Comparative study of the theory of didactical situations and the theory of developmental instruction: teaching mathematics in elementary school

1.4 Interventionist research approaches and their roots
Paper in a Symposium (Symp)
30 minutes
The theory of didactical situations, developed by Brousseau (1988) in 1970-90 became central to the whole study of didactics of mathematics. Currently used by many researchers around the world, this theory joins the constructivist view of learning initially proposed by Piaget. At the same period of time in Russia, Davydov (2008) and his colleagues built a theory of developmental instruction based on the Vygotskian idea of the cultural-historical nature of teaching and learning. Researchers in Russia and in many other countries successfully apply Davydov’s theory by creating new curricula and instructional innovations. Although the philosophies behind the two theories are distinct, the subject matter in both theories is the same: the teaching and learning of mathematics. This leads us to compare some important propositions emerging from the two theories and their implementations in the design of teaching/learning activities. We identified several key ideas within the two theories which we would like to discuss. We will conclude by highlighting the complexity of the subject matter: the process of teaching/learning of mathematics in a school setting. Both theories contribute to our understanding of this process, and both propose important ideas about how it can be regulated in order to achieve better results. However, neither of these theories is complete in the sense that there are still many aspects of learning and teaching that are absent in these theories. For example, new developments in neuro-education challenge our understanding of how new knowledge is absorbed by the brain. We also lack in-depth studies of teacher’s behavior during activities management in the classroom. Further theoretical work is necessary to connect different bodies of knowledge in order to understand the complexity of the teaching/learning process. 
Université du Québec en Outaouais
Université Laval

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