## 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.