International Journal of Computers for Mathematical Learning 

About: International Journal of Computers for Mathematical Learning is an academic journal. The journal publishes majorly in the area(s): Educational technology & Science education. It has an ISSN identifier of 1382-3892. Over the lifetime, 182 publications have been published receiving 7768 citations.

Learning Mathematics in a CAS Environment: The Genesis of a Reflection about Instrumentation and the Dialectics between Technical and Conceptual Work.

Abstract: The last decade has seen the development in France of a significant body of research into the teaching and learning of mathematics in CAS environments. As part of this, French researchers have reflected on issues of ‘instrumentation’, and the dialectics between conceptual and technical work in mathematics. The reflection presented here is more than a personal one – it is based on the collaboration and dialogues that I have been involved in during the nineties. After a short introduction, I briefly present the main theoretical frameworks which we have used and developed in the French research: the anthropological approach in didactics initiated by Chevallard, and the theory of instrumentation developed in cognitive ergonomics. Turning to the CAS research, I show how these frameworks have allowed us to approach important issues as regards the educational use of CAS technology, focusing on the following points: the unexpected complexity of instrumental genesis, the mathematical needs of instrumentation, the status of instrumented techniques, the problems arising from their connection with paper & pencil techniques, and their institutional management.

Managing the Complexity of Human/Machine Interactions in Computerized Learning Environments: Guiding Students’ Command Process through Instrumental Orchestrations

Abstract: After an introduction which addresses some basic questions, this article is organized around three points: (1) The theoretical framework of the so-called “instrumental approach” which has been a theme in the last two CAME symposia; (2) A consideration of two processes (instrumentalization and instrumentation) which interact in the instrumental genesis; and (3) The introduction of the idea of instrumental orchestration as a way of allowing the teacher to assist the student’s instrumental genesis.

The complex process of converting tools into mathematical instruments: the case of calculators

Abstract: Transforming any tool into a mathematical instrument for students involves a complex ‘instrumentation’ process and does not necessarily lead to better mathematical understanding. Analysis of the constraints and potential of the artefact are necessary in order to point out the mathematical knowledge involved in using a calculator. Results of this analysis have an influence on the design of problem situations. Observations of students using graphic and symbolic calculators were analysed and categorised into profiles, illustrating that transforming the calculator into an efficient mathematical instrument varies from student to student, a factor which has to be included in the teaching process.

An Exploration in the Space of Mathematics Educations.

Abstract: A mathematical metaphor frames the intentions of this paper. Imagine that we know how to construct an N-dimensional space, ME, in which each point represents an alternative mathematics education -or ame -and each dimension a feature such as a component of content, a pedagogical method, a theoretical or ideological position. Each \"reform\" of mathematics education introduces new points and each fundamental idea a new dimension. Thus, if one considers a particular point (an ame) in ME, among its many \"coordinates\" are a (metaphorical) measure that runs from informal to formal and another that runs from instructionist to constructivist. In the paper I shall define seven more such oppositional principles that have not been recognized in the past as structuring choices in mathematics education.

Integration of Technology in the Design of Geometry Tasks with Cabri-Geometry.

Abstract: Beginning with the gap in France between the institutional support for the use of technology in mathematics teaching and its weak integration into teacher practice, this paper claims that integrating technology into teaching is a long process. The aim of the paper is to identify and analyse the steps in this integration using as an example the evolution over time (3 years) in the design of teaching scenarios based on Cabri-geometre for high school students. The analysis indicates that the role played by the technology moved from being a visual amplifier or provider of data towards being an essential constituent of the meaning of tasks and as a consequence affected the conceptions of the mathematical objects that the students might construct.