earlier models. It focuses on the notions of contingent knowledge and the connectedness of ‘big ideas’ of mathematics to enact what is described as ‘powerful teaching’. It involves the teacher’s ability to set up and provoke contingent moments to extend children’s mathematical horizons. The model proposed here considers the various cognitive and affective components and domains that teachers may require to enact ‘powerful teaching’. The intention is to validate the proposed model empirically during a future stage of research. Sources of evidence: Contingency is described in Rowland’s Knowledge Quartet as the ability to respond to children’s questions, misconceptions and actions and to be able to deviate from a teaching plan as needed. The notion of ‘horizon content knowledge’ (Ball et al.) is a key aspect of the proposed model and has provoked a discussion in this article about students’ mathematical horizons and what these might comprise. Together with a deep mathematical content knowledge and a sensibility for students and their mathematical horizons, these ideas form the foundations of the proposed model. Main argument: It follows that a deeper level of knowledge might enable a teacher to respond better and to plan and anticipate contingent moments. By taking this further and considering teacher knowledge as ‘dynamic’, this paper suggests that instead of responding to contingent events, ‘powerful teaching’ is about provoking contingent events. This necessarily requires a broad, connected content knowledge based on ‘big mathematical ideas’, a sound knowledge of pedagogies and an understanding of common misconceptions in order to be able to engineer contingent moments. Conclusions: In order to place genuine problem-solving at the heart of learning, this paper argues for the idea of planning for contingent events, provoking them and ‘setting them up’. The proposed model attempts to represent that process. It is anticipated that the new model will become the framework for an empirical research project, as it undergoes a validation process involving a sample of primary teachers. © 2016 NFER.
Showing items related by title, author, creator and subject.
Professional learning for teaching mathematics through problem solving in Indonesian Primary SchoolsSusanta, Agus (2013)This study focused on teacher professional learning about problem solving in the context of selected Indonesian primary schools. Professional learning was conducted via a Lesson Study Cycle. Teachers’ learning was judged ...
An investigation of mathematics teachers' beliefs and practices following a professional development intervention based on constructivist principlesStoker, John (2003)The purpose of this study was to investigate the beliefs and related classroom practices of a selected group of in-service teachers within the context of a mathematics professional development intervention for primary ...
Virtual Field Trips: Using Information Technology to Create an Integrated Science Learning EnvironmentNix, Rebekah Kincaid (2003)This study evaluated a new Integrated Science Learning Environment (ISLE) that bridged the gaps between the traditionally separate classroom, field trip, and information technology milieus. The ISLE model involves a ...