Thomas J. Cooney

Considering the Paradoxes, Perils, and Purposes of Conceptualizing Teacher Development

Mathematics teacher education is a composite of many influences and purposes not the least of which is the propensity of many teachers to provide students with a caring environment in which to learn mathematics in an efficient manner. But reform teaching, rooted in Dewey’s notion of education in a democratic society, is predicated on processes that evoke reasoning and problem-solving not just efficiency of providing information. The education of teachers to teach from such a process-oriented perspective is fraught with difficulty and thus presents a certain moral dimension which is considered in this chapter. Research indicates that change away from predictability and toward the problematic is often a difficult journey for teachers. A theoretical perspective for conceptualizing teachers’ professional development is offered along with an analysis of the paradoxes and perils associated with implementing reform-oriented teacher education programs.

Inservice Mathematics Teacher Education: The Importance of Listening

This chapter addresses issues related to practice and research in inservice teacher education programs. Some issues are addressed through the eyes of Maria, an experienced teacher, who participates in an inservice program and who struggles to improve her teaching of mathematics. Considered are Maria’s personal goals for teaching, her expectations for inservice programs, and her perceptions about self as a teacher researcher as she strives to understand the research literature. The chapter draws upon literature related to both practice and research in teacher education, expectations for inservice programs, and conceptualizing inservice as a context for integrating theory and practice. Fundamental to the chapter is the importance of listening for the creation and conduction of inservice programs.

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.

Content Representation in Mathematics Instruction: Characteristics, Determinants and Effectiveness

Publisher Summary This chapter describes characteristics, determinants, and effectiveness of content representation in mathematics instruction. A characteristic feature of mathematics instruction is that its mathematical content can be represented in a variety of forms. The forms often differ widely in their complexity. Two key aspects of content representation, each captured in one variable, were selected as the foci for studying decisions about content representation. The first variable, VARIETY, was simply a count of the number of different content representations emphasized, or at least used for instruction on a given subtopic. The other aspect of content representation considered here was the relative balance in instruction on a subtopic between perceptual form representations, and symbolic form representations. Perceptual forms were those which depended on a central perceptual or iconic element. Symbolic forms were those which depended primarily on abstract and symbolic elements without the presentation of a figural element.

The Begle Memorial Series on Research in Mathematics Education

This paper is one of a series of presentations at this Congress commemorating the work of Ed Begle. Begle’s (1979) last work, “Critical Variables in Mathematics Education”, served as a basis for these presentations. In particular, I will address “The use of critical variables to organize research, problems of synthesizing research, and the kind of empirical research that would be most useful to mathematics education.”

The Profession of Teaching

The 1975 report of the National Advisory Committee on Mathematical Education (NACOME) identified the lack of data regarding teacher education programs for mathematics teachers, particularly secondary teachers (NACOME, 1975: 144, 145). In response to this need for baseline data the Commisssion on the Education of Teachers of Mathematics (CETM) undertook a survey of preservice mathematics teacher education programs (elementary and secondary). Questionnaires were prepared, tested, and revised. In 1977 the 535 institutions accredited by the National Council for Accreditation of Teacher Education for the preparation of teachers in the U.S. and 48 Canadian institutions involved in such preparations were sent questionnaires. Fifty-six percent of the forms were completed. An analysis of the responses on the basis of size of institution and geographic region satisfied the members of CETM that the survey was representative. The data collected is available through ERIC (Sherrill, James).