Student interactions during class activities: A mathematical model

This paper aims at bridging Mathematical Modelling and Mathematics Education by studying the opinion dynamics of students who work in small groups during mathematics classrooms. In particular, we propose a model which hinges upon the pioneering work of Hegselmann and Krause on opinion dynamics and integrates recent results of interactionist research in Mathematical Education. More precisely, the proposed model incorporates the following features: 1) the feelings of each student towards the classmates (building upon the so-called \I can» -\you can» framework); 2) the different levels of preparation of the students; 3) the presence of the teacher, who may or may not intervene to drive the students towards the correct solution of the problem. Several numerical experiments are presented to assess the capability of the model in reproducing typical realistic scenarios

A specific language towards a new conceptual framework for networking methodologies in the field of affect

This chapter focuses on ways of networking different methodologies used in empirical research in the field of affect. It also aims to develop a specific language and a conceptual framework for the networking of these methodologies. Two situations are presented to exemplify the extent to which two methods can be integrated without losing their characteristic features. The first example regards a case in which two methodologies, with strong commonalities between them, can be synthesized. The result of the synthesis is a new methodology for the examination of the interplay between cognitive-related and emotional/motivational-related variables impacting the outcome of an assessment test. The second example, conversely, presents two methodologies that have much less overlap, yet the commonality of language and shared experiences still allows us to compare them, although at a lesser extent of integration