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ERIC Number: ED525805
Record Type: Non-Journal
Publication Date: 2010
Pages: 268
Abstractor: As Provided
Reference Count: 0
ISBN: ISBN-978-1-1244-7205-8
Investigating the Role of Equipartitioning and Creating Internal Units in the Construction of a Learning Trajectory for Length and Area
Nguyen, Kenny Huy
ProQuest LLC, Ph.D. Dissertation, North Carolina State University
Under current learning trajectories for length and area, researchers examine how students coordinate and systematize measurement using a given external iterating unit. This study investigates the possible cognitive behaviors missing in that approach by giving students the larger task of comparing areas to see how they construct internal units based on related ideas of equipartitioning (Confrey, Maloney, Nguyen, Mojica, & Myers, 2009). It investigates three case studies from a teaching experiment with four third-grade students and examines the strategies, mathematical reasoning practices, and emergent relations and properties that they generated. The results were synthesized into a ten-level learning trajectory: (1) Identification, (2) Conservation of Rigid Transformations, (3) Direct Comparison of Length and Area, (4) Conservation of Decomposition/Composition over Breaking, (5) Indirect Comparison of Length, (6) Non-congruent Rectangles Can Have Equal Areas, (7) Measurement of Area Is Relative to Unit Size, (8) Qualitative Compensation of Area Units, (9) Measurement with Area Units, and (10) Ratio Relationship Between Different Sized Area Units. The research suggests that this learning trajectory can be used in the elementary school curriculum to give students an internal measurement structure that allows for switching between different area units and to concomitantly introduce fractions and ratio, and set the foundation for quantitative area measurement. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page:]
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Elementary Education; Grade 3
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A