Élaboration des analogies en cours de mathématiques à l'école élémentaire

According to experimental studies, analogical reasoning play a central role in mathematics learning and problem solving. However, little is known about how analogy is used in everyday instructional contexts. The aim of this study is to characterize the analogies naturally used in mathematical lessons in elementary school in order to highlight the mechanisms of generation of these analogies. Twenty mathematical lessons were videotaped, 10 sessions in first and second degrees (“cycle 2”, 6-8-year-old), 10 sessions in third, fourth and fifth degrees (“Cycle 3”, 8-11-year-old). Qualitative codes proposed by Richland et al. (2004) were used for the analysis: the study examines patterns of teacher-learners' participation, source and target construction, and contexts for analogy production. These data show that verbal analogies are spontaneously generated from the first to the fifth degree. They are mainly generated by teachers and completed by children. These analogies are both used to discover mathematical concepts and to apply procedures. The nature of analogy generated differs according to the level of children. In first and second levels, sources are concrete familiar situations. In higher levels, most of sources are decontextualized problems. Context of use analogies also varies depending on the level of children. In higher level, source and target construction is more often related to whether the analogy is in response to students' needs for help. These results are discussed in a developmental perspective.