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)

Views the mathematics curriculum in terms of things that can be worked out by someone (necessary) and things about which everyone needs to be informed (arbitrary). This view clarifies the roles that teachers and students have within the complexities of teaching and learning. (Contains 11 references.) (ASK)

Conducts an inquiry into teachers' (N=33) understanding of relevance as it refers to relating students' learning mathematics to their everyday experiences. Presents an excerpt of a discussion of a football log table set in an actual mathematics examination as an illustration of the nature of what occurred in the group interviews. (Contains 19…

Discusses the dichotomy right/wrong in students' images of mathematics as they start to work at becoming teachers. Shares stories as teacher educators with a filter of dichotomies that seem to be avoidable. Identifies ways to overcome those dichotomies. (Contains 18 references.) (ASK)

Investigates the mathematical practices used by a home designer and builder. Points out the existence not only of diverse forms of mathematics, or ethnomathematics, but also of diverse ways of doing mathematics. Argues that these idiosyncratic ways of mathematizing, whether pertaining to individuals or to entire cultural groups, should be…

Follows up in more detail a previous interview-based study in which were outlined some features of a mathematicians' views and research practices on what interviewees had to say about the topic of intuition. Concludes that intuition, insight, or instinct was seen by most of the 70 mathematicians interviewed as a necessary component for developing…

The mechanism of routine practice and problem solving that is used as a method of teaching and learning is not simply interpreted as a way in which students only mechanically imitate and memorize rules and skills. Manipulative practice is the genetic place of mathematical thinking and the foundation of concept formation. (ASK)

Genre analysis is a form of discourse analysis that can provide useful and sometimes surprising new perspectives on understanding teaching and learning. Uses two examples to illustrate the application of genre analysis in mathematics education. (Contains 23 references.) (ASK)

Ten seventh-grade students were interviewed to provide information about the conceptual frameworks they have about points and lines. Their responses are discussed and compared to those given by 10 elementary education seniors. Implications of responses for mathematics instruction are addressed. (JN)

Discusses insufficiency of the linear method and some informal practices (or heuristics) used by expositors in trying to alleviate it. Uses the Cantor-Bernstein theorem to illustrate the linear proof, structuring, and the structure proof. Argues that the informal practices considered be consistently applied to the presentation of pivots and…