Chris Hurst

Seeking a Balance: Helping Pre-Service Teachers Develop Positive Attitudes towards Mathematics as They Develop Competency

Mathematical competence of teachers continues to be an issue of great interest to mathematics educators within tertiary institutions and it is often thought of simultaneously with the notion of mathematics anxiety. While there has been considerable recent research into the latter, no clear conclusions have been able to be drawn about many aspects of the phenomenon and how it is linked to mathematical competence. Most recently, international studies have highlighted notable differences in the standards of teacher preparation in different countries and in Australia new standards for accreditation of teacher education programs have been drafted. This paper reports on a part of on-going research into mathematics anxiety and competence of pre-service teachers. It uses two small samples of pre-service teachers from different cohorts of a Bachelor of Education course and attempts to identify factors that may help develop positive attitudes towards mathematics as they seek to develop their competency in mathematics. In addition, as a response to greater reported levels of anxiety regarding cognitive and knowledge traits, the paper identifies targeted professional learning and social constructivist teaching as key factors as well as the need to identify personal knowledge of mathematics as a prelude to seeking to become more competent.

Provoking contingent moments: Knowledge for ‘powerful teaching’ at the horizon

Abstract 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.

The Education and Development of Practising Teachers

This chapter reviews Australasian research on the education and development of practising teachers of mathematics. We consider developments in theoretical understandings of professional learning (PL) including conceptualisations of teacher learning and capabilities. Reports of PL programs that have been sites of research are reviewed according to their content foci and the approaches to PL that were adopted. The latter are considered in light of current characterisations of PL. Consideration of ways in which PL programs have been evaluated highlights the difficulties inherent in going beyond teacher self-reports and in linking specific PL programs to outcomes in relation to students’ learning as well as system and policy impacts. In conclusion we present avenues for further research. These include addressing issues of scale and sustainability, assessing the affordances of online delivery of PL, enhancing collaboration between mathematics educators and mathematicians, and better understanding the mechanisms and conditions that contribute to effective PL.