Investigating a Student's Distributive Partitioning Scheme: The Case of Gabriel

• In Event: 46.086 - Roundtable Session 16
  In Roundtable Session: 46.086-5 - Investigations Into Elementary Students' Mathematical Thinking

Abstract

To investigate how to differentiate instruction and to explore relationships between students’ rational number knowledge and algebraic reasoning, an 18-episode design experiment was conducted with 9 cognitively diverse middle school students. As a part of the larger study, we conducted a case study of an eighth grade student, Gabriel, who did not construct a distributive partitioning scheme even though he had interiorized three levels of units, constructed advanced fraction schemes, and was enrolled in an algebra class. Gabriel's follow-up interview and four episodes in which the class worked on distributive reasoning were analyzed for this paper. Findings indicate that students may not construct a distributive partitioning scheme unless they experience a necessity to use it to solve problems.

Authors

• Mi Yeon Lee, Arizona State University

• Fetiye Aydeniz, Indiana University - Bloomington