Plenary lectures

Descartes  and Fermat in the 17^th century introduced an arithmetical approach to geometry, allowing for the application of algebra to formerly purely geometrical questions. This initiated the “analytic approach” to curves and subsequently to the Calculus and is now the standard way of starting many pure mathematical topics. The preferred arena for this modern approach is that of the “real numbers”: however these are never really adequately presented, and a clear derivation of their key properties is a gaping logical hole in our subject. Nevertheless, Calculus, Differential Geometry, Algebraic Geometry and much of modern Number theory are supposedly built from this “foundation”.

Modern computer systems are however not as gullible as undergraduate students, and it is clear that they are not capable of incorporating “real number arithmetic” in a computationally explicit way. So we have an increasing divergence between what pure mathematics researchers and educators say — and what their computers can do. “We work over the real numbers!” yet … most of our examples are over the integers or the rational numbers, with a few token “sqrt(2)”s and “pi”s thrown in.

How to transgress from this false orthodoxy? The key is to reassert the primacy of integer arithmetic and its offspring rational number arithmetic. But can we do geometry, and Calculus, and number theory etc. in this framework? Yes we can. Let’s see how this Pythagorean program can be revitalized for modern times.

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4th June, 3 p.m. – 4 p.m. (CET, time in Poland)

Zsolt Lavicza

Professor at the Linz School of Education, Johannes Kepler University, Linz, Austria

Inspiring Teachers’ Classroom Innovations Through The Integration of Augmented/Virtual Reality and 3D Printing into Their Practices

The swift evolution of 3D technologies has opened up diverse opportunities for 3D modelling to be utilised in education both in digital and physical formats. As industries like medicine, construction, and technology design increasingly rely on 3D modelling, its potential applications in education are increasingly gaining traction. This talk, based on studies conducted by the STEAM education research group at the Linz School of Education, Johannes Kepler University, Austria, delves into introducing Augmented/Virtual Reality and 3D printing in teacher education across various countries. We explored teachers’ perceptions, established the requisite educational ecosystem for 3D technologies, evaluated pedagogical approaches for integrating 3D modelling into classrooms, and emphasised the incorporation of arts and culture to inspire students. Our initiatives extend to creating 3D resources for students with disabilities and those from disadvantaged communities, as well as fostering girls’ engagement in STEM studies through 3D modelling. The core objective of our studies is to empower teachers and students as innovators in utilizing these novel technologies. Additionally, we addressed the demand for new theoretical and methodological approaches by expanding our work from mathematics to STEAM, introducing a STEAM+X approach, and supplementing Design Based Research (DBR) with User Experience (UX) research methodologies to adapt to rapid technological changes. In this talk, exemplary practices will be described showcasing secondary and primary education in Europe, Asia, Africa, and Latin America.

4th June, 4 p.m. – 5 p.m. (CET, time in Poland)

James Tanton

Mathematician in Residence at the Mathematical Association of America in Washington D.C.

The astounding visual story of place value: from base 10 to base x

It’s a global phenomenon in mathematics! Over 8 million students and teachers from over 170 countries and territories across the planet have, with a single visual model, re-envisioned mathematics they thought they knew so well and embraced it in stunning new light. Early-school mathematics and high-school mathematics (and beyond!) are united in one beautiful and accessible whole.