This chapter presents a case study intended to exemplify the use of a computer as a cognitive tool for learning that occurs socially. We investigate a particularly important kind of social activity, the collaborative construction of new problemsolving knowledge. Collaboration is a process by which individuals negotiate and share meanings relevant to the problem-solving task at hand. The essential property of collaborative problem solving, we argue, is that it enables the construction of a shared conceptual structure which we call a Joint Problem Space. The Joint Problem Space (JPS) supports problem-solving activity by integrating semantic interpretations of goals, features, operators, and methods. We propose that the fundamental activity in collaborative problem solving occurs via the students’ participation in the creation and maintenance of a JPS.