Modelling is a central aspect of the research process in science, technology, engineering, and mathematics (STEM), which occurs in the cognitive context of an interactive balance between theory, experiment, and computation. The STEM learning processes should then also involve modelling in environments where there is a balanced interplay between theory, experiment, and computation. However, an adequate integration of computational themes in STEM high school and undergraduate university curricula remains to be achieved. In this chapter, we present an approach to embed computational modelling activities in the STEM learning processes which may be fruitfully adopted by curricula at secondary and introductory university levels, as well as be a valuable instrument for the professional development of teachers. To illustrate, we consider the example of physics.
IntroductionScience, technology, engineering and mathematics (STEM) are evolving structures of knowledge which are symbiotically interconnected. On one hand, science is based on hypotheses and models, leading to theories, which have a strong mathematical character as scientific reasoning, concepts and laws are represented by mathematical reason-1 ing, entities and relations. On the other hand, scientific explanations and predictions must be consistent with the results of systematic and reliable experiments, which depend on technological developments as much as these depend on the progress of science and mathematics (see, e.g., Chalmers, 1999; Crump, 2001;Feynman, 1967). The creation of STEM knowledge is a dynamical cognition process which involves a blend of individual and collective actions where modelling occurs with a balance between theoretical, experimental and computational elements (Blum, Galbraith, Henn & Niss, 2007;Neunzert & Siddiqi, 2000;Schwartz, 2007; Slooten, van den Berg & Ellermeijer, 2006). In this process, computational modelling plays a key role in the expansion of the STEM cognitive horizon through enhanced calculation, exploration and visualization capabilities.Although clearly related to real world phenomena, STEM knowledge is thus built upon abstract and subtle conceptual and methodological frameworks which in addition evolve following historical dependent paths. These epistemological and cognitive features make science, technology, engineering and mathematics difficult fields to learn and to teach. An approach to STEM education that aims to be effective and in phase with the rapid scientific and technological development should then be based on pedagogical methodologies inspired in the modelling processes of STEM professional activities. Meaningful learning (see, e.g., Mintzes, Wandersee & Novak, 2005) should then occur when students go through balanced interactive explorations of the different cognitive phases associated with the modelling cycles of STEM research, starting from a qualitative contextualization phase, setting the stage for the definition, exploration, interpretation and validation of the relevant mathematical models, and ...