Mathematics assistants: Meeting the needs of secondary school physics education

Coach is an activity-based, open computer environment for learning and doing mathe­matics, science, and technology in an inquiry approach, developed in the last twenty-five years at the AMSTEL Institute of the University of Amsterdam. It offers a versatile set of integrated tools for data collection, data analysis, modelling and simulation, and for multimedia authoring of activi­ties. In this paper, we present the STOLE concept that underpins the design and imple­menta­tion of systems like Coach. It is an example of how members from the physics education research community came to con­ver­gence on tools for doing investi­gative work and achieved integration of tools. Spe­cial atten­tion goes fur­ther to the mathematical requirements of such a learning envi­ron­ment and to the com­puter support of various representations of one and the same phe­nomenon or scientific concept. We also discuss one of the most complicating factors in the implementation of an integra­ted learning environment for mathe­matics and science, namely that mathematical con­cepts are not al­ways used the same in these fields. Differences between the use of variables, func­tions, and graphs in mathematics and physics are briefly discussed, and consequences for the design of a general-purpose learning envi­ronment are addressed.