ABSTRACT
Mathematical modeling is considered a crucial skills, both in modern life and STEM education. Prior research has identified the relevance of working on complex and authentic modelings problems in education. However, up to this point, little of the courses proposed in this area explicitly focus on the role of comprehensive computing technology during mathematical modeling. We bridge this gap by presenting a design and ready-to-use technology for an interdisciplinary course that introduces students to mathematical modeling of complex systems with comprehensive technology. In the course, students are introduced to grid automatons as basic computing model. Furthermore, they can increase their knowledge of mathematical modeling and algorithmic thinking. In this paper, we develop a didactic structure for such a course and present educational technology developed to support this structure. The structure itself consists of three simulation environments and is based on the following problem: “How can we estimate the time it takes to evacuate our school (without an experiment)?”. We describe the structure of the course and the simulation environments in more details and outline potential exercises for such a course.
- Michal Armoni, Susan Rodger, Moshe Vardi, and Rakesh Verma. 2006. automata theory: its relevance to computer science students and course contents. In Proceedings of the 37th SIGCSE technical symposium on Computer science education.Google ScholarDigital Library
- PD Carey. 1996. DISPERSE: a cellular automaton for predicting the distribution of species in a changed climate. Global Ecology and Biogeography Letters(1996).Google Scholar
- Yimin Chen, Xia Li, Xiaoping Liu, Hu Huang, and Shifa Ma. 2019. Simulating urban growth boundaries using a patch-based cellular automaton with economic and ecological constraints. International Journal of Geographical Information Science 33, 1(2019), 55–80.Google ScholarCross Ref
- Lucian Ciolan and Laura Elena Ciolan. 2014. Two perspectives, same reality? How authentic is learning for students and for their teachers. Procedia-Social and Behavioral Sciences 142 (2014), 24–28.Google ScholarCross Ref
- Andrew Csizmadia, Paul Curzon, Mark Dorling, Simon Humphreys, Thomas Ng, Cynthia Selby, and John Woollard. 2015. Computational thinking-A guide for teachers. (2015).Google Scholar
- Gabriele Di Stefano and Alfredo Navarra. 2012. Scintillae: How to Approach Computing Systems by Means of Cellular Automata. In Cellular Automata.Google Scholar
- Helen M Doerr, Jonas B Ärlebäck, and Morten Misfeldt. 2017. Representations of modelling in mathematics education. In Mathematical modelling and applications.Google Scholar
- Rita Maria Zorzenon Dos Santos and Sérgio Coutinho. 2001. Dynamics of HIV infection: A cellular automata approach. Physical review letters 87, 16 (2001).Google Scholar
- Gerald Futschek. 2006. Algorithmic thinking: the key for understanding computer science. In International conference on informatics in secondary schools-evolution and perspectives. Springer, 159–168.Google ScholarDigital Library
- Vince Geiger. 2011. Factors affecting teachers’ adoption of innovative practices with technology and mathematical modelling. Trends in teaching and learning of mathematical modelling (2011), 305–314.Google Scholar
- Gilbert Greefrath, Corinna Hertleif, and Hans-Stefan Siller. 2018. Mathematical modelling with digital tools—a quantitative study on mathematising with dynamic geometry software. ZDM 50, 1 (2018), 233–244.Google ScholarCross Ref
- Gilbert Greefrath, Hans-Stefan Siller, and Jens Weitendorf. 2011. Modelling considering the influence of technology. Trends in teaching and learning of mathematical modelling (2011), 315–329.Google Scholar
- André Greubel and Hans-Stefan Siller. 2022. Learning about black-boxes: A mathematical-technological model. In Twelfth Congress of the European Society for Research in Mathematics Education (CERME12).Google Scholar
- Andre Greubel, Hans-Stefan Siller, and Martin Hennecke. 2020. Teaching Simulation Literacy with Evacuations. In European Conference on Technology Enhanced Learning. Springer, 200–214.Google Scholar
- Andre Greubel, Hans-Stefan Siller, and Martin Hennecke. 2021. EvaWeb: A Web App for Simulating the Evacuation of Buildings with a Grid Automaton. European Conference on Technology Enhanced Learning (2021).Google ScholarDigital Library
- Lam Bick Har. 2013. Authentic learning. The Active Classroom The Hong Kong Institute of Education (2013).Google Scholar
- Hyewon Jang. 2016. Identifying 21st century STEM competencies using workplace data. Journal of science education and technology 25, 2 (2016), 284–301.Google ScholarCross Ref
- Gabriele Kaiser. 2014. Mathematical Modelling and Applications in Education. Springer Netherlands, Dordrecht, 396–404.Google Scholar
- Gabriele Kaiser, Martin Bracke, Simone Göttlich, and Christine Kaland. 2013. Authentic Complex Modelling Problems in Mathematics Education. Springer International Publishing, Cham, 287–297. https://doi.org/10.1007/978-3-319-02270-3_29Google Scholar
- Kanika, Shampa Chakraverty, and Pinaki Chakraborty. 2020. Tools and techniques for teaching computer programming: A review. Journal of Educational Technology Systems 49, 2 (2020), 170–198.Google ScholarCross Ref
- Jarkko Kari. 2005. Theory of cellular automata: A survey. Theoretical computer science 334, 1-3 (2005), 3–33.Google Scholar
- Lemont B Kier, Paul G Seybold, and Chao-Kun Cheng. 2005. Modeling chemical systems using cellular automata. Springer Science & Business Media.Google Scholar
- Richard Lesh and Guershon Harel. 2003. Problem solving, modeling, and local conceptual development. Mathematical thinking and learning(2003).Google Scholar
- Yang Li, Maoyin Chen, Zhan Dou, Xiaoping Zheng, Yuan Cheng, and Ahmed Mebarki. 2019. A review of cellular automata models for crowd evacuation. Physica A: Statistical Mechanics and its Applications 526 (2019), 120752.Google Scholar
- Katja Maaß. 2006. What are modelling competencies?ZDM 38, 2 (2006), 113–142.Google Scholar
- Anthony D McKenzie, Christopher K Morgan, Kerry W Cochrane, Geoff K Watson, and David W Roberts. 2002. Authentic learning. In Proceedings of the 25th HERDSA Annual Conference. Citeseer, 426–433.Google Scholar
- Kai Nagel and Michael Schreckenberg. 1992. A cellular automaton model for freeway traffic. Journal de physique I 2, 12 (1992), 2221–2229.Google Scholar
- Jan L Plass, Roxana Moreno, and Roland Brünken. 2010. Cognitive load theory. Cambridge university press.Google Scholar
- Mitchel Resnick, Brad Myers, Kumiyo Nakakoji, Ben Shneiderman, Randy Pausch, Ted Selker, and Mike Eisenberg. 2005. Design principles for tools to support creative thinking. (2005).Google Scholar
- Stefan Ruzika, Lynn Knippertz, and Eva Rexigel. 2019. Simulation von Evakuierungen auf Grundlage zellulärer Automaten. Technical Report. Uni. of Kaiserslautern.Google Scholar
- Stefan Ruzika, Hans-Stefan Siller, and Martin Bracke. 2017. Evakuierungsszenarien in Modellierungswochen. In Neue Materialien für einen realitätsbezogenen Mathematikunterricht 3. Springer, 181–190.Google Scholar
- Cynthia Selby and John Woollard. 2013. Computational thinking: the developing definition. (2013).Google Scholar
- Hans-Stefan Siller and Gilbert Greefrath. 2010. Mathematical modelling in class regarding to technology. In Proceedings of the sixth congress of the European Society for Research in Mathematics Education. 2136–2145.Google Scholar
- Thomas Staubitz, Ralf Teusner, Christoph Meinel, and Nishanth Prakash. 2016. Cellular Automata as basis for programming exercises in a MOOC on Test Driven Development. In 2016 IEEE International Conference on Teaching, Assessment, and Learning for Engineering (TALE). https://doi.org/10.1109/TALE.2016.7851824Google ScholarCross Ref
- Antonio J. Tomeu Hardasmal and Alberto G. Salguero. 2020. Teaching Parallelism With Gamification in Cellular Automaton Environments. IEEE Revista Iberoamericana de Tecnologias del Aprendizaje 15, 1(2020), 34–42.Google ScholarCross Ref
- Jeanette Wing. 2011. Research notebook: Computational thinking—What and why. The link magazine 6(2011), 20–23.Google Scholar
Index Terms
- Teaching Mathematical Modeling with Computing Technology: Presentation of a Course based on Evacuations
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