The Changing Role of the Mathematics Teacher
This case-study research investigated changing teacher roles associated with two teachers’ use of innovative mathematics materials at Grade 6. Using daily participant observation and regular interviews with the teachers and the project staff member responsible for providing in-school support, a picture emerged of changing teacher roles and of those factors influencing the process of change. One teacher demonstrated little change in either espoused beliefs or observed practice over the course of the study. The second teacher demonstrated increasing comfort with posing nonroutine problems to students and allowing them to struggle together toward a solution, without suggesting procedures by which the problems could be solved. He also increasingly provided structured opportunities for students’ reflection on activities and learning. Major influences on this teacher’s professional growth appeared to be the provision of the innovative materials and the daily opportunity to reflect on classroom events in conversations and interviews with the researcher.
The Knowledge, Beliefs and Attitudes of the Mathematics Teacher: a model
Official pressure for reforms in the teaching of mathematics overlooks a key factor: the psychological foundations of the practice of teaching mathematics, including the teacher’s knowledge, beliefs and attitudes. Research on teaching and teacher education also under‐emphasises this area, which Shulman terms the ‘missing program’ in research on teacher cognitions. The present paper addresses this lack by proposing an analytic model of the different types of knowledge, beliefs and attitudes of the mathematics teacher, and their relationship with practice. Of particular note is the importance accorded to the teacher’s practical knowledge of the teaching of mathematics (both pedagogical and curricular knowledge), knowledge of classroom organisation, and knowledge of the school context. Also notable is the importance ascribed to the teacher’s beliefs concerning the nature of mathematics, and concerning the processes of teaching and learning mathematics. The model has implications for teacher education, and these are discussed at the end of the paper.
Mathematics Teacher TPACK Standards and Development Model
What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this construct. A Mathematics Teacher Development Model describes the development of TPACK toward meeting these standards. The standards and model provide structured detail to further the work of various groups. The proposals may guide teachers, researchers, teacher educators, professional development consultants, and school administrators in the development and evaluation of professional development activities, mathematics education programs, and school mathematics programs.
Mathematics Teacher Change and Developments
The chapter focuses on impacts of mathematics teachers’ beliefs on their ability and tendency to change. A discussion of common definitions of belief precedes a review of reports about elementary, middle, and high school mathematics teachers’ beliefs from three international research journals (1995–1999). Implications of the reports’ often implicit definitions of beliefs are considered, as well as other implications for teacher change. For example, an assumption that beliefs are dispositions to act in certain ways, rather than simply verbal proclamations, leads to data collection methods that involve both discussions with and observations of teachers. The reports also point out the need to reconsider a tendency to separate teachers’ mathematical and pedagogical beliefs.
Examining the Mathematics in Mathematics Teacher Education
Central to the preparation of mathematics teachers is their preparation in mathematics. Consequently, a careful examination of the nature of teachers’ mathematical experiences is warranted. There are many factors that influence the teaching of mathematics including the historical development of mathematics with its inherent formalism. This linkage will be explored along with a review of research on teachers’ beliefs and knowledge of mathematics as beliefs and knowledge relate to teacher change. We conclude that this research suggests that teachers are not always well positioned to adopt a more reform- and process-oriented teaching style that moves beyond the usual formalism in the teaching of mathematics. Grounded in this review of the literature, three principles for teaching preservice teachers mathematics will be presented. These principles are: (a) treating mathematics as a pluralistic subject, (b) providing teachers with opportunities to understand and reflect on school mathematics, and (c) enabling teachers to experience mathematics as a process. We will discuss and illustrate these principles using a specific mathematical problem solved from a variety of perspectives.
 Clarke, D.M., 1997. The changing role of the mathematics teacher. Journal for Research in mathematics Education, 28(3), pp.278-308.
 Ernest, P., 1989. The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of education for teaching, 15(1), pp.13-33.
 Niess, M.L., Ronau, R.N., Shafer, K.G., Driskell, S.O., Harper, S.R., Johnston, C., Browning, C., Özgün-Koca, S.A. and Kersaint, G., 2009. Mathematics teacher TPACK standards and development model. Contemporary issues in technology and teacher education, 9(1), pp.4-24.
 Wilson, M.S. and Cooney, T., 2002. Mathematics teacher change and developments. In Beliefs: A hidden variable in mathematics education? (pp. 127-147). Springer, Dordrecht.
 Cooney, T.J. and Wiegel, H.G., 2003. Examining the mathematics in mathematics teacher education. Second international handbook of mathematics education, pp.795-828.