Étude de la créativité mathématique dans les solutions aux problèmes proposés dans la communauté virtuelle casmi

Mathematical creativity is a research topic which is relatively recent and not very developed up to this date. In the twenty first century, it is becoming important to equip people with the necessary abilities to be able to solve society's most complex problems in novel and creative ways. This has the effect of elevating the expectations when it comes to teaching and the learning of mathematics. Thus, the mathematics curriculum in New Brunswick and elsewhere in the world emphasizes the development of high order abilities. But, many authors mention that these changes have yet to be observed inside mathematics classrooms (Chan, 2008; Sheffield, 2008). Mathematical problem solving has become the heart of teaching and learning mathematics, but is still based on the application of routine procedures and already prescribed algorithms (Poirier, 2001). Some limited studies show that open-ended problems seem to create opportunities to face more cognitive challenges and to develop different and original problem solving strategies (Klavir et Hershkovitz, 2008), therefore leading to more creative solutions (Leikin, 2007). Also, other researchers say that using virtual learning communities could possibly contribute to this expected change (Piggott, 2007; Renninger et Shumar, 2004). However, we haven't found any research that proves this point. This research is based on the study of mathematical creativity within the CASMI virtual community, which focuses on mathematical problem solving by students (Freiman, Lirette-Pitre & Manuel, 2007) by using an electronic form. This produces what Leikin (2007) describes as a collective solution space, which can possibly contain creative solutions to rich mathematical problems. Our research goals are to verify: whether the mathematical problems posted on the CASMI website are rich, to verify how creative the solutions submitted to the problems posted on the CASMI website are, and if there really exists a link between the two variables. To conduct this quantitative research, we have created two grids which let us analyze first, how rich the mathematical problems posted on the CASMI website are, second, the mathematical creativity of the solutions submitted to the problems. We have selected a random sample of 50 problems and their solutions and analyzed the richness of the problems and the mathematical creativity of the solutions (defined as the fluency, flexibility and originality of the solutions). Finally, using the Likelihood ratio (chi square test), we determined whether there is a relationship between the mathematical creativity in the virtual collective solution space and the richness of the mathematical problems posted on the CASMI website. Our research shows that in general, richer problems seem to bring more creative answers and original solutions. We also make practical recommendations in order to help improve the development of mathematical creativity using the CASMI virtual community.

Name thesis:degree_name

Maîtrise en éducation (enseignement)

Level thesis:degree_level

2e cycle

Discipline thesis:degree_discipline

Faculté des sciences de l'éducation

Grantor dc:publisher

Université de Moncton

Year dc:date.issued

2010

Author dc:creator

• Manuel, Dominic

Advisor dc:contributor.advisor

• Freiman, Viktor

• Mathématiques
• Étude et enseignement (Primaire)
• Apprentissage par problèmes
• Résolution de problème
• Créativité (Éducation)
• Technologie éducative
• Technologies de l'information et de la communication pour l'éducation
• Interdisciplinarité en éducation

Statement dc:rights

• Author

Language dc:language.iso

iso639-2b, fre

Identifier

oclc: 726191856

Dc Identifier Other

umir:1527

OAI identifier oai:identifier

oai:umoncton.scholaris.ca:20.500.14658/6942