SNF Project ReCoRePro
Study of devolution and institutionalization processes in a mathematics problem-solving instruction. Collaborative approach and development of a resource for teachers.
Original title (in French): Étude des processus de dévolution et d’institutionnalisation dans le cadre d’un enseignement de la résolution de problèmes en mathématiques. Approche collaborative et élaboration d’une ressource pour les enseignant·es.
Conducted by Maud Chanudet, Jean-Luc Dorier, Stéphane Favier and Isaline Ruf
Supervised by Maud Chanudet and Jean-Luc Dorier
Supported by the Swiss National Science Foundation (Subside no100019_212761)
Conducted from 2023 to 2027
Keywords: Problem solving, mathematics, teaching practices, students' learning, collaborative research, devolution, institutionalization
Resume: Problem solving is an important aspect of mathematics, its learning and its teaching, particularly in the context of the research, that of French speaking Switzerland. It constitutes the core of the curriculum of mathematics. However, research shows that it remains complex to make it a classroom reality. In that sense, the processes of devolution and institutionalization present a certain complexity when it comes to managing students’ engagement in problem solving and their effective learning.
Therefore, our goal is to better understand what is at stake between teachers' practices and students' learning around problem solving in mathematics. More precisely, we want to know how teachers can help students to better appropriate a problem, help them to progress in its resolution without doing too much for them, and finally support the development of the associated mathematical learning.
On the one hand, we want to know more about teachers' practices when they teach mathematical problem solving. Our previous work gave us results for the secondary level, we will continue this work for the primary school level through the study of some cases.
On the other hand, we collaborate with secondary school mathematics teachers (it is also planned to collaborate with primary school teachers at a later stage) to better understand what students do in class when they solve a problem and what can be done to support and encourage their work and learning.
We rely on the design, implementation and analysis of the sessions to develop an in-service training tool to equip teachers.
Our work is based on a collaborative research process, which is, according to us, necessary to a better appropriation of the results obtained. Different theoretical frameworks from didactics of mathematics are mobilized to build the research methodology and to analyze the data.
This page will be completed as the research progresses.
References:
Chanudet, M., Dorier, J.-L., & Favier, S. (2023). Improving the Teaching of Mathematical Problem Solving – A Collaborative Research Based on Theoretical Findings from Two PhD Dissertations. In M. A. Ashraf & S. M. Tsegay (Éds.), STEM Education—Recent Developments and Emerging Trends. IntechOpen.
Our previous research related to this project:
Chanudet, M. (2019). Assessing Inquiry-Based Mathematics Education with Both a Summative and Formative Purpose. In P. Liljedahl & M. Santos-Trigo (Eds.), Mathematical Problem Solving (pp. 177–207). Springer.
Chanudet, M. (2023). Types of Mathematical Reasoning Promoted in the Context of Problem-Solving Instruction in Geneva. In T. L. Toh, M. Santos-Trigo, P. H. Chua, N. A. Abdullah, & D. Zhang (Eds.), Problem Posing and Problem Solving in Mathematics Education- International Research and Practice Trends (pp. 51–72). Springer.
Favier, S. (2017). Analyse du fonctionnement du processus d’institutionnalisation durant la mise en commun qui suit un travail de groupe lors d’une activité de découverte d’une notion mathématiques au cycle 3. [Mémoire de Master non publié] Université Clermont Auvergne.
Favier, S. (2022). Étude des processus de résolution de problèmes par essais et ajustements en classe de mathématiques à Genève [Thèse de doctorat en Sciences de l’Éducation, Université de Genève]. https://archive-ouverte.unige.ch/unige:159466
Favier, S., & Dorier, J. L. (2024). Heuristics for the analysis of students’ work in mathematical problem solving. Educational Studies in Mathematics.
Other references (on which the project is based on):
Allal, L. (2020). Assessment and the co-regulation of learning in the classroom. Assessment in Education: Principles, Policy & Practice, 27(4), 332–349. https://doi.org/10.1080/0969594X.2019.1609411
Allal, L., & Mottier Lopez, L. (2005). Formative assessment of learning: A review of publications in French. In Formative Assessment—Improving Learning in Secondary Classrooms. (pp. 241–264). OECD Publication.
Allard, C. (2015). Étude du processus d’institutionnalisation dans les pratiques de fin d’école primaire: Le cas de l’enseignement des fractions [Thèse de doctorat en didactique des mathématiques]. Université Paris Diderot.
Allard, C. (2018). Etude du processus d’institutionnalisation dans les pratiques effectives en fin d’école primaire: Le cas de l’enseignement des fractions. In J. Pilet & C. Vendeira (Eds.), Actes du séminaire de didactique des mathématiques de l’ARDM (pp. 192–209). Irem de Paris.
Artigue, M., & Houdement, C. (2007). Problem solving in France: Didactic and curricular perspectives. ZDM, 39(5–6), 365–382. https://doi.org/10.1007/s11858-007-0048-x
Black, P., & Wiliam, D. (1998). Assessment and Classroom Learning. 5(1), 7–74.
Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21(5), 5–31. https://doi.org/10.1007/s11092-008-9068-5
Borko, H., & Potari, D. (2020). ICME study 25. Teachers of mathematics working and learning in collaborative groups.
Brousseau, G. (1986). Théorisation des phénomènes d’enseignement des mathématiques [Thèse de Doctorat]. Bordeaux I.
Brousseau, G. (2003). Glossaire de quelques concepts de la théorie des situations didactiques en mathématiques. http://perso.orange.fr/daest/guy-brousseau/textes/Glossaire_Brousseau.pdf
Choquet-Pineau, C. (2014). Une caractérisation des pratiques de professeurs des écoles lors de séances de mathématiques dédiées à l’étude de problèmes ouverts au cycle 3 [Thèse de doctorat en didactique des mathématiques]. Université de Nantes.
Conférence Intercantonale de l’Instruction Publique de la Suisse romande et du Tessin (CIIP). (2010). Commentaires généraux du domaine Mathématiques et Sciences de la nature (premier cycle). In Plan d’études romand (pp. 5–11). CIIP. http://www.plandetudes.ch/documents/10273/36537/PER_print_MSN_CG.pdf
Coppé, S., & Dorier, J.-L. (in press). La résolution de problème au cœur de l’activité mathématique. Quels enjeux pour l’apprentissage ? GPA Éditions.
Desgagné, S. (1997). Le concept de recherche collaborative: L’idée d’un rapprochement entre chercheurs universitaires et praticiens enseignants. Revue des sciences de l’éducation, 23(2), 371–393. https://doi.org/10.7202/031921ar
Earl, L. M. (2003). Assessment As Learning: Using Classroom Assessment to Maximize Student Learning. Corwin Press.
Goulet-Lyle, M.-P., Voyer, D., & Verschaffel, L. (2020). How does imposing a step‑by‑step solution method impact students’ approach to mathematical word problem solving? ZDM, 52, 139–149. https://doi.org/10.1007/s11858-019-01098-w
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasonning. Journal for Research in Mathematics Education, 28(5), 524–549.
Houdement, C. (2009). Une place pour les problèmes pour chercher. Annales de Didactique et de Sciences Cognitives, 14, 31–59.
Jeannotte, D. (2015). Raisonnement mathématique: Proposition d’un modèle conceptuel pour l’apprentissage et l’enseignement au primaire et au secondaire [Thèse de doctorat en didactique des mathématiques]. Université du Québec à Montréal.
Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96, 1–16.
Julo, J. (1990). Surface features, representations and tutorial interventions in mathematical problem solving. European Journal of Psychology of Education Volume, 5, 255–272.
Julo, J. (1995). Représentation des problèmes et réussite en mathématiques: Un apport de la psychologie cognitive à l’enseignement. Presses universitaires de Rennes.
Lajoie, C., & Bednarz, N. (2014). La résolution de problèmes en mathématiques au Québec: Évolution des rôles assignés par les programmes et des conseils donnés aux enseignants. Education et Francophonie, XLII(2), 7–23.
Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem Solving in Mathematics Education (G. Kaiser, Ed.; Springer Open).
Margolinas, C. (1993). De l’importance du vrai et du faux dans la classe de mathématiques. La pensée sauvage.
Margolinas, C., & Laparra, M. (2011). Des savoirs transparents dans le travail des professeurs à l’école primaire. In J.-Y. Rochex & Y. Crinon (Eds.), La construction des inégalités scolaires (Rennes: Presses universitaires de Rennes., pp. 19–32).
Poitrenaud, S. (1998). La représentation des procédures chez l’opérateur. Description et mise en oeuvre des savoir-faire. [Thèse de doctorat en didactique des mathématiques]. Université de Paris 8.
Pólya, G. (1945). How to solve it. Princeton University Press.
Richard, J.-F. (2004). Les activités mentales (4e ed.). Armand Colin.
Rott, B. (2012). Heuristics in the problem solving processes of fifth graders. In T. Y. Tso (Ed.), Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 35–42).
Ruiz-Primo, M. A., & Furtak, E. M. (2004). Informal Formative Assessment of Students’ Understanding of Scientific Inquiry (CSE 639).
Ruiz-Primo, M. A., & Furtak, E. M. (2007). Exploring Teachers’ Informal Formative Assessment Practices and Students’ Understanding in the Context of Scientific Inquiry. Journal of Research in Science Teaching, 44(1), 57–84.
Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press Inc.
Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum documents. Journal of Mathematical Behavior, 24, 341–350.
Toh, T. L., Quek, K. S., Leong, Y. H., Dindyal, J., & Tay, E. G. (2011). Assessing Problem Solving in the Mathematics Curriculum: A New Approach. In Assessment in the Mathematics Classroom Yearbook 2011, Association of Mathematics Educators (pp. 33–66). World Scientific Publishing.
Toh, T. L., Santos-Trigo, M., Chua, P. H., Abdullah, N. A., & Zhang, D. (2023). Problem Posing and Problem-Solving in Mathematics Education: International Research and Practice Trends. In T. L. Toh, M. Santos-Trigo, P. H. Chua, N. A. Abdullah, & D. Zhang (Eds.), Problem Posing and Problem Solving in Mathematics Education- International Research and Practice Trends (pp. 1–6). Springer.