A Multivocal Analysis of Pivotal Moments for Learning Fractions in a 6th-Grade Classroom in Japan

Abstract

In this chapter, learning fractions in a 6th-grade Japanese classroom provides the focus for three analytical approaches, each identifying “pivotal moments” within the interaction. The data consists of an English-subtitled video in Japanese of six students folding origami paper and of one teacher monitoring their progress on the blackboard and an accompanying transcription of their talk and gestures. One analyst sought where the personal foci of learners originate; what happens in the interaction once a learner focuses on, for example, shapes or production methods; and how learner outcomes are related to such foci. Another identified the semantic content of “voices” and their interanimation patterns in a polyphony framework. A third analyst applied statistical discourse analysis to the dataset in order to see whether recent sequences of utterances affected the likelihood of creating utterances categorized as new ideas, correct ideas, micro-creativity, or justifications. Through a discussion of what constituted a pivotal moment, we identified nine lessons in productive multivocality that all show how an analyst may surpass the limits of a particular method. Ways of doing this include redefining the unit of analysis and the unit of interaction in light of other researchers’ analyses, interpreting other researchers’ pivotal moments in one’s own framework, and comparing the semantics of and the relations between analytical concepts.