This paper offers a critical analysis of Dubinsky et al. (On Learning Fundamental Concepts of Group Theory; 1994) and proposes, as an alternative to the four axioms and the standard definitions, that permutation and symmetry may be regarded as the fundamental concepts of group theory. (Author)

Addresses the impact of algebraic calculators on mathematics education. Shows how teaching with technology can lead to more efficient teaching and learning, more student-centered learning, and increase teacher value. Recommends that technology is fully embraced in order to perform the mathematics, thus freeing time for students to concentrate on…

Discusses various mathematics topics and focuses on three questions: (1) "What is mathematics?"; (2) "What are good ingredients of teaching/learning mathematics?"; and (3) "What is the role of technology?" (Author/ASK)

This paper presents an analysis of the different types of meanings that an individual may assign to a collection of algebraic symbols depending on the mathematical context in which the symbols are presented and the mathematical knowledge possessed by that individual. Four contexts for the Quadratic Theorem are used to illustrate the ways in which…

The concept of function is considered as foundational in mathematics. Yet, it proves to be elusive and subtle for students. A generic image that can act as a cognitive root for the concept is the function box. This is not a simple pattern-spotting device, but a concept that embodies the salient features of the idea of function, including process…

This book brings together papers by scholars from around the globe on the historiography and history of mathematics and their integration with mathematical pedagogy. Of the three articles in Part 1, "Historiography and Sources", one identifies research trends in the history of mathematics, the second discusses the centrality of problems, and the…

Attempts to describe a notion parallel to number sense, called symbol sense, incorporating the following components: making friends with symbols, reading through symbols, engineering symbolic expressions, equivalent expressions for non-equivalent meanings, choice of symbols, flexible manipulation skills, symbols in retrospect, and symbols in…

Presents a theory of the development of algebraic abstraction that extends Sfard's and Mason's ideas on learners' progress from operational or process-oriented thinking to the abstract or structural perspective. Analyzes secondary school students' approaches to classifying a set of complex equations. (Author/MKR)

The study was conceptualized within the social critical perspective to investigate the effect of gender and socioeconomic background on the students' classroom communication and the hidden curriculum. Year 9 mathematics classrooms in two single-sex private schools were observed during the course of learning one chapter from the same textbook. One…

Discussed are the rationale for, and the benefits accrued from, the use of graphing calculators within all aspects of the secondary mathematics curriculum. Examples are included that highlight specific features of graphing calculators. (JJK)

Discusses areas where teachers may harbor mistaken assumptions about their students' understanding when using graphing calculators: (1) confidence and competence with order of operations, (2) integration of algebraic and graphical knowledge, and (3) scaling a graph. (MKR)

Describes one teacher's reflection concerning the quest to develop an understanding of school mathematics that promotes and sustains students' opportunities for exploration and conjecture. Recounts that a particular student's exploration of the features of parabolas eventually led to an understanding of the quadratic formula precisely because of…

Describes the relationship between language concepts and the basic patterns of mathematical expressions. Suggests ways to improve the reading comprehension, writing ability, and reasoning skills of school and college students by integrating language topics into the mathematics curriculum. Discusses the use of language concepts in algebraic…

Presents the results of a preliminary investigation into the feasibility of teachers constructing their own animations for the mathematics classroom using computer animation tools. Provides examples of animation constructed using "Ani ST" and "Mathematica" programs. Concludes that computer animation has potential to be a…

Advocates that mathematics education reform in urban schools cannot happen without socioeconomic efforts to lessen poverty in inner cities and protect urban America's youth. The paper argues that the most successful reform initiatives will be holistic in nature and that the covert racism and ethnocentrism in educational materials that…