We consider the influence of a CAS context on a learner's process of constructing a justification for the bifurcations in a logistic dynamical process. We describe how instrumentation led to cognitive constructions and how the roles of the learner and the CAS intertwine, especially close to the branching and combining of constructing actions. The…

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…

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…

This paper introduces the language associated with a polygon microworld called Polygon R&D, which has the mathematical crispness of Logo and has the discreteness and simplicity of a Turing machine. In this microworld, polygons serve two purposes: as agents (similar to the turtles in Logo), and as data (landmarks in the plane). Programming the…

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…

The goal of this paper is to demonstrate the infrastructural nature of many modern conceptual technologies. The focus of this paper is on conceptual tools associated with elementary types of data modeling. We intend to show a variety of ways in which these conceptual tools not only express thinking, but also mold and shape thinking. And those ways…

This paper sits within the research on the affordances of new technologies in the mathematics classroom and focuses on a specific feature that is available in dynamic geometry environments, i.e. measuring tools, within the context of conjecturing and proving in open geometry problems. We develop a classification of different modalities of…

Describes research using a pedagogic strategy developed during an exploratory work called Active Graphing in which access to spreadsheets allows graphs to be used as analytic tools within practical experiments. Identifies aspects of student interaction with the experiment itself, the data collected and the graphs, and traces the emergence of…

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)

Describes and reports some results from a project designed to evaluate the use of information technology (IT) for teaching and learning on a range of undergraduate mathematics courses at a U.K. university. Focuses on students' tales of resistance, although many students were positive about the use of IT. Suggests that these tales spring from…

This article illustrates how four teacher educators in training were challenged with respect to their epistemology and perceptions of teaching and learning mathematics through their interactions with expressive digital media during a professional development course. The research focused on their experience of communally constructing artifacts and…

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…

The emergence of powerful mathematical computing environments, the growing availability of correspondingly powerful (multi-processor) computers and the pervasive presence of the Internet allow for mathematicians, students and teachers, to proceed heuristically and "quasi-inductively." We may increasingly use symbolic and numeric computation,…