LEARNING MATHEMATICAL PROOF IN HIGHER EDUCATION: A QUESTION OF POLYSEMY? AN EXPLORATORY STUDY IN FRENCH WEST INDIES

Mickaelle Ramassamy, Antoine Delcroix

Abstract


The notion of proof is a pivotal issue in mathematical teaching. In France, school curricula have been associating this notion with the term Demonstration. The term Preuve is lesser used. In French, the words démontrer, justifier, prouver are considered equivalents, but some researchers emphasize differences between them. For indeed, Balacheff and Soury-Lavergne (1996) consider that a proof is an accepted explanation, whereas the word Démonstration designates an explanation accepted by mathematicians because of its particular structure.

This polysemy could have an impact on mathematical learning, especially in ultramarine contexts, where learners are exposed to multicultural and multilingual environments but are asked to follow the same curricula as in mainland. Following our hypothesis, we conduct a longitudinal survey in a French ultramarine context (the French West Indies): 168 students are questioned about their conception of the meaning of the terms Demonstration and Justification at three steps of their course. They were also questioned about the evolution of their ability to argue, reason, and write a proof. We observed the evolution of their abilities. We also established causal links between the various observed conceptions of students on the meaning of these terms and the evolution of their capacity. The results we obtained suggest that there is some adequacy between these conceptions and perception of how their ability to demonstrate a result in mathematics evolve.

 

Nell’ambito dell’insegnamento della matematica, il concetto di prova è fondamentale. In Francia, i programmi scolastici hanno solitamente associato tale concetto alla nozione di dimostrazione, preferendola a quella di prova. In francese, in effetti, i termini dimostrare, giustificare, provare sono considerati equivalenti ma vari ricercatori hanno sottolineato che esistono alcune importanti differenze e che la prova dovrebbe essere considerata come una spiegazione valida, mentre la dimostrazione definirebbe una spiegazione convalidata dalla comunità matematica data la sua struttura.

Una tale polisemia potrebbe avere un impatto sull’apprendimento della matematica, soprattutto in quei territori della Francia d’oltremare in cui gli studenti sono esposti a un contesto multiculturale e plurilinguistico ma ai quali si richiede di seguire gli stessi programmi scolastici della madrepatria. A partire da tale ipotesi, abbiamo realizzato una ricerca longitudinale in un territorio d’oltremare (le Antille francesi). Una coorte di 168 studenti universitari ha partecipato al nostro studio. La coorte è stata analizzata in tre momenti distinti al fine di valutare i cambiamenti di significato attribuiti ai termini dimostrare e giustificare. Inoltre, ai partecipanti è stato richiesto di valutare le proprie capacità a ragionare, argomentare e redigere una prova matematica al fine di valutare le eventuali evoluzioni. I risultati ottenuti ci permettono di identificare un nesso causale tra le concezioni che gli studenti associano a ciascuno dei termini in questione e le rappresentazioni che sviluppano riguardo l’evoluzione delle loro competenze.


Parole chiave


Didactics of mathematics, higher education, mathematical proof, Overseas France

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DOI: https://doi.org/10.32043/gsd.v6i4.706

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