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 speci_ c materials and strategies for strengthening preservice and in-service teachers' procedural knowledge.
Ziv Feldman, Mathematics Education Program, School of Education 714, Boston University, Boston, MA 02215; firstname.lastname@example.org
Matt B. Roscoe, Mathematical Sciences Department, Math 213, University of Montana, Missoula, MT 59812; email@example.com