Examines how components of the concept of function (variable, domain, and range) and the process-object duality in its nature emerge as highly relevant to student learning in various mathematical contexts related to linear and abstract algebra. (Contains 22 references.) (ASK)

Critical mathematics education cannot be translated into principles. Aims to search for a working philosophy of mathematics for critical mathematics education. Concludes that aporism attempts to consider mathematics in its social, cultural, and political complexities, and to express uncertainties about mathematics' possible role as an educational…

Describes a study which took place in a grade 9 classroom that consisted of five groups with 3-5 pupils in a group. Pupils were required to calculate the areas of a number of shapes on a geoboard. Concludes that a teacher working with pupils in small groups brings new challenges for mathematics teachers. (Contains 11 references.) (ASK)

Addresses the concept of mathematical definition as well as the definitions of different mathematics concepts. Focuses on the possibility of defining a mathematical concept in several ways based on logical relationships between different mathematical statements related to the concept. The choice of one of these statements as definitional plays a…

Discusses the elements of an interactional theory concerning content-related learning in classroom situations. Clarifies the concept of culture and outlines the narrative character of the reconstructed classroom culture. Presents empirical results to create elements of a theory of interaction of content-related learning. (Contains 37 references.)…

Investigates magical mathematical moments in order to seek to understand what they are and how they happen, to look for examples, and to reflect on their impact on students' mathematics learning. Describes magical moments as they appear in references in the literature and characterizes those moments. Provides examples from classrooms. (Contains 27…

Describes the different types of reasoning in scientific research activity. Outlines three different but complementary ways to integrate history into the presentation of science. Considers and illustrates the close historical relationship between mathematics and physics. (Contains 50 references.) (ASK)

Discusses Brousseau's work on the theory of didactical situations in mathematics and its applications in mathematics classrooms which do not address the collection of obvious components, but instead discuss phenomena by analyzing knowledge in given situations. Meanings emerge in situations engineered by analyzing a situation and developing an…

Explores how teachers can support English-language learners in learning mathematics. Uses discourse perspective to analyze participation in mathematical discussions. Examines a lesson from a third-grade mathematics discussion of the geometric shapes of a tangram puzzle. Contains 20 references. (ASK)

Discusses the gap between educational theories and practice and focuses on constructivism in mathematics classrooms. Contains 12 references. (ASK)

Focuses on books by Brown, Dowling, and Davis that constitute significant and substantial attempts to broaden and deepen the nature of discourse about, and activities in, the field of mathematics education. (ASK)

Provides examples of algebraic geometry mathematicians who operated as philosophers of mathematics. Argues that there is no good reason why philosophizing about mathematics should be part of any given mathematician's activities. (ASK)

Describes the meanings given to the word "ethnomathematics." Discusses three important publications on ethnomathematics, the new inspiration provided by the First International Conference on Ethnomathematics, and examines the critical mathematical direction represented by Powell and Frankenstein's collection. Contains 14 references. (ASK)

Word problems have several purposes in mathematics education. Concentrates on two of these purposes--word problems as applications and word problems as mental manipulatives--and compares them with each other. (ASK)

Describes the experience of being a researcher in mathematics classrooms. Offers background-research information and describes the research context. Presents a series of episodes to stimulate reflections. Contains 12 references. (ASK)