In recent years computer algebra systems (CAS) have become an integrated part of the upper secondary school mathematics program. Despite the many positive possibilities of CAS, there also seems to be a flip side of the coin in relation to actual difficulties in learning mathematics, not least because a strong dependence on CAS for mathematical…

In certain digital environments, "hot-spots" are key infrastructural pieces that allow the dynamic construction and re-construction of mathematical figures. We shall discuss their existence with respect to what we call user-environment co-actions, describing how they are sustainable bi-directional processes that have the potential to ground and…

The algebraic expertise that mathematics education is aiming for includes both procedural skills and conceptual understanding. To capture the latter, notions such as symbol sense, gestalt view and visual salience have been developed. We wonder if digital activities can be designed that not only require procedural algebraic skills, but also invite…

The ability of mathematics teachers to decompress mathematics and to move between representations are two key features of mathematical knowledge that is usable for teaching. This article reports on four pre-service secondary mathematics teachers learning the mathematics of annuities. In working with spreadsheets students began to make sense of…

Discusses children's use of spreadsheets and the access that this gives to the instantaneous production of a variety of graphs. (10 references) (MKR)

Discusses the view of numeracy as the culture of utility in mathematics education in more technological society. Provides examples from different cultures of the workplace and computer uses in mathematics classrooms. Contains 30 references. (ASK)

Reflects on some aspects of learning mathematics that emerged along the way in creating a turtle-based exploratory tool for non-Euclidean geometry. Contains 14 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.…

Presents a case study as a framework within which to discuss the concepts of function and their representations. (KHR)

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)

Outlines the approach of a study that aimed to observe young children as they constructed meanings for randomness in computer-based setting. Provides a snapshot of two children working with the tools made available in that setting. Uses this picture to begin the formulation of a theoretical framework for the construction of meaning in one…

Presents a study to describe and understand the thinking processes of students in a computer environment while undertaking mathematical tasks related to the differentiation of functions defined on real numbers. Describes two different approaches, the visual and the algebraic approach, in the thinking processes of calculus students. (Contains 19…

Investigates young people's expression of mathematical ideas with a computer, the nature of mathematical practices, and the problem of mathematical meaning from cognitive and socio-cultural perspectives. Describes a mathematical activity system designed for learning and the role of digital technologies in helping to understand and reshape the…

Discusses the impact that the relationship between people and mathematics could have on the development of pure and applied mathematics. Argues for (1) a growing interest in philosophy, history and sociology of science; (2) new models in educational and psychological research; and (3) a growing awareness of the human factor in technology,…

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)