The traditional system of education is no longer fulfilling the need for knowledge for the generations that experience the actual leap of information and technology. To go exponentially beyond the actual way of thinking elicits a dynamic, adaptable and customized system of education, approachable by connecting fields and notions. Inter-disciplines become a solution and a necessity - "The strongest argument for interdisciplinarity is the very fact that life is not divided into disciplines." (J. Moffett). Learning beyond meaning is not an issue - youngsters need a visual, interdisciplinary, hands-on approach that may be accomplished by our method: DigiMathArt is an interdisciplinary field that covers the need to cross the bridge towards the education of the future. The proposed method emphasizes the simplicity and elegance of mathematic modeling combined naturally with graphical programming, alien concepts for most of those who need them the most - scientists, architects, game developers, artists. It provides an interactive, highly visual and holistic road to access essential information and skills. The course is structured in three modules: mathematic modeling based on function operations and composition, fractal generation, and light-effects rendering. Similar in approach to more sophisticated resources, such as Grasshopper and WolframAlpha, our method is, however, gradual and palatable for anyone who lacks this basic training in the field but craves for it. The presented method is already implemented and used as a holistic tool in centers for informal education. Evaluations of method's results, acceptance and effects are underway, based on structured feedback questionnaires as well as EEG recordings and analysis.
One of the modern modeling methods, implemented in several advanced CAD systems, is parameterized modeling. While these systems support powerful parametric modeling, they are rather oriented toward production and less towards education, even if the related mathematical concepts are somehow difficult for most users. Thus, they are hardly usable in the learning of related mathematical concepts, programming, and general STEM education. In this paper we describe our parameterized modeling method, intuitive and easier to use, based on repetitive function composition and interactive variation of their parameters. The method is particularly adequate for learning mathematics by visually perceiving the effect of functions composition and parameters variation. Our method shares some common aspects with parametrized modeling tools from existing CAD systems, such as: enables modifying the parametric equations of graphical primitives, applies function composition and interactive modifying parameters. In addition to these basic aspects, our method has distinctive characteristics, such as: a specific formalism and implementation, oriented towards understanding the shapes and how they are affected, and can be evolved iteratively through functions’ composition; large set of basic, intuitive functions, with clearly observable explanations and visual effects; variations to the simple, classical functional composition, such as translational composition; because the modeling method is based on a repetitive mechanism, it can lead to the modeling of fractal-like shapes, but they are different from those obtained with classic fractal models. Our modeling system acts as a powerful tool for deeply understanding mathematical functions and their composition through interactive visualization, for a wide range of users, with various backgrounds and levels of mathematical training. In addition, by visualizing the source code which uses the mathematical model for graphical rendering, the system can naturally be used as a tool for learning programing. Because learning is visual and interactive, it’s engaging, immersive and attractive. Furthermore, as more brain areas are simultaneously involved and stimulated, it leads to the development of intelligence and the accelerated learning of mathematics, a process which we are in the process of evaluating through EEG measurements and analysis.
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