THIS is a thoroughly good book which deserves to run through many editions. It is not (as its title might suggest) a book on mathematical logic or philosophy: it deals not with the nature of mathematics but with its content. Its purpose is to show, not by general disquisitions but by concrete examples, drawn from almost every branch of pure mathematics, how mathematicians think and what they do. What is Mathematics? An Elementary Approach to Ideas and Methods. By Richard Courant and Herbert Robbins. Pp. xix + 521. (London, New York and Toronto: Oxford University Press, 1941.) 25s. net.

What is Mathematics

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Eurasia Journal of Mathematics, Science & Technology Education

This article addresses issues related to the ways teachers learn mathematics and the teaching of mathematics and the relevance of those ways to their professional development. Preservice teachers' understanding of school mathematics lacks sophistication, a situation that needs to be addressed in mathematics teacher education programs. What is critical is the means by which they encounter and explore the mathematics they will be teaching. Fundamentally, their mathematical experiences need to be congruous with the kind of teaching we would expect of a reflective, adaptive teacher. The article contains both practical and theoretical considerations of how these experiences might be structured. Theoretical orientations for conceptualizing teachers' belief structures are offered as a foundation for conceptualizing teachers' ways of knowing. The moral dimension of teacher education is considered as a backdrop for understanding how teachers come to know.

Conceptualizing Teachers’ Ways of Knowing

Beyond Missionaries or Cannibals: Who Should Teach Mathematics to

Guided by a general critique that asks, Highly qualified for whom?, I problematize recent characterizations of highly qualified mathematics teachers by focusing on the question, Who should teach mathematics to African American children? I discuss how responses to this question in mainstream mathematics education research and policy contexts have drawn on discursive frames that support color-blind racism, that focus only on achievement outcomes, and that propose "missionaries" and "cannibals" as the kinds of teachers most appropriate for African American children. I propose a refocusing of mathematics education research and policy that gives meaningful attention to the ways that African American children experience mathematics in schools and life as African Americans.

Beyond Missionaries or Cannibals: Who Should Teach Mathematics to African American Children?

Scholars of decades past, current researchers, and various reform documents all deal, directly or indirectly, with the question of what constitutes good mathematics teaching. Often good teaching is situated in the context of broader educational goals, such as preparing literate citizenry. Researchers generally define good teaching implicitly with attention to various processes such as reasoning and problem solving. In a series of three interviews, we examined nine experienced and professionally active teachers’ views of good mathematics teaching and how it develops. The interviews were couched in the context of the teachers mentoring student teachers. In general, these teachers thought good teaching requires a sound knowledge of mathematics, promotes mathematical understanding, engages and motivates students, and requires effective management skills. Furthermore, the teachers felt that good teaching is developed from experience, education, personal reading and reflection, and interaction with colleagues. Experience was considered the primary contributor. The article compares and contrasts the teachers’ notions of good teaching with those of various scholars and researchers and positions stated in various reform documents.

What Constitutes Good Mathematics Teaching and How it Develops: Nine High School Teachers’ Perspectives

A Dynamic Way to Teach Angle and Angle Measure.

Sound Off!: Who? How? What? A Strategy for Using History to Teach Mathematics

Who? How? What? A Strategy for Using History To Teach Mathematics.

In this qualitative research study, we sought to understand teachers' conceptions of integrated mathematics. The participants were teachers in the first year of implementation of a state-mandated, high school integrated mathematics curriculum. The primary data sources for this study included focus group and individual interviews. Through our analysis, we found that the teachers had varied conceptions of what the term integrated meant in reference to mathematics curricula. These varied conceptions led to the development of the Conceptions of Integrated Mathematics Curricula Framework describing the different conceptions of integrated mathematics held by the teachers. The four conceptions—integration by strands, integration by topics, interdisciplinary integration, and contextual integration—refer to the different ideas teachers connect as well as the time frame over which these connections are emphasized. The results indicate that even when teachers use the same integrated mathematics curriculum, they may have varying conceptions of which ideas they are supposed to connect and how these connections can be emphasized. These varied conceptions of integration among teachers may lead students to experience the same adopted curriculum in very different ways.

Patricia S. Wilson

Papers

What Constitutes Good Mathematics Teaching and How it Develops: Nine High School Teachers’ Perspectives

A Dynamic Way to Teach Angle and Angle Measure.

Sound Off!: Who? How? What? A Strategy for Using History to Teach Mathematics

Who? How? What? A Strategy for Using History To Teach Mathematics.

Teachers' Conceptions of Integrated Mathematics Curricula.