CME’18 took place in Warsaw, Poland on 11 – 14 July 2018 and was hosted by the University of Warsaw.

**CME 2018 plenary speakers were:**

- Fragkiskos Kalavassis – Greece
- Christine Knipping – Germany
- Zbigniew Marciniak – Poland
- Mogens Niss – Denmark

**Titles and abstracts of the plenary lectures**

**Fragkiskos Kalavasis**, University of the Aegean, Greece

**Mathematics and the real world in a systemic perspectithe school**

We will approach the variety of the debates about mathematics and/or reality in the framework of the interdisciplinary and institutional environments of teaching and learning mathematics. These environments form a complexity that includes and is at the same time included in the didactic of mathematics situations. Therefore, there emerges a new variety of approaches of the relation between mathematics and reality, in which the cognitive, the psychological, the social and the digital are interconnected. It is hard to model the interactions of these variety with the underlying epistemological or philosophical one, because of the complexity of roles and intentionalities in school. The educational need of use various discipline sources to understand complex phenomena implies a permanent presence of mathematics and this is complexifing their relations to reality because it passes across their relation to the others disciplines, which is often ignored by formal school reality. The frontiers among the priority of the real world or of the noetic structures which made the opposite poles in the philosophical disputes about mathematics and/or reality, became permeable and porous in these environments. Observation and intuition, comprehension and invention, modelization and application, adaptation and transformation seem synchronic in the mathematical thinking. The role of representations and symbolic languages, so much crucial into mathematics, becomes a kind of obstacle in the interdisciplinary learning path of the students in the everyday school timetable across the different disciplines. The well studied didactical transposition is enriched with the praxeological transposition. We will try to present concrete examples of the history and epistemology of mathematics as well of the reforms in mathematical education and more particular the influence of Jean Piaget works, to animate the discussion between mathematics and real world in this and of the systemic approach of the school.

**Christine Knipping**, University of Bremen, Germany

**Understanding optimisation as a principle**

Optimisation problems are classic problems in mathematics and the real

world. Since the 1980s the landscape of solving optimisation problems has

fundamentally changed in the era of high dimensional computing capacities

as can be used today. Numerical approaches cap analytical ones since then.

This shift recasts currently processes in industry as well as modelling of

nature, climate change and so forth. In order to allow students to understand

how mathematics and specifically optimisation is used and needed today to

solve complex application problems, such as landing a spaceship on the

moon, controlling robots to place objects precisely or to run a smart farm,

mathematicians and mathematics educators need to work together. Inviting

mathematics classes from schools to the university to learn about this, is one

way of making this knowledge and these new approaches accessible to

students and teachers. Principles of this approach and how these can be

made accessible to students are presented in this plenary.

**Zbigniew Marciniak,**University of Warsaw, Poland

**Winds of change in math education**

The talk will report on the current discussions concerning the changing expectations with respect to math education in XXI century, in the context of the development of the new math framework for the 2021 OECD PISA test.

**Mogens Niss**, IMFUFA/INM Roskilde University, Denmark

**How can we use mathematics education research to uncover, understand and counteract mathematics specific learning difficulties?**

Mathematics education research from the last four decades has helped us to understand more and more about the nature and processes of mathematical learning. This has further helped us to uncover and understand characteristic obstacles that most learners of mathematics – and not only those with general learning difficulties – encounter during their attempts to learn mathematics, some even to a detrimental degree. Mathematics specific learning difficulties seem to be of a rather universal nature across cultures, countries and students. In my lecture I shall highlight some of these difficulties with a focus on recent work and findings. I shall further present a research based in-service education programme for upper secondary school teachers enabling them to detect and diagnose upper secondary students with mathematics specific learning difficulties and eventually to remedy or reduce these difficulties.

**Working seminars**

**The leaders of CME’18 working seminars were:**

- kindergarten (3–6-year-olds): Chrysanthi Skoumpourdi, Greece
- primary school (7-9-year-olds0: Jan de Lange, the Netherlands
- primary school (10–12-year-olds): Ineta Helmane, Latvia
- secondary school (13–15-year-olds): Zoltán Kovács, Hungary

**Descriptions of the CME’18 working seminars:**

**1.Kindergarten mathematics in the real world.**

**Chrysanthi Skoumpourdi**, University of the Aegean, Greece

The working seminar ‘Kindergarten mathematics in the real world’ will focus on the correlations between kindergarten mathematics and real world situations and on the importance of this dynamic connection. The following issues will be discussed:

- What do we mean by ‘mathematics in the real world’?
- Is a real situation for us, always real for kindergarten children?
- Which concepts, of the core mathematical units that are taught in kindergarten, can be related with real-world situations?
- Which real-world situations could be used as a context for designing mathematical activities for kindergartners?
- Under what circumstances are real-world mathematics activities motivate children’s mathematical learning?
- What triggers children’s interest to participate to these activities?
- Does educational material play a role to this dynamic connection between kindergarten mathematics and real world situations?
- Could we distinguish the factors that are necessary both for designing activities and for creating educational material appropriate for kindergarten mathematics in the real world?

During the seminar (four sessions, 1.5 hour each) we will work together, discuss and exchange experience and ideas in order to design real-world mathematical activities, as well as educational material for the teaching practice.

**2. The secrets of challenging activities for younger children**

**Jan de Lange**, Emeritus Professor Utrecht University, the Netherlands, Founder Director Jonge Ouder Academie/Young Parents Academy

The hypothesis for the working group will be challenging:

The learning the mathematics should take place in the real world context of challenging activities, facilitating ample exploration, and used in applications. In this way executive functions will be developed. This hypothesis is based on the following observations from research:

Importantly, executive functions may be developed in learning the mathematics in the context of challenging activities, not in “exercising” the mathematics once learned. (Doug Clements 2016)

Exploration is major stimilus for developing executive functions (Moyer 2014, Bryce 2014)

‘Challenging tasks’ is the best present for your brain (Erik Scherder 2018)

Curious Minds, serious play are the essential ingredients for scientific reasoning (Jan de Lange, since 2005)

During the workshop we will discuss four topics:

- The validity of the hypothesis based on the opinions, experiences and knowledge of the participants.
- The desirability of math education in this age range of the integration of arithmetic, mathematics and geometry.
- The role of STE of STEM in M(athematics).
- Design and Examples (bring your own!) of materials fitting the hypothesis.

We expect a very dynamic and positive workshop that will contribute to making further advances in math education for younger kids.

**3. How to create tasks in mathematics based on the thematic approach?**

**Ineta Helmane**, University of Latvia, Faculty of Education, Psychology and Arts, Latvia

Participants of the workshop will get acquainted with and will analyze materials about the nature of the thematic approach as well as aspects of the thematic choice in the acquisition of mathematics content using the thematic approach in primary school. Teaching mathematics thematically emphasises the application of mathematics around a central theme whereas teaching in topics predominantly focuses on the mathematical content. Mathematics content in the framework of the thematic approach is associated with the development of skills in practical activities, the so called ‘hands on’, the correlation of the acquired knowledge based on the theme or a concept; also, skills that can be applied in lifetime actions as well as the development of a sound personal attitude, values and goals. The topicality should be linked with happenings in one’s personal life as well as the latest developments in the community life, socio-economic processes or a scientific context. Applying the thematic approach in mathematics content, we must use such thematic aspects which pupils could encounter in real life associating them with happenings in the private or community life, socio-economic processes or with a scientific context, for example: pupils’ personal experience and situations, socio-economic processes, calendar time, scientific and technological processes, topics related to the content of other school subjects.

The thematic approach has to be implemented in levels: the 1st or object level, the 2nd or information and event level, the 3rd or topic level, the 4th or thematic level. The levels of the implementation of the thematic approach are closely connected with the content of the chosen thematic aspect. It is characteristic that the level of implementation of the thematic approach is lower if pupils master new skills and knowledge in mathematics. The mathematics content, which has to be acquired, dominates in the process of obtaining new skills. However, in the process of developing and strengthening the mastered mathematics content, the level of implementation of the thematic approach is higher.

Participants will have the opportunity to create tasks and activities for acquiring mathematics applying the thematic approach.

**4. Problem posing – tasks and challenges**

**Zoltán Kovács**, University of Nyíregyháza and University of Debrecen, Hungary

Polya suggested in his famous book (“How to solve it”, 1945) that “The mathematical experience of the student is incomplete if he never had an opportunity to solve a problem invented by himself. The teacher may show the derivation of new problems from one just solved, and doing so, provoke the curiosity of the students”.

In the group we focus on the role of problem posing in mathematics education, and several aspects and perspectives of problem posing are presented in the literature.

Problem posing is a feature of inquiry-oriented instruction.

Problem posing is a prominent feature of mathematical activity.

Problem posing is a means to improve students’ problem solving skills.

Problem posing gives an insight into students’ mathematical understanding.

Problem posing improves students’ attitudes toward mathematics.

(Silver, E. A. On mathematical problem posing. For the Learning of Mathematics, 19-28, 1994.)

Each day of the seminar we are going to work out a problem variation chain deriving from an initial problem. The first part of the seminar models the classroom situation, while in the second part we are going to discuss the methods applied. Participants are to discuss how the group leader copes with the open nature of problem posing episodes. We are going to summarize the challenges the teacher may face during problem posing activities. The working seminar is to provide hands-on experience with tasks from various mathematical domains.