Teachers' Uses of a Learning Trajectory for Equipartitioning

Recent work by some researchers has focused on synthesizing what is known about students' thinking of particular concepts. These syntheses elaborate core progressions called learning trajectories that articulate how thinking matures from informal ideas to increasingly complex understandings. Though useful at the level of curriculum, assessment, and standards development, it remains to be shown that learning trajectories can be incorporated into teachers’ practice and become a tool to understand students’ thinking, for planning instructional activities, for interacting with students during instruction, and for assessing students’ understandings. Further, the impact of such incorporation in the classroom on students’ learning is unknown. This design study investigated K-2 teachers’ uses of a learning trajectory for equipartitioning in instruction. Thirty-three teachers participated in 20 hours of professional development focused on a learning trajectory for equipartitioning and key instructional practices including clinical interviewing, task selection and adaptation, analysis of student work, and classroom interactions. A subset of the participants was observed teaching a lesson on equipartitioning and gains in students' learning were measured with pilot items for a diagnostic assessment system. Findings from the study indicate that the introduction of the learning trajectory assisted teachers to varying degrees in building more precise and adequate models of students’ thinking, identifying specifically what students need to learn next, deepening their own understandings of equipartitioning, and facilitating coherent instruction. These findings suggest that learning trajectories can act as a tool for coordinating (1) a student’s behaviors and verbalizations with cognition, (2) various models of thinking among groups of students, and (3) these models with instructional practices.

Author dc:creator

• Wilson, Peter Holt II

Advisors dc:contributor.advisor

• Jere Confrey, Committee Chair
• Karen Hollebrands, Committee Member
• Allison McCulloch, Committee Member
• Roger Woodard, Committee Member

• rational number reasoning
• equipartitioning
• learning trajectories
• mathematics education

Statement dc:rights

• I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dis sertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.

Dc Identifier Other

etd-10142009-142710

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https://repository.lib.ncsu.edu/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Arepository.lib.ncsu.edu%3A1840.16%2F2994