Mathematics Teaching and Learning as a Mediating Process: The Case of Tape Diagrams

This article examines how visual representations may mediate the teaching and learning of mathematics over time in Japanese elementary classrooms. Using the Zone of Proximal Development Mathematical Learning Model (Murata & Fuson, 2006 Murata, A. and Fuson, K. C. 2006. Teaching as assisting individual constructive paths within an interdependent class learning zone: Japanese first graders learning to add using ten. Journal for Research in Mathematics Education., 37(5): 421–456. [Web of Science ®] , [Google Scholar]; Fuson & Murata, 2007 Fuson, K. C. and Murata, A. 2007. Integrating the NRC principles and the NCTM process standards: Cognitively guided teaching to individualize instruction within whole-class activities and move all students within their learning path. National Council of Supervisors of Mathematics Journal, 10(1): 72–91.  [Google Scholar]), the process of mediation is explicated. The tape diagram, a central visual representation used in Japanese mathematics curriculum, is explored for its roles and the student learning that is intended to be mediated over time, illuminating aspects of the process. The study argues that the consistent and coherent use of one representation can bridge student understanding over time, focusing on mathematical relationships and problem-solving processes. The study also suggests different instructional approaches between U.S. and Japanese curricula that are reflected in the uses of representations.