Abstract
Scientific modelling of dynamical systems; towards a pedagogy for secondary education Computer models of complex dynamical systems play a major role in science, as well as in societal debate about issues such as climate change, and insight in models and modelling is an important learning aim in science education. However,
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in teaching practice, it has proven difficult to give computer modelling an integrated role in the curriculum. We took a design research approach to gain insight in the pedagogy of modelling complex dynamical systems. We designed a physics course in which students constructed, evaluated and refined computer models of the climate system. Our design objectives were to get the students engaged in a meaningful modelling process, while retaining essential characteristics of the scientific modelling process. The teaching design was classroom-tested with four teachers and, after being revised, again with one teacher. The overall conclusion is that, although the models become more and more complex along the way, the content and level of the module are well within the range of pupils’ capacities. However, the evaluation of both research cycles revealed some critical problems that hindered the achievement of the teaching goals. Based on what seemed feasible as well as problematic we formulated guidelines for the designing of a modelling curriculum. It is important that modules geared at gaining authentic modelling experience only follow after the teaching of relevant and necessary content knowledge. Focussing on the scientific modelling process should not be combined with substantive content goals. Teaching the paradigmatic models of a domain may be a powerful tool to enable pupils to apply their knowledge in a variety of contexts. Developing these models and teaching pupils how to use them then coincides with teaching the regular physics concepts. We found that students find it difficult to explain behaviour in terms of ‘rules of change’. Therefore, we propose that teaching dynamics focuses on describing the rules of change in terms of differential equations, even for rather simple systems that can be described analytically. Next, we touched upon the delicate balance between guidance and freedom. While some guidance is needed to provide a sense of direction, too much guidance may also hinder insightfulness. In a directive approach in which the teacher shows an expert modelling process, pupils may develop advanced models. However, their own ideas about the system and about how to approach the problem remain unknown. In a pupil-oriented approach it is easy to underestimate the need for explicitly motivating model decisions by the pupils as well as those made by the teacher, in order to establish a truly purpose-driven process. In our tests, teachers were little inclined to let the students evaluate their own contributions, and the students were not used to it either. Thus, if students are to become independent modellers, this will affect the whole classroom culture. Also, experiencing the modelling cycle repeatedly does not guarantee that pupils become more independent modellers themselves. They would benefit from systematic reflection on modelling activities which specifies clearly what each activity should yield and how these yields are achieved.
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