Colette Laborde’s research while affiliated with Joseph Fourier University and other places

The survey addresses the use of technology in upper secondary mathematics education from four points of view: theoretical analysis of epistemological and cognitive aspects of activity in new technology mediated learning environments, the changes brought by technology in the interactions between environment, students and teachers, the interrelations between mathematical activities and technology, skills and competencies that must be developed in teacher education. Research shows that the use of some technologies may deeply change the solving processes and contribute to impact the learning processes. The questions are which technologies to choose for which purposes, and how to integrate them, so as to maximize all students’ agency. In particular the role of the teacher in classrooms and the content of teacher education programs are critical for taking full advantage of technology in teaching practice.

This survey addresses the use of technology in upper secondary mathematics education from four points of view: theoretical analysis of epistemological and cognitive aspects of activity in new technology mediated learning environments, the changes brought by technology in the interactions between environment, students and teachers, the interrelations between mathematical activities and technology, skills and competencies that must be developed in teacher education. Research shows that the use of some technologies may deeply change the solving processes and contribute to impact the learning processes. The questions are which technologies to choose for which purposes, and how to integrate them, so as to maximize all students’ agency. In particular the role of the teacher in classrooms and the content of teacher education programs are critical for taking full advantage of technology in teaching practice.

Our paper aims at showing how the instrumented learning of the properties in Euclidean geometry can be introduced in continuity with the mathematical competences developed at the elementary school. The principle founder of our research is based on the relation of subordination between the constraints of a property, posed using dynamic geometry software, and a necessary conclusion. Starting from an experimentation carried out in classes of 12-14 years old in France and in Quebec, our study presents a critical analysis of results where the ultimate objective of the activities suggested to the students relates as well to the significance of elementary properties, as on the understanding of the necessity of the link between the antecedents to the consequents of a deduction. Before ending by the didactic consequences of our approach, the text introduces the concept of instrumented figural inference as a means, employed by certain students, to justify a step of structured reasoning. A reconciling of the semiotic, instrumental and discursive aspects is offered throughout the paper.

Although subject matter didactics did not prevail in France as it did in Western Germany in the 1960s and 1970s, the design of the mathematical content to be taught and the preparation of its teaching gave rise to numerous local and national research projects in France. Subsequently, subject matter didactics became part of the didactical engineering research method that was forged in the 1980s. After considering subject matter didactics from a praxeological point of view, this article aims at unfolding how didactical engineering emerged from a subject-focused approach and developed over time. It analyzes some of the salient features of didactical engineering by means of examples.

This group provided a forum for discussion of the teaching and learning of geometry, with a focus especially on the middle and secondary school and university levels. The focus of the group was on theoretical, empirical, or developmental issues related to (1) Curriculum studies of new curriculum implementation, challenges and issues, discussion of specific issues such as place and role of transformations, (2) An application of geometry on the real world and other subjects, (3) The use of instrumentation such as computers in teaching and learning of geometry, (4) Explanation, argumentation and proof in geometry education, (5) Spatial abilities and geometric reasoning, (6) Teacher preparation in geometry education.

As so often stated since the time of ancient Greece, the nature of mathematical objects is, by essence, abstract. Mathematical objects are only indirectly accessible through representations (D'Amore 2003, pp. 39–43) and this contributes to the paradoxical character of mathematical knowledge: The only way of gaining access to them is using signs, words or symbols, expressions or drawings. But at the same time, mathematical objects must not be confused with the used semiotic representations (Duval 2000, p. 60). Other researchers have stressed the importance of these semiotic systems under various names. Duval calls them registers. Bosch and Chevallard (1999) introduce the distinction between ostensive and nonostensive objects and argue that mathematicians have always considered their work as dealing with non-ostensive objects, and that the treatment of ostensive objects (expressions, diagrams, formulas, and graphical representations) plays just an auxiliary role for them. Moreno Armella (1999) claims that every cognitive activity is an action mediated by material or symbolic tools.

Synonymsadidactic; Equilibration; Mathematical concepts; MilieuImagine a teacher who knows that she/he must miss a class next week and wants to communicate the lesson plan to a replacement colleague. How might the teacher convey the critical features of the lesson so that the colleague can reproduce (1) the same learning outcomes for the students and (2) the same meanings for the knowledge acquired by the students? One of the aims of the theory of didactical situations (hereafter denoted TDS) is to identify the critical conditions for situations that can be presented to students and within which students will carry out activities that will enable them to construct specific meanings and understandings of a given concept.Several dimensions are intertwined in a teaching situation focused on specific learning outcomes. These dimensions include cognitive, epistemological, cultural, and social concerns. Hence, several theoretical frameworks have contributed to the development of TDS. One suc ...