A Video Analysis of Fractional Reasoning in Interaction

Sean Lewis

Norton conducted a month long teaching experiment of Kadyeisha, a fifth grade African American female student and Issac, a fifth grade Caucasian American male student, participating in a math recovery program. The first problem presented to the students involved a whole (candy bar) that was 5 times bigger than theirs was, and they had to produce their candy bar. In order to solve this task, the students must have an understanding of splitting as an available operation. According to McCloskey and Norton (2009), once a student becomes a "splitter" they can develop more powerful and advanced fraction schemes, "such as the reversible partitive fractional scheme" (McCloskey & Norton, p. 46). Through analysis, a model of specific tasks that help to identify Kadyeisha as a splitter shows how interactions with Norton and Issac aided Kadyeisha's development of advanced fractional schemes. This has implications in the general classroom where grouping students can provide support for students' mathematical understanding.