Enhancing science and mathematics education with computational modelling

The development of knowledge in science and mathematics involves modelling processes where theory, experiment and computation are dynamically interconnected. For education in these fields to be in contact with their rapid progress and closer to the nature of research, it is crucial that both curricula and learning environments from high school to university manifest effectively a balanced interplay between theoretical, experimental and computational elements. We present an approach to improve the integration process of computational modelling in the science and mathematics high school and university curricula while respecting the cognitive balance between theoretical aspects, experimentation and scientific computation. As strategy, we propose the creation of learning activities built around exploratory and expressive computational modelling experiments which are presented in digital documents where the fundamental concepts and problem solving processes are explained using interactive text, images and embedded movies. To design the activities, special emphasis is given to cognitive conflicts in the understanding of scientific and mathematical concepts, to the manipulation of multiple representations of mathematical models and to the interaction between analytical and numerical solutions. We discuss illustrative examples constructed with Modellus which are relevant for the high school and undergraduate university curricula in mathematics and physics

Computers, modelling and meaningful learning in science and mathematics

Scientific computation is an essential component for the development of knowledge in science and mathematics. However, the balance that exists in research between computation, experimentation and theory is still far from being adequately incorporated in the corresponding high school and undergraduate university curricula. In this article we discuss the theoretical rationale supporting the development of curricula and learning environments that integrate computational modelling, while balancing the different knowledge components of science and mathematics. We discuss the advantages of using Modellus as a central element of such modelling approach and illustrate with an interactive computational modelling activity in physics. We also report the results of the implementation of this approach in several undergraduate university courses

Learning introductory physics with computational modelling and interactive environments

For the modern physics research community there is no doubt that the development of physics knowledge and cognition involves modelling processes that balance different elements of theory, experimentation and scientific computation. However, the majority of the current introductory physics curricula and learning environments for science, technology, engineering and mathematics education do not always reflect this range of epistemological characteristics. Changing this situation requires introductory physics curricula and learning environments structured around pedagogical methodologies inspired in the modelling cycles of physics research, to help students create and explore balanced learning paths that go through the different cognitive stages associated with the modelling processes involved in the development of physics knowledge and cognition. In this paper we present an approach to this problem that is based on the development of interactive engagement learning activities built around exploratory and expressive computational modelling experiments implemented in the Modellus environment. We illustrate with activities implemented in the general physics and biophysics courses of the biomedical and informatics engineering majors at FCT/UNL. We report on student receptivity to our modelling approach and discuss its effect on the learning process

Modellus: Learning Physics with Mathematical Modelling

Tese de doutoramento em Ciências da Educação, área de Teoria Curricular e Ensino das CiênciasComputers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge