A Change–Resistance Account of Children's Difficulties Understanding Mathematical Equivalence

Most elementary school children in the United States have difficulties understanding mathematical equivalence in symbolic form (e.g., 3 + 4 = 5 + 2, 7 = 7). This is troubling because a formal understanding of mathematical equivalence is necessary for success in algebra and all higher level mathematics. Historically, children's difficulties with mathematical equivalence have been attributed to something that children lack relative to adults (e.g., domain-general logical structures, working memory capacity, proficiency with basic arithmetic facts). However, a change–resistance account suggests that children's difficulties are due to inappropriate generalization of knowledge constructed from overly narrow experience with arithmetic. This account has not only enhanced our understanding of the nature of children's difficulties with mathematical equivalence but also helped us identify some of the malleable factors that can be changed to improve children's understanding of this concept.

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