Enhancing science and mathematics education with computational modelling

Abstract

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.