The social context of mathematical development
Abstract
This study considers children's mathematical learning in social context. In particular, the learning of place value concepts and the interpretation and use of the standard addition algorithm were studied in the context of third-grade textbook-based instruction. Modifications in the mathematical beliefs and constructions of three children from a second-grade Purdue Problem-Centered Mathematics Project class were studied as they were acculturated into the tradition of elementary school mathematics. Twenty-seven of the daily mathematics lessons were video-taped over an eight week period. Analysis of transcripts from a socioconstructivist perspective provides an empirically grounded description of the constitution of interaction patterns and of the process by which mathematical practices become institutionalized in a classroom community. Case studies based on Piagetian clinical interviews were used to document the children's mathematical constructions before and after instruction. Classroom transcripts were also analyzed for evidence of the children's mathematical activity during the observation period. The analysis of interaction patterns showed that the mathematical discourse of this classroom community was characterized by a definition of mathematical activity as the following of procedural instructions set forth by the teacher, and by an absence of explanations and justifications on the part of either student or teacher. The case studies demonstrated that the influence of this type of discourse on the children's beliefs about mathematics and on their mathematical constructions was undesirable. One of the three children initially held instrumental beliefs compatible with those held by this community, and quickly learned to complete the tasks correctly despite her concept of ten as an abstract singleton. Another child was able to complete the assigned tasks appropriately because she did not try to please the teacher by following procedural instructions. Instead, she tried to interpret the school-taught procedures in terms of her personally meaningful methods. The third child was unable to complete tasks correctly despite his efficient self-generated algorithms. This occurred because he tried to please the teacher by following her procedural instructions, but without understanding them.
Degree
Ph.D.
Advisors
Wood, Purdue University.
Subject Area
Curricula|Teaching|Mathematics education|Elementary education
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