S2HEP - EducTice - Institut français de l'Éducation, École Normale Supérieure de Lyon, 15 parvis René-Descartes, BP 7000, 69342 Lyon cedex 07

East China Normal University, Shanghai

From potential to practical variations in the teaching of functions: contrasting Chinese and French cases in higher secondary schools

Teaching and learning mathematics through variation has a long history in China and has been used consciously or unconsciously by teachers (Bao et al., 2003). To figure out and analyze the situation of teaching through variation in France and also in China, we construct a model of variation based on the present theoretical frameworks (Brousseau,1986 & Gu et al., 2004). We apply the model to study the variations in teachers' documentation work and the observation in class focusing on the teaching of function. The aim of this study is to better understand the role of variation in mathematics teaching, paying particular attention to the design of resources (Trouche, et al., 2019). We will study the transformation of potential variation into practical variation, aiming at improving the effectiveness of teaching.

Des variations potentielles aux variations pratiques dans l’enseignement des fonctions: approche contrastée des cas chinois et français dans les établissements d’enseignement secondaire supérieur

 Le fait d’enseigner et apprendre les mathématiques par la variation a une longue histoire en Chine et est utilisé consciemment ou inconsciemment par les enseignants (Bao et al., 2003). Pour comprendre et analyser la situation de l’enseignement par la variation en France et en Chine, nous avons proposé un modèle de variation basé sur différents cadres théoriques, en particulier (Brousseau,1986 & Gu et al., 2004) et nous avons mis à l’épreuve ce modèle en étudiant le travail documentaire des enseignants pour l'enseignement des fonctions numériques. Le but de cette étude est de mieux comprendre le rôle des variations dans l’enseignement des mathématiques, en accordant une attention particulière à la conception des ressources (Trouche, et al., 2019). Nous étudierons la transformation de la variation potentielle en variation pratique, en visant l’amélioration de l’efficacité de l’enseignement. 

Bao, J., Huang, R., Yi, L., & Gu, L. (2003). Continued study of “Bianshi Jiaoxue” [Teaching with variation]. Mathematics Teaching, 2, 6-10. 

Brousseau, G. (1986). Fondements et méthodes de la didactique des mathématiques, Recherches en didactique des mathématiques, 7(2), La pensée sauvage.

Gu, L., Huang, R., & Marton, F. (2004). Teaching with variation: A Chinese way of promoting effective mathematics learning. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 309–347). Singapore : World Scientific.

Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199-218. 

Trouche, L., Gueudet, G., & Pepin, B. (2019). The ‘resources’ approach to mathematics education (Eds.). Springer series Advances in Mathematics Education. Cham : Springer.

Implication dans des projets 

Publications ou communications

Publications

• Zhang, L. (2020). Potential, actual and practical variations for teaching functions: cases study in China and France. Teaching Mathematics and Computer Science. 18/3 (2020): 157-166. DOI: 10.5485/TMCS.2020.0489
• Zhang, L. (2018). A comparative study on the content and use of mathematics teaching resources between China and France: from the exercise perspective (poster), In V. Gitirana, T. Miyakawa, M. Rafalska, S. Soury-Lavergne, & L. Trouche (Eds.), Proceedings of the Re(s)sources 2018 International Conference (pp. 132-134). ENS de Lyon, retreived at https://hal.archives-ouvertes.fr/hal-01764563v3/document

• Zhang, L. (2021). Journée d’étude LDAR–SPHere. Paris, France, 13 October, 2021.
• Zhang,L. (2021). DG6. Variations and Series of Tasks, Crossing the Approaches. team members of discussion group. ICME-14 Conference. China, Shanghai, 11-18 July 2021. 
• Zhang, L. (2021). Potential, actual and practical variations for teaching functions: cases study in China and France. Accepted as long oral presentation. ICME-14 Conference. China, Shanghai, 11-18 July 2021. 
• Zhang, L. (2021). From potential to practical variations in the teaching of function: contrasting Chinese and French cases (présentation jeunes chercheurs). Séminaire National de Didactique des Mathématiques. A distance, via Zoom, 21-22 janvier 2021.
• Zhang, L. (2019). From potential to practical variations in the teaching of functions: A case study in France. Varga 100 Conference. Budapest, Hungary, 5-8 novembre 2019.
• Zhang, L. (2019). Theoretical frameworks of variations in the teaching (presentation). Penser des variations et des séries de problèmes pour l’enseignement des mathématiques: Réflexions historiques, didactiqueset méthodologiques, ENS de Lyon, 7 janvier 2019.
• Zhang, L. (2018). Variations in the teaching of functions (presentation). Crossing views on mathematics teachers' resources in China and France - A JoRISS Seminar for PhD students in education, ENS de Lyon, 10-16 December 2018.

• Zhang, L. (2018). Variations in teaching mathematics through the lens of resources: a comparative study between China and France at secondary level. Yess 9- Young ERME Summer School. Montpellier, France, 20-25 Aug. 2018.
• Zhang, L. (2018). A comparative study on the content and use of mathematics teaching resources between China and France: from the exercise perspective (poster). Re(s)sources 2018 International Conference. ENS de Lyon, 28-30 May, 2018. Young researchers post conference, May 31, June 1, 2018.

• Igliori, S., & Zhang, L. (2018). Session 7 - Ressources des enseignants: analyse d'exercices dans deux contextes différents (presentation). Ressources 2017-2018. ENS de Lyon, 10 April 2018.

• Zhang, L. (2017). Variation problems and their roles in teaching the notion of function: contrasting Chinese and French mathematics textbooks of higher secondary schools. MaTRiTT project final seminar. IFÉ, ENS de Lyon, 13 December 2017.

• Zhang, L. (2016). Shanghai sixth grade students’ performance on number sense-a case study. Oral presentation in TSG 23 Mathematical literacy ICME 13th, Hamburg, 24-31 July 2016.

• Zhang, L., Ji, W., & He, R. (2015). Mathematics teaching based on the idea of integration of STEM. Mathematics education Graduate Forum, Shanghai, China, 28-30 May 2015.

Scientific Activities

• 26 juin 2019. Journée scientifique autour des travaux de Luc Trouche, à ENS de Lyon.
• octobre 2018, 2019. Fête de la science.
• 28-30 May, 2018. Attended Re(s)sources 2018, Young Researcher Workshop of Session B - Sequencing learning activities – roles of didactic metadata. Lyon, France.
• 28 Sep., 2016. Attended the first plenary meeting of Shanghai mathematics education and teaching research base. Shanghai, China.
• 20-22 May, 2016. Attended mathematics education graduate forum (focused on the mathematical literacy). Suzhou, China.
• 16-21 Aug., 2015. Attended workshop on learning progressions. Beijing Normal University, Beijing, China.