Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

Advancement of self-regulation during complex problem solving and the development of strategical reasoning are among the central educational goals linked to 21st century skills. In this paper we introduce the notion of "Stepped Tasks", which are specially designed in Top-Down structure to achieve these goals in mathematics instruction.…

Video recordings of instruction have been a mainstay for supporting conversations about teaching by representing particularities of instruction and by presenting the viewer with a multitude of details for interpretation. In this essay, we contrast non-fictional videotapes of actual classroom interaction with fictional animations of classroom…

The mathematical curriculum of the next millennium should harness children's motivation without losing their mathematics. Envisages that the computer might offer just the context to help do this. Presents snapshots from two case studies. (Contains 18 references.) (ASK)

Discussed are supercalculator capabilities and possible teaching implications. Included are six examples that use a supercalculator for topics that include volume, graphing, algebra, polynomials, matrices, and elementary calculus. A short review of the research on supercomputers in education and the impact they could have on the curriculum is…