Dynamic models

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Use of modern technologies in education is not only a question of support and development of the existing teaching methods, but also the question of how to innovate the content taught, how to set new types of problems to pupils, how to achieve a situation in which pupils gain new types of knowledge. The paper focuses on one specific way of the use of computers in mathematics classrooms-the dynamic models. What is characteristic for dynamic models is the use of a new dimension-movement. The use of movement and its recording enables not only to present new problems to pupils but also to deepen and extend their existing knowledge. While working with pupils and students, the author tried to identify and subject to further study the areas where the use of dynamic models is of benefit to pupils and the kind of new knowledge pupils may gain thanks to the use of dynamic models. The author of this paper focuses primarily on knowledge that pupils would hardly gain if computer technology were not used. The paper characterizes four types of problems in which dynamic models introduce efficiently new knowledge that could be hard to visualize using traditional means and that would probably have to be derived analytically. These are: Emphasis of invariants-Dynamic models allow us to emphasize elements that are invariant even when parameters change, e.g. intersection points of straight lines or relative position of points on a circle. Discovery of shared properties-Dynamic models may help us discover regularities in elements whose behaviour changes. Discovering the limits-These are situations in which the properties of the model change considerably. Step change-The last type of observation using dynamic models is observing step changes in objects. In some cases a radical change in the model's behaviour points at secondary solutions that are hidden in the place of the sudden change. Results indicate that dynamic models are suitable for development of mathematical thinking. We managed to identify several areas in which dynamic models may develop or extend understanding of different concepts. They bring new knowledge that would be hard to gain using traditional means, all this in an illustrative, visual and clear way. Results from experiments show that the knowledge pupils gain through the use of dynamic models is transferrable also to situations when pupils solve problems using traditional methods, as they support pupils' skills to visualise and their creativity.




Jančařík, A. (2015). Dynamic models. In Proceedings of the European Conference on e-Learning, ECEL (pp. 264–271). Academic Conferences Limited. https://doi.org/10.4324/9781351032148-3

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