mathematics, teacher training


This teaching experiment used design-based research (DBR) to document the norms and practices that were established with respect to fractions in a mathematics content course for prospective elementary teachers. The teaching experiment resulted in an instructional theory for teaching fractions to prospective elementary teachers. The focus was on the social perspective, using an emergent framework which coordinates social and individual perspectives of development. Social norms, sociomathematical norms, and classroom mathematical practices were considered. A hypothetical learning trajectory (HLT) including learning goals, instructional tasks, tools and imagery, and possible discourse, was conjectured and implemented in the mathematics class. Video tapes of the class sessions were analyzed for established norms and practices. Resulting social norms were that students would: (a) explain and justify solutions, (b) listen to and try to make sense of other students' thinking, and (c) ask questions or ask for clarification when something is not understood. Three sociomathematical norms were established. These were expectations that students would: (a) know what makes an explanation acceptable, (b) know what counts as a different solution, and (c) use meaningful solution strategies instead of known algorithms. Two classroom mathematical practices with respect to fractions were established. The first was partitioning and unitizing fractional amounts. This included (a) modeling fractions with equal parts, (b) defining the whole, (c) using the relationship of the number of pieces and the size of the pieces, and (d) describing the remainder in a division problem. The second practice was quantifying fractions and using relationships among these quantities. This included: (a) naming and modeling fractions, (b) modeling equivalent values, and (c) using relationships to describe fractions. Finally, recommendations for revising the HLT for a future teaching experiment were made. This will contribute toward the continuing development of an instructional theory for teaching fraction concepts and operations to prospective elementary teachers.


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Graduation Date



Dixon, Juli


Doctor of Education (Ed.D.)


College of Education


Teaching and Learning Principles

Degree Program

Curriculum and Instruction








Release Date

June 2008

Length of Campus-only Access


Access Status

Doctoral Dissertation (Open Access)