Each participant is invited to be a member of one of the working seminars. Discussions and exchange of experiences and ideas are the essential aspects of these activities. They are designed as an opportunity for participants who want to create something useful for their future work, based on the ideas gathered during the conference. The working seminars participants are not expected to present ready-made results, but to work together to create something new.

The working seminars in CME’24 will focus on three educational levels and will be led by the following researchers:

- kindergarten and primary school (3–9-year-olds): Eva Nováková (Czech Republic), Paola Vighi (Italy)
- primary school (10–13-year-olds): Ingrid Semanišinová (Slovakia)
- secondary and upper-secondary school (14–18-year-olds): Lambrecht Spijkerboer (The Netherlands)

**Descriptions of the CME’24 working seminars:**

**From artistic paintings to mathematics**

**Eva Nováková**

Assistant professor

Department of Mathematics

Masaryk University, Brno

Czech Republic

**Paola Vighi**

Professor of Mathematics

University of Parma

Italy

The aim of the seminar is to show some examples of evolution of geometrical knowledge in the environment of art. In other words, we want to show ways of supporting early geometrical thinking and understanding based on particular artworks.

The geometry often plays only limited role in early mathematical education. However, geometry is an integral part of the development of the mathematical component of education in young children. The ability to recognize shapes is substantial part of early geometrical knowledge, and deep teacher’s insight into geometry is essential for the efficiency of their teaching.

Two activities will be discussed. Participants will be involved in problem solving and subsequent analysis. They will be also asked to analyze some videos The first activity will be based on the reproduction of a painting by manipulation of cardboard shapes.It involves the concept of space, the analysis of geometrical figures and their mutual positions and especially the geometrical transformations. The second activity will deal with transparent coloured shapes, and it will show how new shapes could be created by superimposing two transparencies with different colors.

During the working seminar, participants are expected to work together and to exchange opinions and experiences.

2. **Designing activities to support the development of the mathematics teacher’s specialised knowledge**

**Ingrid Semanišinová**

Associate professor

Pavol Jozef Šafárik University in Košice

Faculty of Science

Institute of Mathematics

Slovak Republic

ingrid.semanisinova@upjs.sk

Current research in mathematics education shows that one of the main factors influencing the quality of mathematics learning is teachers’ knowledge. To bridge the gap between teacher education and the practice that teachers will carry out in the classroom, we should keep in mind what a teacher must do when he or she is teaching. The workshops will therefore focus on creating activities and tasks for pre-service teachers and in-service teachers with the aim of developing the mathematics teacher’s specialised knowledge in two main areas – mathematical knowledge and pedagogical content knowledge of the mathematics teacher. We will focus on creating tasks and activities that are formulated in the context of primary school practice and that aim to deepen understanding of mathematical content and uncover pedagogical problems. Indeed, much of the training of pre-service teachers cannot take place directly in the classroom but can be carried out using appropriate materials.

The teacher’s work begins long before the lesson, and after the lesson, the teacher must reflect on the lesson and plan the next one. For this whole process to be effective, it is useful to have a formal framework to help us reflect systematically on different aspects of pupils’ learning progress. The Mathematics Teacher’s Specialised Knowledge (MTSK) model (Carrillo et al., 2018) will be such a framework for us during the workshop. The MTSK model serves as a conceptualisation that guides the kind of knowledge that pre-service teachers should construct. Therefore, in the first part of the workshop we will be introduced to the MTSK model. We will demonstrate and solve specific tasks and activities for primary school teachers that focus on the different components of the model. In the second part of the workshop, we will use the materials provided to create appropriate activities and tasks aimed at developing the different components of the MTSK model. The workshops will be based on group work with intensive interactive discussion.

Reference

Carrillo, J., Climent, N., Montes, M., Contreras, L., Flores-Medrano, E., Escudero-Ávila, D., Muñoz-Catalán, M. C. et al. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20, 236–253.

3. **Dealing with differences in the mathematics classroom**

**Lambrecht Spijkerboer**

Trainer/consultant for education

Independent Entrepreneur

STA

The Netherlands

STA@Lambrechtspijkerboer.nl

In mathematics classrooms we are faced by (big) differences among students in their performance. There are low and high achievers, there are students with a lack of motivation, there are students with math anxiety, there are slow starters, etc. Some students have the skills but are not interested enough in mathematics, others are working hard but nevertheless have low scores. Mathematics teachers should be able to handle those differences in a way that more students will get connected to the mathematics lessons.

In this working seminar we will use different approaches to deal with differences in the mathematics classroom. There are many theories on learning, teaching and motivation, and we will try to make use of these findings to transform our lessons into challenging and motivational experiences for students. Among other possibilities, working with materials and other educational resources are one of the options to explore. This working seminar is not only a presentation of possible solutions; we will also share different experiences of the participants to learn from the differences of each other.

The following issues will be on our focus:

- Stages in learning with materials, including examples for the mathematics classroom.
- Designing lessons by different ways of working to deal with differences in the mathematics classroom.
- Working with level-raising questioning and designing SSDD-exercises (same surface, different deep).
- Implementation of formative assessment and self-responsibility in learning mathematics.

References

Haenen, J. (2001). Outlining the teaching–learning process: Piotr Gal’perin’s contribution. *Learning and Instruction*, *11*(2), 157-170.

Hattie, J. (2009). *Visible learning*. Routledge.

Van Ast, M., de Loor, O, & Spijkerboer, L. (2024). *Effectief leren, de docent als regisseur* [Effective learning, the teacher as director]. Noordhoff.