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Norton, Anderson; Ulrich, Catherine; Kerrigan, Sarah – Journal for Research in Mathematics Education, 2023
This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in…
Descriptors: Graphs, Fractions, Short Term Memory, Preservice Teachers
Norton, Anderson; Wilkins, Jesse L. M.; Xu, Cong ze – Journal for Research in Mathematics Education, 2018
Through their work on the Fractions Project, Steffe and Olive (2010) identified a progression of fraction schemes that describes students' development toward more and more sophisticated ways of operating with fractions. Although several quantitative studies have affirmed this progression, the question has remained open as to whether it is specific…
Descriptors: Foreign Countries, Fractions, Mathematics Instruction, Grade 5
Norton, Anderson; Wilkins, Jesse L. M. – Journal for Research in Mathematics Education, 2012
Piagetian theory describes mathematical development as the construction and organization of mental operations within psychological structures. Research on student learning has identified the vital roles of two particular operations--splitting and units coordination--play in students' development of advanced fractions knowledge. Whereas Steffe and…
Descriptors: Numbers, Psychology, Piagetian Theory, Grade 8
Wilkins, Jesse L. M.; Norton, Anderson – Journal for Research in Mathematics Education, 2011
Teaching experiments have generated several hypotheses concerning the construction of fraction schemes and operations and relationships among them. In particular, researchers have hypothesized that children's construction of splitting operations is crucial to their construction of more advanced fractions concepts (Steffe, 2002). The authors…
Descriptors: Mathematics, Experiments, Teaching Methods, Cognitive Processes