CLASSROOM MATHEMATICAL PRACTICES OF THE SEVENTH GRADERS ABOUT RATIO AND PROPORTION CONCEPTS

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SSO_CMPsoftheseventhgraders.pdf

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2023-2-22

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Sözen Özdoğan, Sinem

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The purpose of this study is to examine the Classroom Mathematical Practices (CMPs) of seventh-grade students with regard to ratio and proportion concepts through the implementation of a specific instructional sequence. The study was conducted using an educational design research methodology and was based on the Classroom Hypothetical Learning Trajectory and related instructional sequence developed by Stephan et al. (2015). The instructional sequence was mainly carried out by an experienced middle-grade mathematics teacher in a public school in Yenimahalle, Ankara with the support of design team. The data was collected through classroom observations, teacher interviews, field notes, and student and teacher documents. The observations mainly took place over 34 lesson hours. The argumentation components described by Toulmin (1958), taken-as-shared ideas, and the CMPs embedded in the classroom discussions were analyzed using a three-phase documentation approach to establish the CMPs (Rasmussen & Stephan, 2008). The study found five CMPs that enhanced student learning: reasoning about discrete/continuous objects and the rule of the ratio; linking and iterating composite units; covariation among composite units in a ratio table; representing ratio and proportion symbolically; and adapting strategies for comparing non-equivalent ratios. These practices demonstrate various aspects of proportional reasoning and suggest that the instructional sequence has the potential to improve the teaching of ratio and proportion concepts in terms of unitizing, linking and iterating composites representing, data organizing, conducting operations, comparing the ratios, applying build-up and multiplicative relations, creating, and analyzing equivalent ratios. This study contributes to the ongoing effort to define an instructional design for helping seventh-grade students understand ratio and proportion.

Subject Keywords

Classroom Mathematical Practices, Ratio, Proportion, Educational Design Research, Proportional Reasoning

URI

https://hdl.handle.net/11511/102089

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Graduate School of Social Sciences, Thesis

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Citation Formats

S. Sözen Özdoğan, “CLASSROOM MATHEMATICAL PRACTICES OF THE SEVENTH GRADERS ABOUT RATIO AND PROPORTION CONCEPTS,” Ph.D. - Doctoral Program, Middle East Technical University, 2023.