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Jacobs, Victoria R.; Franke, Megan Loef; Carpenter, Thomas P.; Levi, Linda; Battey, Dan – Journal for Research in Mathematics Education, 2007
A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…
Descriptors: Faculty Development, Algebra, Mathematical Logic, Thinking Skills
Carpenter, Thomas P.; Franke, Megan Loef; Levi, Linda – 2003
This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…
Descriptors: Algebra, Arithmetic, Elementary Education, Mathematics Activities
Peer reviewed
Carpenter, Thomas P.; Franke, Megan L.; Jacobs, Victoria R.; Fennema, Elizabeth; Empson, Susan B. – Journal for Research in Mathematics Education, 1998
Presents a three-year longitudinal study investigating the development of children's (n=82) understanding of multidigit number concepts and operations in grades one through three by using interview processes. Provides an existence proof that children can invent strategies for adding and subtracting and illustrates both what that invention affords…
Descriptors: Addition, Arithmetic, Concept Formation, Creative Thinking