Abstract
This article describes some of the results of the European project mcSquared (http://mc2-project.eu/) regarding the use of Op'Art and optical illusion pieces as a tool to foster modeling and creative mathematical thinking in students. We present briefly the c-book technology and some results we got experimenting it. The Op'Art movement, with artists such as Victor Vasarely, Julio Le Parc or Bridget Riley, uses algorithms to create geometric patterns. It is a goldmine for mathematical thinking, from early ages, with the use of narratives to describe the paintings and produce new ones in a controlled way, up to higher education with generative art produced by the implementation of algorithm. The outcome is that technology, far from hindering the creative process actually can be used to help putting it on firm grounds, narrowing the diverging phase into a converging one by giving means to objectify the description and creation of the artwork itself and making explicit the choices made, allowing for the creative exploration of new original ways: what if… . This objectivation is done differently by different audiences but comprises the same phases of identifying the relevant variables (disks, squares, colors, position), describing their relationships (the color of the disks depends on their position in such a way) and exploring the space of configurations the modeling gives rise to.
Highlights
If mathematics is the queen of science, geometry is the queen of mathematics
The use of interactive geometry as a mean to explore complex configuration spaces and as a lever towards abstraction has been pointed out many times (Laborde-Sträÿer, 2010), but linking it to narratives or language issues (Bulf-MathéMithalal, 2015) and even more interactive storytelling is a rather recent phenomenon: The M C Squared project created the C-book technology, an infrastructure allowing for the blending of hyper-text, images and widgets of diverse origins into a single interactive narrative, an electronic book aimed at promoting creative mathematical thinking in its users
Technology is lurking behind the scene and does promote advanced creative mathematical thinking, a basic unplugged version is doing the job of fostering creative mathematical thinking and might be preferable as an introduction: Paper printed versions were preferred even though the electronic versions allowed for electronic color picking or precise measurements
Summary
If mathematics is the queen of science, geometry is the queen of mathematics. this paramount subject has not been well treated in recent curricula reforms in Europe. The use of interactive geometry as a mean to explore complex configuration spaces and as a lever towards abstraction has been pointed out many times (Laborde-Sträÿer, 2010), but linking it to narratives or language issues (Bulf-MathéMithalal, 2015) and even more interactive storytelling is a rather recent phenomenon: The M C Squared project (see acknowledgments) created the C-book technology, an infrastructure allowing for the blending of hyper-text, images and widgets of diverse origins into a single interactive narrative, an electronic book aimed at promoting creative mathematical thinking in its users. The description of the technological infrastructure of this project is not the focus of this article, suffice to say that students can create and share pictures, programs and interactive geometry figures of different origins, and discuss about them on the same page, accumulate these pages in an electronic book. The data collected and discussed here are their electronic productions only but the exchanges and interplays were not recorded, our interpretation is discussed here
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