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GISMO Team presentations PME-NA 2012

Thursday, November 1 through Sunday, November 4,

GISMO Team presentations at the Annual Meeting of the Psychology of Mathematics Education–North American Chapter.  Kalamazoo, Michigan


Friday, November 2, 2012

Dr. Jere ConfreyArticulating a Learning Sciences Foundation for Learning Trajectories in the CCSS-M (Plenary Presentation)

1:00 to 2:30 pm

The paper describes the history of how learning trajectories (LTs) were associated with the Common Core State Standards for Mathematics (CCSS-M) and discusses the degree to which the two correspond faithfully. It reports on a website,, which organizes the K–8 standards into 18 LTs describing the development of big ideas over time, informed by empirical studies of learners. The paper illustrates how descriptors for each LT identify: (1) conceptual principles; (2) strategies, representations, and misconceptions; (3) meaningful distinctions and multiple models; (4) coherent structure; and (5) bridging standards.  The design principles for the website are illustrated describing how the CCSS-M are related to a learning trajectory on division and multiplication.


Saturday, November 3, 2012

Dr. Kenny Nguyen, Dr. KoSze Lee, and Dr. Jere Confrey : Unpacking the Common Core State Standards for Mathematics: The Case of Length, Area and Volume

10:30 to 11:10 am

Adoption of Common Core State Standards presented challenges to school districts, school administrators and teachers. Teachers need resources to understand how the Standards can be sequenced in a way that is pedagogically coherent and sound. In this proposal, we present our work on unpacking the CCSS-M Standards for the Length, Area and Volume Learning Trajectory. The overarching theme of “genetic epistemology” and a five-characteristic framework guided our work of unpacking the Standards. As a result, a coherent structure of unpacked LT emerged across length, area, and volume. The unpacked LT document will be disseminated. Brief discussion about future work follows.


Sunday, November 4, 2012

Drew Corley and Dr. Jere Confrey :Students’ Transition from Proto-Ratio to Ratio and Proportional Reasoning Through Co-Splitting and Equipartitioning

9:40 to 10:20 am

This paper presents preliminary findings on the strategies used by third-grade students while working with the topic of covariation, within equipartitioning, and how students develop an understanding of the concept based on prior learning experiences. The range of these strategies are discussed as to how they pertain to a movement from proto-ratio reasoning to more fluent and sophisticated ratio and proportional reasoning, eliciting implications for equipartitioning as a strong foundation on which to create such a transformative move in thinking.