Encouraging Teachers to Make Use of Multiplicative Structure

The literature has shown that preservice elementary school teachers (PSTs) struggle to adequately attend to a number’s multiplicative structure to determine divisibility. This study describes an intervention aimed at strengthening preservice and in-service teachers’ procedural knowledge with respect to using a number’s prime factorization to identify its factors, and presents evidence of the impact of the intervention. Results point toward improved abilities to use a number’s prime factorization to sort factors and nonfactors across four factor subtypes, to create factor lists, and to construct numbers with particular divisibility properties. Implications for mathematics teacher education include providing specific materials and strategies for strengthening preservice and in-service teachers’ procedural knowledge.

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