# MaTRiTT - JORISS

Mathematics Teachers Resources in a Time of Transitions

##
Final seminar: IFÉ, ENS de Lyon, 13 December 2017, 10am-12am

*Coordinators*: Luc Trouche (IFÉ, ENS de Lyon) & Jiansheng Bao (ECNU, Shanghai)

This MaTRiTT project (2017) is an answer to the Xu Guangqi call of the French Ambassy in Beijin. It is a new step for the collaboration, in the domain of mathematics education, between the French Institute of Education (ENS de Lyon) and ECNU (Shanghai). This collaboration gave matter to previous seminars (for example here) and common papers (for example Pepin *et al.* 2016). This collaboration developed within the joint educational research platform hosted by JoRISS. The current project involved two researchers in IFÉ (Luc Trouche and Sophie Soury-Lavergne), two researchers in ECNU (Jianshen Bao and Binyan Xu) and three Ph.D. students (ECNU and ENS de Lyon, S2HEP, EPIC) co-supervised by these researchers (see their presentations below).

MaTRiTT means Mathematics Teachers Resources in a Time of Transitions. Transitions means curricular transitions, and digital transitions. These transitions imply a metamorphosis of mathematics teachers work, that the MaTRiTT project analyses throughout their interactions with their resources. Situated in the frame of the documentational approach to didactics (Gueudet & Trouche 2009), MaTRiTT is particularly interested in teachers’ resource systems, and in teachers’ collective work. This project analyses this metamorphosis in opening two windows on Chinese and French math teachers documentation work. The MaTRiTT project is associated to the PREMaTT French project (Penser les ressources des enseignants de mathématiques dans un temps de transitions), developing in the region of Lyon. A better understanding of the metamorphosis at stake is hoped to be gained from this confronting point of view.

Three issues are structuring the MaTRiTT project, and are addressed by three Ph.D students, each of them co-supervised by a Chinese and a French researcher. Their MaTRiTT contribution corresponds to their own interest of research, and is a part of their Ph.D.: Luxizi Zhang (co-supervised by Pr. Bao and Pr. Trouche) analyzes the structure and use of textbooks in China and France (a preliminary contribution has been given in ECNU last September, see picture above, left side); Fangchun Zhu (co-supervised by Pr. Xu and Pr. Soury-Lavergne), analyzes the use of dynamic geometry software in China and France (a preliminary contribution has been given in ECNU last October, see picture above, right side); Chongyang Wang (co-supervised by Pr. Xu and Pr. Trouche) analyzes teachers’ collective documentation work in China and France.

This seminar (see picture below) constitutes the final event for the MaTRiTT project. It gathers, thanks to videoconferencing, the two teams, in Shanghai and Lyon, and benefits of the participation of a researcher from Japan, currently present in Lyon, Takeshi Miyakawa. The slides supporting the seminar contributions are available here.

These contributions gave matter to a report, published in February 2018:

Trouche, L. (Ed.) (2018). *Mathematics Teachers Resources in a Time of Transitions. The French-Chinese MaTRiTT report*. ENS de Lyon (to be downloaded here)

References

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

Pepin, B., Xu, B., Trouche, L., & Wang, C. (2016). Developing a
deeper understanding of mathematics teaching expertise: An examination
of three Chinese mathematics teachers’ resource systems as windows into
their work and expertise. *Educational studies in Mathematics, 94*(3), 257-274, online

### Luxizi Zhang

*Variation problems and their roles in teaching the notion of function: contrasting Chinese and French mathematics textbooks of higher secondary schools*

Teaching and learning mathematics through variation is a widespread idea in China as reflected in the old Chinese maxim, “Only by comparing can one distinguish”(有比较才有鉴别) (Gu *et al.* 2017). In this chapter, the author examined and contrasted the tasks of the notion of function in mathematics textbooks through variation between China and France with the background of evolution of curriculum and textbooks. The results implied that textbooks in China and France both contain variation problems, and focus on setting scaffolding activities and presenting different situations for one mathematics topic. However, contrasted with Chinese textbooks, the organization of tasks in French textbooks lacks the process of letting students themselves to “think” and to “compare” the variant and invariant elements among these tasks, which is a good learning opportunity for students to deepen and consolidate conceptual understanding (Huang *et al.* 2015, p. 104). Finally, the author discussed how variation problems in textbooks can promote deep teaching and learning of mathematics in classrooms.

Gu, F., Huang, R., & Gu, L. (2017). Theory and development of teaching through variation in mathematics in China. In Huang, R., & Li, Y. (Eds.). *Teaching and Learning Mathematics through Variation. Confucian Heritage Meets Western Theories* (pp. 13-41). Rotterdam: Sense Publishers.

Huang, R., & Han, X. (2015). Developing mathematics teachers’ competence through parallel Lesson study. *International Journal for Lesson and Learning Studies, 4*(2), 100–117.

### Fangchun Zhu

*Sequencing Mathematics Tasks in a Dynamic Geometry Environment: contrasting French and Chinese cases*

Dynamic geometry software affects teachers’ choice and decision of mathematics tasks and their organization. But there is the deep gap between real status in teaching and the results of didactical research. To solve this gap, this study focus one critical elements: teachers and their knowledge shown in their choice of different types of tasks (Laborde 2001; Soury-Lavergne 2017), which is related to different ways to use dynamic geometry, and their sequence, which is related teachers’ orchestration of instrument (Trouche 2004; Drijvers 2010). Two examples from China and France were chosen to contrast the tasks and possible orchestration of different teachers. In Chinese example, software is used to generate new tasks and suggests a teacher-centered way to use the software. The role software played in French tasks is more like an amplifier of paper-pencil activities, supporting a more student-centered organisation of the class.

Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. *Educational Studies in mathematics, 75*(2), 213-234.

Laborde, C. (2001). Integration of technology in the design of geometry tasks with Cabri-Geometry. *International Journal of Computers for Mathematical Learning, 6(*3), 283-317.

Soury-Lavergne, S. (2017). *Duos d’artefacts tangibles et numériques et objets connectés pour apprendre et faire apprendre les mathématiques *(Habilitation à diriger des recherches, Ecole Normale Supérieure de Lyon, France).

Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: Guiding students’ command process through instrumental orchestrations. *International Journal of Computers for mathematical learning, 9(*3), 281-307.

*Teachers’ resources choices for collective lesson preparations: two contrasted cases in China and France*

This presentation focuses on micro-collective lesson preparations in two contrasting cases, one in China (experienced teacher Gao and her apprentice Yao), one in France (two experienced teachers Anna and Cindy). The two lesson preparations happened both as part of teachers’ regular work, but in a time of transition (curricular transition in France, and professional transition in China). Taking into account the different contexts of collective working and resources environments, we will contrast teachers’ documentation work, analyzing both the process of lesson preparation and the state of teachers’ resource systems. From this cross analysis, we will try to deepen the notion of teachers’ documentation expertise (Pepin et al. 2016, Wang to be published), which is the heart of our Ph.D

Pepin, B., Xu, B., Trouche, L., & Wang, C. (2016). Developing a deeper understanding of mathematics teaching expertise: An examination of three Chinese mathematics teachers’ resource systems as windows into their work and expertise. *Educational studies in Mathematics, 94*(3), 257-274, online

Wang, C. (to be published). Mathematics teachers’ expertise in resources work and its development in collectives. A French and a Chinese Cases. In L. Fan, L. Trouche, S. Rezat, C. Qi, & J. Visnovska (Eds.), *Research on Mathematics Textbooks and Teachers’ Resources: Advances and issues.* Springer.