This paper describes students' interactions with dynamic diagrams in the context of an American geometry class. Students used the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK[cent sign] model of conceptions, suggests that incorporating technology in mathematics classrooms…

This article explores ways of conceptualizing the design of innovative learning tools as emergent from dialectics between designers and learner-users of those tools. More specifically, I focus on the reciprocities between a designer's objectives for student learning and a user's situated activity in a learning environment, as these interact and…

What makes Dynamic Geometry Environment (DGE) a powerful mathematical knowledge acquisition microworld is its ability to visually make explicit the implicit dynamism of thinking about mathematical geometrical concepts. One of DGE's powers is to equip us with the ability to retain the background of a geometrical configuration while we can…

In this paper, we describe a design experiment aimed at helping students to explore and develop concepts of infinite processes and objects. Our approach is based on the design and development of a computational microworld, which afforded students the means to construct a range of representational models (symbolic, visual and numeric) of…

Analyzes to what extent the computational model of the geometry implemented in a dynamic geometry environment provides models for physical motion, focusing on the continuity issues related to motion. Addresses the issue of the computable representation of knowledge. (Author/MM)

We propose to use didactical theory for the design of educational software. Here we present a set of didactical conditions, and explain how they shape the software design of Cabri-Euclide, a microworld used to learn "mathematical proof" in a geometry setting. The aim is to design software that does not include a predefined knowledge of problem…

Focuses on the role of tools provided by a computer microworld (C.AR.ME) on the strategies developed by 14-year-old students for the area measurement of a non-convex polygon. Interprets and classifies student strategies on a transformation and comparison task into categories in terms of the tools used for their development. (Author/MM)

The capacity of the "Geometer's Sketchpad" to trace the path of points by drawing the position of the point at different times provides a powerful tool to help see how velocities are related. Provides a snapshot of the process, along with the traces. (Author/ASK)

The advent of powerful, affordable output devices offers the potential for a vastly expanded landscape of computationally-enriched mathematical craft activities in education. Craft activities have both intellectual and emotional affordances that are relatively lacking in "traditional" computer-based education. Describes three software applications…

Describes the design and assessment of a video-intensive case-based multimedia tool called HyperMeasure for educating prospective teachers about primary children's mathematical reasoning on linear, area, and volume measure. Reports on a descriptive study of the individual learning of preservice teacher candidates (N=12) using HyperMeasure.…

While many technological capabilities are under development and may turn out to be an optimal future microworld, it is necessary to study the current widespread solution of supporting exploration and learning of school algebra with packages of mathematics software components. Describes and discusses software tools for school algebra. (Contains 45…

Uses of Dynamic Geometry Software (DGS) are often limited purely to a verifying role. Presents a case study that emerged from a project in which DGS formed an integral part of the pedagogical arrangement. The study demonstrates how the contrasting power of DGS might be utilized in a guided discovery setting. (Contains 17 references.) (Author/ASK)

Explores the role of software tools in geometry problem solving and how these tools, in interaction with activities that embed the goals of teachers and students, mediate the problem solving process. Through analysis of successful student responses, shows how dynamic software tools can not only scaffold the solution process but also help students…

Discusses two approaches to solving word problems that consider the verbal text of the problem, and analyze it to obtain its mathematical expression, as well as its numerical solution. Uses two computerized programs for word problems to capture the various strategies employed by the problem solvers. Contains 21 references. (Author/ASK)

Discusses geometry and Dynamical Geometry Software (DGS). Analyses the way DGS-use influences traditional geometry. Highlights changes in the interactions between geometry, computers, and DGS and human users, focusing on changes in the teaching and learning of geometry. Concludes that DGS deeply changes geometry if it is taken as a human activity…