The Research Projects

    2003-2007. The 2003-2007 project, which was titled, “The Intertwining Development of Technique and Theory in Technology-Based Algebra Learning,” focused on the learner. The main research question was: In which ways does the interaction between technique and theory foster students’ algebraic thinking when working in a combined Computer Algebra System (CAS) / paper-and-pencil environment? The theoretical perspective that guided the study was the Anthropological Theory of the Didactic elaborated in 1999 by Chevallard, who describes the four components of practice by which mathematical objects are brought into play within didactic institutions: task, technique, technology, and theory -- components that were summarized by the three Ts of Task, Technique, and Theory, within the technology-supported environment of the project. In brief, the main finding of the project was that technique and theory emerge in mutual interaction: Technique gives rise to theoretical thinking and theoretical reflections lead to the further development and use of techniques. The spontaneous need for students to reconcile CAS work and theory was achieved both by calling upon the CAS to check their theoretical thinking and by using paper-and-pencil techniques.

    2007-2013.  The 2007-2013 project, which was titled, “Teachers’ Practice vis-à-vis the Technical/Theoretical Dialectic in Mathematics Learning within Computer Algebra System (CAS) Environments,” and which focused on teaching, aimed at observing and analyzing the practice of teachers in CAS-equipped algebra classrooms, with a view to identifying those factors that are characteristic of effective teaching practice with respect to fostering algebraic thinking. This project was directly related to the previous one in that we had a clear perspective on the nature of the learning to be supported. One of the central theoretical tools used in the analysis of the data was documentational genesis, as developed in 2009 by Gueudet and Trouche, whereby resources are considered to both shape and be shaped by teachers in their practice. In brief, the findings of the project illustrated a much greater tendency to shape rather than be shaped by the designed resources among participating teachers. Teachers' personal beliefs, mathematical goals, and habitual classroom practice did not always align with the epistemological and pedagogical assumptions underlying the design of the CAS resources and led in some cases to considerable adaptation of these resources.