Mariam Haspekian

An "Instrumental Approach" to Study the Integration of a Computer Tool into Mathematics Teaching: The Case of Spreadsheets

This article reports on research focused on the integration of a specific computer tool, the spreadsheet, into mathematics teaching. After presenting some important results obtained by research in this area, we revisit these in the light of an instrumental approach, which we perceive as essential to analyse the construction of mathematical meanings in spreadsheet environments and to understand better the questions of technological integration. Then, these theoretical elements are used in order to design an exploratory experiment with grade 7 pupils and analyse its results.

Connecting and Integrating Theoretical Frames: The TELMA Contribution

This paper presents the methodology developed within TELMA for connecting and integrating the theoretical frames used by the different teams for studying the design and use of interactive learning environments in mathematics education. Two case studies are then analysed and compared in order to illustrate the methodology and the results it can lead to. The papers ends by a more general discussion about the outcomes of the experimental work developed within TELMA and the perspectives it offers for approaching theoretical fragmentation.

Teachers' instrumental geneses when integrating spreadsheet software

The spreadsheet is not a priori a didactical tool for mathematics education. It may progressively become such an instrument through the process of professional geneses on the part of teachers. This chapter describes the beginning of such a genesis, and presents some results concerning teachers’ professional development with ICT by examining the outcomes of two different sets of data. Theoretical notions, such as instrumental distance and double instrumental genesis supported the analysis of data leading to a comparison of a teacher integrating spreadsheets, for the first time in her practices, with the practices of teachers who are more expert with spreadsheets. The similarities found in the ways they use the tool leads to some hypotheses on the importance of these common elements as key issues in teachers’ ICT practices.

Introduction to the Theory of Didactical Situations (TDS)

The chapter briefly introduces the Theory of Didactical Situations (TDS) by referring to the data from Chap. 2. TDS provides a systemic framework for investigating teaching and learning processes in mathematics, and for supporting didactical design. The theory is structured around the notions of a-didactical and didactical situations and includes a corpus of concepts relevant for teaching and learning in mathematics classrooms.

Starting Points for Dealing with the Diversity of Theories

This chapter presents the main ideas and constructs of the book and uses the triplet (system of principles, methodologies, set of paradigmatic questions) for describing the theories involved. In Part II (Chaps. 3, 4, 5, 6, and 7), the diversity of five theoretical approaches is presented; these approaches are compared and systematically put into a dialogue throughout the book. In Part III (Chaps. 9, 10, 11, and 12), four case studies of networking practices between these approaches show how this dialogue can take place. Chapter 8 and Part IV (Chaps. 13, 14, 15, 16, and 17) provide methodological discussions and reflections on the presented networking practices.

Preparing Young Researchers in Mathematics Education: Beyond Simple Supervising

The mentoring of doctoral students towards research in mathematics education is seldom considered in scientific debates. The Artigue Colloquium provided an opportunity both for paying tribute to Michele Artigue’s work as a supervisor of young researchers, and for engaging in a debate about this specific, complex, but crucial, mission of researchers. This chapter, beyond highlighting outcomes of the session held at the Colloquium, offers an entry into a more general reflection on the preparation of young researchers in mathematics education.