Online resources are widely used for educational purposes, such as the training of skills. For algebra education in particular, online resources are expected to contribute to skill mastery in an efficient and effective way. However, studies that underpin these claims through a randomized experiment are scarce. To experimentally investigate the…

In this paper we describe a touchscreen application called "TouchCounts," which is designed to support the development of number sense in the early years. We first provide an a priori analysis of its affordances. Then, using Sfard's communicational approach, augmented by a focus both on the role of the body--particularly the fingers…

The increasing availability of new technologies in schools provides new possibilities for the integration of technology in mathematics education. However, research has shown that there is a need for new kinds of task that utilize the affordances provided by new technology. Numerous studies have demonstrated that dynamic geometry environments…

This article analyses students' thinking as they interacted with a dynamic geometric sketch designed to explore eigenvectors and eigenvalues. We draw on the theory of instrumental genesis and, in particular, attend to the different dragging modalities used by the students throughout their explorations. Given the kinaesthetic and dynamic…

The design and arrangement of appropriate automatic feedback in digital learning environment is a widely recognized issue. In this article, we investigate the effect of feedback on the design and the results of a digital intervention for algebra. Three feedback principles guided the intervention: timing and fading, crises, and feedback variation.…

How do instructors guide students to discover mathematical content? Are current explanatory models of pedagogical practice suitable to capture pragmatic essentials of discovery-based instruction? We examined videographed data from the implementation of a natural user interface design for proportions, so as to determine one constructivist tutor's…

In this paper, we describe the design and implementation of computer programming activities aimed at introducing young students (9-13 years old) to the idea of infinity, and in particular, to the cardinality of infinite sets. This research was part of the "WebLabs" project where students from several European countries explored topics in…

This paper reports from a case study with teachers at two schools in Norway participating in developmental projects aiming for inquiry communities in mathematics teaching and learning. In the reported case study, the teachers participated in one of the developmental projects focusing on implementation and use of computer software in mathematics…

In an attempt to study the emerging questions about design of mathematical tasks that could support the solving of challenging problems, we designed two settings of interactive diagrams that share an example represented as an animation of multi-process motion but differ in their organizational functions. The interactive settings, each comprising…

Integrating technology in school mathematics has become more and more common. The teacher is a key person in integrating technology into everyday practice. To understand teacher practice in a technological environment, this study proposes using two theoretical perspectives: the theory of technological pedagogical content knowledge to analyze…

Seeking to contribute to our understanding of the role of educational technology in mathematical learning, this paper takes a socio-genetic approach to tracing the ways technology becomes part of classroom mathematical activity. It illuminates the reflexive processes of inscription, translation and re-inscription as technologies evolve by…

In this paper I report a lengthy episode from a teaching experiment in which 15-Year 12 Greek students negotiated their definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the notion of derivative and to the general case of tangent to a function graph. Its design was based on…

This paper presents the development process of a "praxeology" (theory-of-practice) for supporting the teaching of proofs in a CAS environment. The characteristics of the praxeology were elaborated within the frame of a professional development course for teaching analytic geometry with CAS. The theoretical framework draws on Chevallard's…