Opening Multiplicative Reasoning Doors for all Students: Task Design for Transfer-Empowering Learning

• In Event: Poster Session 17
  In Poster Session: Instrumentation for Measuring Teacher Knowledge for Teaching

Abstract

We propose an approach for designing tasks that facilitate students’ development of a transfer-empowering, anticipatory stage of mathematical understanding. Using a constructivist framework, we conducted 15 teaching episodes with eight 4th graders and one 5th grader in an urban setting. We focus on two students’ work on tasks designed to foster their multiplicative reasoning. Haley seemed to construct an anticipation of structural similarity among tasks; she found a multiplicative total via coordinating the unit-rate and number of composite units (e.g., 7 towers x 3 cubes each = 21 cubes). Sam constructed a more advanced conception and transferred it to novel situations. We demonstrate how their anticipations of structural similarity empowered transfer to other multiplicative contexts.

Authors

• Heather Lynn Johnson, University of Colorado - Denver

• Ron Tzur, University of Colorado - Denver

• Evan McClintock, New York University

• Rachael Ann Risley, University of Colorado - Denver

• Kristin King, University of Colorado - Denver

• Yan Ping Xin, Purdue University

• Luo Si, Purdue University