Learning Mathematics

The common theme that links the six contributions to this volume is the emphasis on students' inferred mathematical experiences as the starting point in the theory-building process. The focus in five of the chapters is primarily cognitive and addresses the processes by which students construct increasingly sophisticated mathematical ways of knowing. The conceptual constructions addressed include multiplicative notions, fractions, algebra, and the fundamental theorem of calculus. The primary goal in each of these chapters is to account for meaningful mathematical learning -- learning that involves the construction of experientially-real mathematical objects. The theoretical constructs that emerge from the authors' intensive analyses of students' mathematical activity can be used to anticipate problems that might arise in learning--teaching situations, and to plan solutions to them. The issues discussed include the crucial role of language and symbols, and the importance of dynamic imagery. §The remaining chapter complements the other contributors' cognitive focus by bringing to the fore the social dimension of mathematical development. He focuses on the negotiation of mathematical meaning, thereby locating students in ongoing classroom interactions and the classroom microculture. Mathematical learning can then be seen to be both an individual and a collective process.