Date and Place of birth: Oct. 6th, 1991 Zhejiang, China

Phone number : +33 0771938173 - Email : Luxizi Zhang

• Sep. 2014 - Sep. 2017 : Master study in East China Normal University (Shanghai, China), major in Mathematics Education

• Oct. 2015 - Jun. 2017: Being selected as a master’s student of PRoSFER program (Programme of Sino-French Education for Research) 

• Sep. 2010 - Jun. 2014 : Bachelor study in Zhejianggongshang University (Hangzhou, China), Major in Mathematics and Applied Mathematics (Bachelor of Science).

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

Thesis defended on September 15, 2022, in front of the jury composed of: Pr. Jiansheng Bao (Shanghai), Pr. Ghislaine Gueudet (Paris), Pr. Christian Mercat (Lyon), Pr. Soury-Lavergne (Lyon), Pr. Luc Trouche (Lyon), Pr. Jianpan Wang (Shanghai), and Pr. Binyan Xu (Shanghai), 

Teaching mathematics through variation appears an important topic as soon as we study task design, many teachers teaching consciously or unconsciously in varying these tasks. This thesis is situated in between China and France, crossing two traditions and cultural contexts, aiming to think fruitful interactions between them and improve the effectiveness of mathematics teaching by understanding the role and evolution of teaching through variation. 

Variation appears in two traditions of research in mathematics education, BIANSHI jiaoxue (Gu et al., 2004) in China and theory of didactical situations (Brousseau, 2002) in France. We propose a preliminary model of “teaching mathematics through variation” by combining these two theoretical approaches with the Documentational Approach to Didactics (Trouche, Gueudet & Pepin, 2020). Our preliminary model distinguishes potential variation, actual variation and practical variation. 

The thesis aims at improving this model from a case study in France and in China, focusing on the topic of function (grade 10). In this perspective, an analytical framework is built, and the concept of variation path is proposed. The thesis opens new perspectives for the enrichment of teachers' resource systems, for teacher professional development, and for the modeling of teachers' work.

Brousseau, G. (2002). Theory of Didactical Situations in Mathematics. Netherlands: Springer.

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

Trouche, L., Gueudet, G., & Pepin, B. (2020). The documentational approach to didactics. In S. Lerman (Eds.) Encyclopedia of Mathematics Education (2nd edition, pp. 307-313). Cham, Switzerland: Springer. doi:10.1007/978-3-319-77487-9_100011-1 

Professional experience 

Publications / 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, October 13). From potential variations to practical variations in the teaching of functions through a series of tasks: contrasting Chinese and French cases [Conference presentation]. Variations en histoire et didactique des mathématiques, Journée d’étude LDAR–SPHere, Paris, France.

• Zhang, L. (2021, July 14). DG 6. Variations and Series of Tasks, Crossing the Approaches [Team member of the discussion group]. ICME-14 Conference, Shanghai, China.

• Zhang, L. (2021, July 11-18). Potential, actual and practical variations for teaching functions: cases study in China and France [Accepted as long oral presentation]. ICME-14 Conference, Shanghai, China.

• Zhang, L. (2021, January, 21-22). From potential to practical variations in the teaching of function: contrasting Chinese and French cases [Conference presentation]. Séminaire National de Didactique des Mathématiques, via Zoom.

• Zhang, L. (2019, November 5-8). From potential to practical variations in the teaching of functions: A case study in France [Conference presentation]. Varga 100 Conference, Budapest, Hungary.

• Zhang, L. (2019, January 7). Variations in the teaching of functions [Conference presentation]. Penser des variations et des séries de problèmes pour l’enseignement des mathématiques : Réflexions historiques, didactiques et méthodologiques, ENS de Lyon, France.

• Zhang, L. (2018, December 10-16). Variations in the teaching of functions [Conference presentation]. Crossing views on mathematics teachers’ resources in China and France - A JoRISS Seminar for PhD students in education, ENS de Lyon, France.

• Zhang, L. (2018, August 20-25). Variations in teaching mathematics through the lens of resources: a comparative study between China and France at secondary level [oral presentation]. Yess9-Young ERME Summer School, Montpellier, France.

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

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

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

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