“What Do You Think She’s Going to Do Next?” Irresolution and Ambiguity as Resources for Collective Engagement

Abstract

Understanding how learning environments productively mobilize children’s ideas as resources for participation in joint activity is an ongoing focus of research on classroom instruction. We investigated whole-class mathematics conversations in which multiple students participated in ways previous research suggests are consequential for learning. We found that in such conversations, students rarely presented the entirety of their solutions before other students engaged. Rather, incomplete explanations and written representations that emerged over time created entry points for other students to contribute in mathematically substantive ways. These aspects of student participation operated in combination with teachers’ in-the-moment responses to create opportunities for, and publicly recognize, different kinds of contributions as resources for collective work. Our findings suggest that, rather than challenges to communication that must be overcome, students’ vague, unfinished, and ambiguous ideas present productive contributions that can be leveraged to support collective mathematical work.

Acknowledgments

We would like to thank Angela Chan Turrou for her ongoing contributions to our thinking, and the anonymous reviewers for their thoughtful comments and suggestions on previous versions of the manuscript. We are especially grateful to the children and teachers who made this work possible by opening their classrooms and sharing their practice with us. We continue to learn so much from you all.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 All names are pseudonyms.

2 We also use the term “conversations” to follow one of the teachers in our study, who sometimes opened strategy sharing by asking, “who would like to start the conversation?”

3 Across the six lessons in each classroom, most students contributed to whole-class conversations multiple times (Mean 4.66, SD = 2.75). Participation patterns across the two classrooms (both in terms of overall participation [t(43) = −0.77, p = .45] and in terms of explanation [t(43) = −0.41, p = .68] and engagement with others’ ideas [t(43) = −0.83, p = 0.41]) were not different.

4 In our data set, responsibility for creating written representations corresponded with the phase of the lesson. In strategy sharing conversations that followed the problem solving phase of the lesson, strategy authors recreated their written representations for the class on the board or document camera. In strategy sharing conversations during the warm-up (e.g., a Number Talk or True/False number sentence), teachers took on the role of recording students’ ideas.

5 In partitive (as opposed to measurement) division contexts, the story problem reflects a situation where the total (93) is shared equally between or split evenly into a given number of groups (3). The amount in each group is unknown, rather than the number of groups.

6 In these three episodes, others’ engagement was spontaneous (not specifically invited by the teacher) and the teacher did not follow up on their specific contribution.

Additional information

Funding

The research reported in this article was funded in part by a National Academy of Education/Spencer dissertation fellowship, and by grants from the Spencer Foundation [201500046] and UCLA Academic Senate Council on Research [2018 Faculty Research Grant]. The opinions expressed are those of the authors and do not reflect those of the funding agencies.