Supporting the development of a second-grade classroom’s conceptions of multiplication through a hypothetical learning trajectory

Kandil, Semanur
The first aim of this study is to develop, test, and revise a Hypothetical Learning Trajectory and corresponding instructional sequence for teaching multiplication in second grade. The second aim is to document second graders’ classroom mathematical practices that emerged related to conceptualizations of multiplication and to use those practices for making revisions to the HLT and the instructional sequence. An instructional sequence was developed in line with Realistic Mathematics Education theory to achieve these goals. This sequence was implemented and revised in a design experiment in a year with a design research perspective. Data were collected from a second-grade classroom in a public school in the Çankaya District of Ankara with the collaboration of the classroom teacher. The emergent perspective, which coordinates social and individual perspectives and supports collective learning, was used as an interpretive framework for data collection and analysis. The data collected through the video recordings of class sessions, students’ written works, and the researcher’s field notes were analyzed by adapting Toulmin’s argumentation model to establish classroom mathematical practices. Five classroom mathematical practices emerged related to students’ conceptualizations of multiplication concepts. The study has important implications for students, teachers, mathematics education researchers, and educational resource designers in practical and theoretical ways.


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Citation Formats
S. Kandil, “Supporting the development of a second-grade classroom’s conceptions of multiplication through a hypothetical learning trajectory,” Ph.D. - Doctoral Program, Middle East Technical University, 2022.