Creativity and Technology in Mathematics: From Story Telling to Algorithmic with Op'Art (original) (raw)

From Subjective Storytelling to Algorithm

2017

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 choic...

TECHNOLOGY AND ART TO IMPROVE MATHEMATICS LEARNING

The technology is rapidly changing our world, especially the labor market. Consequently, education has to deal with other challenges provoking a re-conceptualization of teaching processes in order to enhance and amplify the learning achievements. On the other hand, the performance results in mathematics achieved by an essential part of European students in the international surveys, such as Program for International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS) are below the Organisation for Economic Cooperation and Development (OECD) average, against the best performances achieved by some Asian countries. This also has been demonstrated by the decreasing interest and motivation of young students in professional and research careers based on science and technology. One of the major cause of the current situation is the resistance of some teachers towards innovative changing and their persistence in the managing of their classes with traditional teaching and learning methods. In fact, the traditional teaching approaches introduce " mathematics " as too abstract subject for students avoiding to emphasise the strict connections that are between scientific topics and reality. Therefore, students can't see the immediate application of science to their everyday life. This situation is intensified, firstly, by the fact that some teachers are lacking digital skills jeopardizing a real and effective integration of technology in their everyday lessons. But where teachers have a good digital literacy, they need more support on how to exploit all the learning potentialities in the use of new technological tools. In this context, a different interdisciplinary and multidisciplinary approach is required to improve and develop science and mathematics skills and to stimulate actively students' interest in the scientific study and for their future careers. An innovative combination between the technology and arts is proposed in this research work ensuring the interconnection of different languages, such as visual, sensory, verbal and non-verbal in the mathematics study. Although the official school curricula are not oriented to underline the existing relations between science and art, the use of painting, dance, theatre, poetry in the mathematics teaching makes science more interesting and attractive and facilitates the development of creative and complex ideas in students. This article discusses the introduction of the technological tools and art-works on the base of the three phases, as defined in Singapore's method applied to mathematics study, that can guide students to the discovery of the challenging connections between math and reality. In particular, the pathway consists in the following basic steps: the objects manipulation (concrete-the first phase), the visual representation (pictorial-the second phase) and the abstract representation of the mathematical concept or formula (abstract-the third phase). In addition, the introduction and integration of technology and art-works in the whole process will allow students to reinforce their conventional, conceptual and procedural understanding based on the theory of variability.

Examples of using mathematics to create artistic products for elementary students

Dong Thap University Journal of Science

Art has generally been associated with aesthetics, emotion, and senses. On the contrary, mathematics has been associated with logic, precision, and truth. It is necessary to understand that throughout history, the two disciplines have been more united than many might consider. Various characteristics believed to be antagonistic have proved to be more convergent than divergent. Both disciplines use patterns, shapes, lines, fractions, and proportions, etc. These concepts are extremely important to both artists and mathematicians. Furthermore, art is now part of the disciplines in education regarding science, technology, engineering, art, and mathematics (STEAM). Mathematical concepts are explicitly and implicitly used to create visual works. Many masterpecies can be seen to be made up of repeating sequences of simple geometric shapes, lines such as M.C. Escher, Wassily, Kandinsky, Paul Klee, and Dalí. This article offers some products that can involve the knowledge of mathematics to c...

A Journey through the geometrical alchemies of art: an example of constructivist teaching

2016

This paper illustrates a teaching setting which adopts a constructivist approach, and is centered on the combination of Mathematics and Art. The aim is to appeal to those minds that have a curiosity for a discipline which has long interacted with artistic expression, and to introduce new perspectives in the teaching of Mathematics in the light of the latest technological challenges. The trigger element - a decorative spiral frieze - has led to a process of Euclidean geometrical construction first with traditional tools, and then through the use of simple algorithms implemented in the MatCos programming environment. The drawing of the spiral curve represents a learning opportunity, a practice which combines analysis and synthesis, a journey between past and present which offers the student the opportunity to acquire some basic conceptual and instrumental implications in the age-old relationship between Mathematics and Art.

Art, Design, and Mathematics: Software programming as artifice in the creative process

Design Culture(s). Cumulus Conference Proceedings Roma 2021, Volume #2, 2021

This article seeks to address the creative qualities of programming in an artistic context. When questioning the limitations of graphical interfaces, we can reflect on the contribution of Programming as a resource to go deeper into a creative process in the context of digital media, robotics, interactivity, generativity, and other possibilities. An exploratory research study was conducted through interviews with laboratory coordinators from educational institutions in Rio de Janeiro, who have explored the possibilities between Art and Technology for at least a decade. Among the main findings that mark the creative process are experimentation and multidisciplinarity. Distaste for Mathematics appears as the main barrier to the insertion of Programming in an artistic context.

Diagrammatic Experiment in Mathematics and in Works of Art

Proceedings of the 37th Annual Meeting of the Semiotic Society of America (Semiotics 2011), 2012

This paper aims to compare the theory of diagram presented in Peirce’s philosophy of mathematics and reflections on the work of art formulated by Henry Van Lier and René Thom. The Peircean Theory of diagram states that a diagram is a visual configuration characterized as a totality that is necessary and at the same time dynamic and experimental. In his lectures about the relation between the local and the global in art (Apologie du logos, 1990), Thom traces a theory of contours of forms that is very similar to the conception of diagram in Peirce’s philosophy. For Thom, beauty is the result of strategies of framing and of composing parts in a dynamic totality. Van Lier’s reflections on works of art develop the idea of a perfect totality characterized by a syntax of traits that are at the right place and that couldn’t be organized in any other way, without which the work of art would have no efficacy. For my part, I aim to explore these similar conceptions of a necessary totality in the arts (aesthetic necessity) and in mathematical diagrams (the necessity in demonstration through forms) in order to describe the differences and the similarities between the theories and the domains of application.