Theories of Mathematical Learning

By Leslie P. Steffe; Pearla Nesher et al. | Go to book overview

8
Learning Mathematics as Participation in Classroom Practice: Implications of Sociocultural Theory for Educational Reform

Ellice Ann Forman University of Pittsburgh

Educational reformers in the United States are calling for sweeping changes in instructional practices, such as the new standards for mathematics instruction from the National Council of Teachers of Mathematics ( NCTM, 1989, 1991). They argue that students need to be actively involved in practicing mathematics by working in small groups, negotiating ways to define and organize the data in open-ended problems, arriving at multiple solutions, and explaining their ideas to each other. These practices are in contrast to what is seen in more traditional North American mathematics classrooms in which whole-class, teacher-dominated didactic instruction and individual seatwork are the norm. In addition to changes in the processes of instruction, the reform movement is also calling for new instructional goals: from the memorization of number facts and the accurate use of computational algorithms to greater understanding of mathematical concepts and more effective use of problem-solving strategies. Enhancing students' abilities to communicate and to collaborate with others is also emphasized. In addition, the reform movement is interested in changing students' attitudes toward learning mathematics: from anxiety and passive obedience to authority to enthusiasm, confidence, and active involvement in problem solving. Although the reformers call for change in practice as well as content, the new standards for mathematics instruction, for example, contain more information about the latter than the former. More seriously, there is very little justification provided for the connections between changes in practice and desired instructional outcomes.

A number of North American educational reformers have based their proposals on a family of psychological and anthropological theories referred to as sociocultural theory ( Brown, Collins, & Duguid, 1989; Forman, Minick, &

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