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Modelling process and validation competences The process of applying mathematical concepts and methods to realistic situations can be described by a modelling cycle. For example, Blum and Leiss (2007) proposed seven steps which persons go through in their modelling process: understanding the situation, simplifying the situation, setting up a mathematical model, working in this model, interpreting the mathematical results, validating the modelling process, and presenting the result to the situation. Niss (1994) concludes that validating the process is one of the major competences because in many modelling processes it is necessary to modify the initial mathematical model. However, research identifies students’ problems in validating the process (Hankeln, 2020): they seldom validate their modelling process and do not see the relevance of this step. Concerning motivation in mathematics, it is assumed that modelling tasks can enhance students’ motivation because the relevance of mathematical concepts and methods gets visible. However, Krug and Schukajlow (2013) and Krawitz and Schukajlow (2018) have shown that students in secondary school assign more interest and more value to intra-mathematical tasks than to modelling tasks. Experimentation as an approach to foster competences and motivation and hypotheses of the project One approach to foster students’ modelling competences and motivation is to combine experimentation and modelling tasks (e. g., Beumann, 2016; Ganter, 2013): students collect data in one experiment and analyse these data in the following modelling process. By using their own data, students are probably more interested in the modelling process and experimentation is often fun to students. Such an approach probably leads to more motivation, in particular to more interest, as conducting the modelling process with given data. In addition, experimental data has the feature that measurement errors occur. Because of measurement errors, the validation activity is a sensible learning activity because not only one mathematical model fits well to the data (Zell & Beckmann, 2009). We assume that using experimental data supports students’ modelling competences, in particular validation competences, in contrast to using smoothed data, no matter if the experimental data is self-generated or given. Research design Learning environments, each consisting of three 90-minutes lessons were developed. In each lesson, a modelling task is presented to the students: in the first lesson burning off a candle, in the second lesson decay of beer forth, and in the third lesson cooling off tea. These modelling tasks can be solved by setting up a linear or an exponential function. The learning environments differ concerning two conditions: a) form of data which were analysed in all lessons and b) hints or no hints for validating in the second lesson. The form of data is in the first group self-generated experimental data, in the second group given experimental data, and in the third group given smoothed data. Each of these groups are split up by the conditions of b) – getting hints for validation or getting no hints for validation. In sum, students are divided into six different groups. Students of grade 9 to 12 participate in our study. These students know linear and exponential functions from previous lessons. Whole classes are assigned to one of the conditions of a). Then the class is split up by the conditions of b). We use a pre-post design to analyse changes in students’ modelling competences and motivation. In addition, we will measure students’ motivation and perceptions during working on the mathematical modelling tasks and the products of their work. Literature Aeschlimann, B., Herzog, W., & Makarova, E. (2016). How to foster students’ motivation in mathematics and science classes and promote students’ STEM career choice. A study in Swiss high schools. International Journal of Educational Research, 79, 31–41. https://doi.org/10.1016/j.ijer.2016.06.004 Beumann, S. (2016). Versuch´s doch mal: Eine empirische Untersuchung zur Förderung von Motivation und Interesse durch mathematische Schülerexperimente [Just try it: an empirical study concerning the promotion of motivation and interest with mathematical experiments] (Dissertation). Ruhr-Universität Bochum. Blum, W., & Leiss, D. (2007). How do students and teachers deal with modelling problems. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering, and economics (pp. 222–231). Horwood. Ganter, S. (2013). Experimentieren – ein Weg zum Funktionalen Denken: Empirische Untersuchung zur Wirkung von Schülerexperimenten [Experiments – a way to functional thinking: an empirical study concerning the effect of student experiments]. Dr. Kovac. Hankeln, C. (2020). Mathematical modeling in Germany and France: a comparison of students’ modeling processes. Educational Studies in Mathematics, 103, 209–229. https://doi.org/10.1007/s10649-019-09931-5 Krawitz, J., & Schukajlow, S. (2018). Do students value modelling problems, and are they confident they can solve such problems? Value and self-efficacy for modelling, word, and intra-mathematical problems. ZDM, 50(1–2), 143–157. https://doi.org/10.1007/s11858-017-0893-1 Krug, A., & Schukajlow, S. (2013). Problems with and without connection to reality and students’ task-specific interest. In A. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 209–216). PME. Niss, M. (1994). Mathematics in society. In R. Biehler, R. W. Scholz, R. Sträßer, & B. Winkelmann (Eds.). Didactics of Mathematics as a Scientific Discipline (pp. 367–378). Kluwer Academic Publishers. Zell, S. & Beckmann, A. (2009). Modelling Activities While Doing Experiments to Discover the Concept of Variable. In V. Durand-Guerrier, S. Soury-Lavergne & F. Arzarello (Eds.), Proceedings of CERME 6 (pp. 2216–2225). INRP.
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