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Kindergartners' Understanding of Additive Commutativity within the Context of Word Problems

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Abstract:

Baroody and Gannon (1984) proposed that children's understanding of additive commutativity progresses through several levels of understanding based on a unary view of addition (change meaning) before developing a “true” level of understanding based on a binary conception (part-whole meaning). Resnick (1992) implied that children have both a unary and a binary conception of additive commutativity from the earliest stages of development. Fifty-three 5- and 6-year-old (M = 6-0) kindergartners' unary and binary understanding of additive commutativity was investigated using performance on tasks involving change-add-to and part-part-whole word problems, respectively. The data were inconsistent with the predictions of both models and suggest three alternate theoretical explanations. Moreover, the data indicate that success on a task involving change-add-to problems may be a more rigorous test of understanding of additive commutativity than that involving part-part-whole problems.

Keywords: addition; commutativity; early childhood; kindergarten; mathematics education; word problems.

Document Type: Research Article

Affiliations: 1: Virginia Polytechnic Institute and State University 2: University of Illinois at Urbana-Champaign

Publication date: May 1, 2001

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