Learning Mathematics: Constructivist and Interactionist Theories of Mathematical Development - Hardcover

Hardcover

ISBN 10: 079232823X ISBN 13: 9780792328230

Publisher: Springer, 1994

Synopsis

The first five contributions to this Special Issue on Theories of Mathematical Learning take a cognitive perspective whereas the sixth, that by Voigt, takes an interactionist perspective. The common theme that links the six articles is the focus on students' inferred experiences as the starting point in the theory-building process. This emphasis on the meanings that objects and events have for students within their experiential realities can be contrasted with approaches in which the goal is to specify cognitive behaviors that yield an input-output match with observed behavior. It is important to note that the term 'experience' as it is used in these articles is not restricted to physical or sensory-motor experience. A perusal of the first five articles indicates that it includes reflective experiences that involve reviewing prior activity and anticipating the results of potential activity. In addition, by emphasizing interaction and communication, Voigt's contribution reminds us that personal experiences do not arise in a vacuum but instead have a social aspect. In taking a cognitive perspective, the first five contributions analyze the pro­ cesses by which students conceptually reorganize their experiential realities and thus construct increasingly sophisticated mathematical ways of knowing. The conceptual constructions addressed by these theorists, ranging as they do from fractions to the Fundamental Theorem of Calculus, indicate that experiential approaches to mathematical cognition are viable at all levels of mathematical development. Although the authors use different theoretical constructs, several additional commonalities can be discerned in their work.

About this title

Synopsis

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.

Edition details

• Publisher: Springer
• Publication date: 1994
• Language: English
• ISBN 10: 079232823X
• ISBN 13: 9780792328230
• Binding: Hardcover
• Edition number: 2
• Number of pages: 200
• Editor: Cobb Paul