Fostering Inquiry and Creativity in Abstract Algebra: The Theory of Banquets and Its Reflexive Stance on the Structuralist Methodology

This chapter centres around the “theory of banquets”, an invented structure outside the standard Abstract Algebra syllabus. This theory has been elaborated to facilitate students’ access to structuralist thinking at large through the use of the meta-lever. Students are guided in an investigation of the meaning of a “structure” as they engage in crucial steps of the structuralist method. The study has been carried out with the methodology of didactic engineering: the activity has been designed, implemented and analyzed using Brousseau’s Theory of Didactic Situations and an epistemological and semio-cognitive framework, the “objects-structures dialectic”. The purpose of this chapter is both to introduce the non-francophone community to this research, published in Recherches en Didactique des Mathématiques, and to connect and contrast it with selected other studies. The results of a classroom experiment with third year Bachelor students are presented and discussed synthetically. New data are also presented in the form of lab sessions, with more advanced students, in order to emphasize the inquiry and creativity that the theory of banquets is able to generate. Theoretical ideas from Fischbein and Tall are thus combined with the objects-structures dialectic in order to account for creativity processes.