Categorizes the purposes of proof in mathematics and the mathematics classroom as proofs that convince or explain knowledge about mathematical truth, proofs that justify the use of terminology, and proofs that illustrate technique. Includes suggestions for pedagogy. (KHR)

Discusses a number of Theo van Doesburg's paintings concerning arithmetic composition. (KHR)

Describes episodes from work with a small group of 8th grade students who were working independently on a geometry course. Uses Geometer's Sketchpad for the tasks. Discusses students' reasoning skills and their interpretation of the painting in terms of the mathematical properties and relationships. (KHR)

Presents and discusses numeracy as an everyday competence in which mathematics is an integrated but identifiable part. Describes differences between numeracy at work and mathematics in school from the study of semi-skilled workers' tasks and functions. Outlines possible consequences for adult vocational education. (KHR)

Focuses on the activity system of school-teaching mathematics and the impact of mathematical modeling. Describes the Applications of and Modeling in School Mathematics Project (AMSMAP) which investigates teachers' mathematical modeling and its relationship to a hypothesized school mathematical modeling activity system. Discusses the notion of an…

Investigates what the role of arguments from physics within mathematical proof is, and how this role should be reflected in the classroom. Presents examples showing the fruitfulness of center of gravity arguments in terms of geometrical configuration and the laws of the lever. Discusses educational advantages of the use of arguments from physics…

Reports on a case study of a student who constructs formalism not from processes of quantification, but from his own visuospatial imagery. Rather than construct new objects from cognitive processes, the student reflects on mental objects already in mind and refines them to build an interpretation of the formal theory. This example leads to…

Reviews issues related to the field of ethnomathematics. Discusses ethnomathematics from the south of Brazil with the signs of inequality and injustice that prevail there. Analyzes methodological aspects of research on the "ethnomathematics approach". (Author/MM)

Discusses a class on subtraction or difference-finding, problems such as "There are eight white flowers and five red flowers, how many more white flowers are there than red flowers?" used in the teaching of Japanese first grade children. Describes three instances of introductory teaching of "difference-finding" problems in the first grade.…

Describes and reflects on a research journey from a theoretical perspective which sought to understand what it means in practice to "become critical". Based on a South African curriculum that reflects upon aspects of conflict and dialogue in mathematics pedagogy. (MM)

Proposes that recent shifts in the representation of knowledge to a focus on practices and activities have profound implications for students' learning of mathematics. Discusses relationships between knowledge, practice, and identity in the mathematics classroom. (Author/MM)

Considers what value there could be in talking of institutional trauma and connecting it to elements of the theory of trauma in a psychoanalytic setting. Seeks out the origin of these traumas in the successive crises that the mathematical knowledge of secondary teachers has had to confront over the course of history. (Contains 12 references.) (ASK)

Discusses some aspects of learning to read the process of the variation in congruence and relate it to the original geometry of the sphere since it touches on more general questions about how models are appropriated and used. Presents a learning episode that implemented projective models for both spherical and hyperbolic geometry in Object Logo.…

Discusses the question "why teach mathematics to all students"? Clarifies, elaborates, and abdicates a previous article on the same subject. (Contains 18 references.) (ASK)

The aesthetic dimension plays a central role in determining what mathematics proves personally and epistemologically relevant to children. Presents an example of a learning environment that attempts to explore this dimension and describes a small study that examined the responses of middle school students to this environment. (Contains 27…