On October 29, at 4:00 p.m., a session of ISEP Webinars will be held, organized by “Instituto Superior de Engenharia do Porto” (ISEP).        

The seminar will be presented by Thierry (Noah) Dana-Picard and will focus on the theme “Fruitful dialogue between technologies as a central tool for a STEAM approach.”

To access the seminar, please click here.

Abstract

We present a bunch of activities relying on an experimental approach to various topics. This switches from the traditional segment definition-theorem-proof-examples towards a more modern approach, namely exploration-experimentation-conjecture-proof.

This approach relies on automated methods, especially in geometry and real algebraic geometry, but not only. It enables extensions of the curriculum towards multi-disciplinary activities, modelling, and art creation.

The dialog is needed because of the different abilities of different packages, mostly Computer Algebra Systems (CAS) and Dynamic Geometry Systems (DGS). At the beginning, CAS focused on symbolic computations and DGS more on dynamics and visualization. Mixing both has developed, yielding a stronger synchronization between different registers of representations of mathematical objects. Recall that CAS provides generally one-directional switching from algebra to geometry (plots), and CAS is bidirectional. The introduction of 3D printing into the activities yields a new register, not limited to a screen, and enabling to grasp mathematical objects with hands.

In our talk, we will illustrate this with examples from real algebraic geometry (construction and automated analysis of properties), models of planetary motion (trigonometric presentations and dynamics), and others. The terrain for implementation of these activities is undergraduates and graduate students in engineering or in math and science education.

Bio

Thierry Dana-Picard (born 1954, France) is an Israeli mathematician, full professor of mathematics, and a former president of the Jerusalem College of Technology (JCT) from 2009-2013. He holds two PhDs (Nice University, France, 1981, and Bar Ilan University, Israel, 1990). He has been teaching at JCT for several years and published more than 150 scientific articles in  integral calculus and combinatorics, real algebraic geometry, mathematics education, etc.. He is strongly involved in engineering education is and in teacher training, and a member of several international editorial boards and scientific committees. His research fields include geometry, real algebraic geometry, technology-based mathematics education (including AI), strongly oriented towards STEAM education.