Responding to children’s mathematical thinking in the moment: an emerging framework of teaching moves


This case study contributes to efforts to characterize teaching that is responsive to children’s mathematical thinking. We conceptualize responsive teaching as a type of teaching in which teachers’ instructional decisions about what to pursue and how to pursue it are continually adjusted during instruction in response to children’s content-specific thinking, instead of being determined in advance. Building on earlier work, we present an emerging framework of teaching moves using examples from the interactions of a highly skilled teacher who was selected because of her expertise in responsive teaching. We draw from her interactions with children around fraction story problems in both one-on-one interviews and class lessons. The framework identifies categories of teaching moves, rather than specific comments or questions, because how teachers enact a category depends on the situation. We discuss four major categories of teaching moves: (a) ensuring the child is making sense of the story problem, (b) exploring details of the child’s existing strategy, (c) encouraging the child to consider other strategies, and (d) connecting the child’s thinking to symbolic notation. Our findings also highlight both the potential usefulness of one-on-one interviews for professional developers and researchers and the need for increased attention to the part of class lessons in which teachers circulate and engage in one-on-one conversations with children.

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  1. 1.

    We recognize that teachers can be responsive to students in a class setting in many productive ways. In this article, we use responsive teaching to refer to the part of teaching that is responsive to children’s mathematical thinking.

  2. 2.

    Our ultimate goal is to generate a framework that applies to both whole-number and fraction problem solving, and we believe that all the subcategories generated here would also apply in whole-number situations, but this assumption merits further study.

  3. 3.

    All children’s names are pseudonyms.


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This research was supported in part by the National Science Foundation (DRL–1316653), but the opinions expressed do not necessarily reflect the position, policy, or endorsement of the supporting agency. We thank Ms. Keith and her students who participated in our study, for without them, this work would not be meaningful or possible.

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Correspondence to Victoria R. Jacobs.

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Jacobs, V.R., Empson, S.B. Responding to children’s mathematical thinking in the moment: an emerging framework of teaching moves. ZDM Mathematics Education 48, 185–197 (2016).

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  • Responsive teaching
  • Teaching practices
  • Children’s thinking
  • Elementary school
  • Fractions
  • Teacher learning