Yankelewitz, Dina. The development of mathematical reasoning in elementary school students' exploration of fraction ideas. Retrieved from https://doi.org/doi:10.7282/T3KW5G01
DescriptionReformers and educators across the U.S. and internationally have called for an increased emphasis on the learning and teaching of reasoning, justification, and proof in K-12 and post-secondary mathematics education. Numerous studies have established that students experience difficulty with these processes. Recently, however, analysis of videotape data of sixth grade student work in an informal mathematics program has identified the use of multiple forms of reasoning by middle school students. This qualitative study, drawing on data from seventeen sessions from a longitudinal study conducted by Rutgers University in a fourth grade class of twenty-five students in a suburban/rural school in New Jersey, identified and traced the development of the forms of reasoning and argumentation used by elementary school students as they were introduced to fraction as number concepts and as they used Cuisenaire® rods and other manipulative materials to make sense of number relationships.The following research questions guided this study: 1. What forms of reasoning and argumentation are elicited as students work on tasks involving the building of fraction ideas? 2. How does students’ reasoning change as they revisit tasks introduced previously in the study and as they progress in their development of mathematical understandings?
Data for the study included forty-six videotapes, students’ collected written work, and researcher field notes that were recorded during the seventeen 60-80 minute class sessions. The methodology of Francisco, Powell, and Maher (2003) was used for video data analysis. The video data was transcribed, verified, and coded for forms of reasoning, and a storyline and narrative was constructed to describe the results. Supplementary document analysis was used to verify and ensure validity of results. Analysis of the data showed that students used varied forms of reasoning and argumentation. Several tasks were flagged as supportive of the elicitation of varied forms of reasoning, and factors of those tasks and of the environment that encouraged the development of reasoning in the students were explored. The study has implications for effective strategies for the development of mathematical reasoning in the elementary school and ways that argumentation and proof can be introduced during the early school years.