Rosamaria Crisci - Study on the viability conditions of an algorithmic- and programming-based approach to the learning of Euclidean division in primary school

The aim of our thesis is to give a contribution to the study of the viability of an algorithmic- and programming-based approach to teaching and learning mathematical concepts in primary school. For this purpose, we have considered a teaching sequence on the concept of Euclidean division, created by researchers from the EXPIRE project in the programming environment of Scratch. We have focused on three lines of research: 1) the didactic modelling of knowledge relating to the sequence; 2) the study of the sequence's viability in the bosom of the French primary school curriculum; 3) the study of the conditions and constraints which weigh on the didactic transposition of the sequence in the context of an ecological approach.
We subscribe to the Anthropological Theory of the Didactic and, more specifically, we have used a formalization of the praxeological model defined in T4TEL. Concerning the first line of research, thanks to a Reference Praxeological Model, we have built a knowledge pattern that highlights certain features of the praxeologies involved, considered problematic for didactic transposition through games. We have handled the second line through a statistical study of the pupils' productions collected before and after the implementation of the sequence. This research has involved approximately 2500 pupils from the 4th and 5th years of primary school in the 2017/2018 academic year. Lastly, to deal with the third line, we have shown the results of an analysis of didactic praxeologies made by five teachers during the internal didactic transposition of the sequence in their classes to bring forth and institutionalise the mathematical knowledge that is needed.
The results suggest that such approach complies with the 2016 French primary school curricula institutional request of introducing an "initiation to programming", without impacting the school's ecology. The viability conditions shown in this study are related to the teachers’ necessity to take advantage of this approach's characteristics, creating some verbalization and de-contextualization actions during the process of internal didactic transposition.