
The Research Projects
20032007. The 20032007 project, which was
titled, The Intertwining Development of Technique and Theory in
TechnologyBased 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) / paperandpencil 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 technologysupported 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 paperandpencil techniques.
20072013. The 20072013 project, which
was titled, Teachers Practice visàvis 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 CASequipped 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.
