University of the Aegean
Title: Mathematics and the real world in a systemic perspective of the 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.
University of Bremen
Title: 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.
University of Warsaw
Title: What mathematics we should teach in the XXI century?
IMFUFA/INM Roskilde University Roskilde
Title: 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.