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.