TY - JOUR
TI - Can students justify the correctness of an arithmetic algorithm? A case-study at the primary-secondary transition
AU - Chorlay, Renaud
T2 - Recherches En Didactique Des Mathématiques
AB - This study aims to explore to what extent arithmetic algorithms provide opportunities for argumentation in ordinary classrooms. We designed an experiment in which French students in grades 5 and 6 were asked to describe and justify an algorithm for halving whole numbers which they had not studied earlier, but whose correctness rests on mathematical facts with which they ought to be familiar. Drawing on established results on the teaching and learning of whole number arithmetic, we account for students’ engagement in justification by combining a didactical theory aimed for the analysis of explanation and proof – namely Balacheff’s notion of conception – and inputs from the history of mathematics on algorithms, their expression and their justification. The results show that (1) young students can regard arithmetic algorithms as objects to study and not only as tools to use, and that (2) different valid conceptions of whole numbers provide unequal opportunities for argumentation and lead to arguments of unequal epistemic strengths.
DA - 2021///
PY - 2021
VL - 41
IS - 2
SP - 177
EP - 216
J2 - RDM
LA - EN
SN - 0246–9367
UR - https://revue-rdm.com/2021/can-students-justify-the-correctness-of-an-arithmetic-algorithm-a-case-study-at-the-primary-secondary-transition/
ER -