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…

Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as "designing for abstraction." In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing…

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…

The study we present here concerns the consequences of integrating online resources into the teaching of mathematics. We focus on the interaction between teachers and specific online resources they draw on: e-exercise bases. We propose a theoretical approach to study the associated phenomena, combining instrumental and anthropological…

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…

Use of spreadsheets in a beginning algebra course was investigated mainly with regard to their potential to promote generalization of patterns. Less is known about their use in promoting understanding and learning of transformational activities. The overall purpose of this paper is to consider the conceptual aspects of learning a transformational…

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…

This paper focuses on the different ways in which students in lower secondary school (14-16 year olds) experience compound random events, presented to them in the form of combined junctions. A carefully designed ICT environment was developed enabling the students to interact with different representations of such structures. Data for the analysis…

This paper addresses the dialectical relation between theoretical thinking and technique, as they co-emerge in a combined computer algebra (CAS) and paper-and-pencil environment. The theoretical framework in this ongoing study consists of the instrumental approach to tool use and an adaptation of Chevallard's anthropological theory. The main aim…

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…

In undergraduate mathematics courses, pre-service elementary school teachers are often faced with the task of re-learning some of the concepts they themselves struggled with in their own schooling. This often involves different cognitive processes and psychological issues than initial learning: pre-service teachers have had many more opportunities…