Teacher Noticing of Mathematical Thinking in Young Children’s Representations of Counting

Counting is fundamental to early mathematics. Most studies of teaching counting focus on teachers observing children count. The present study compares mathematical ideas that 12 PK, transitional kindergarten (TK), and kindergarten teachers noticed from observing their own students count during a classroom session of Counting Collections with ideas that they noticed outside class time in the same students’ representations of counting on paper. Inviting teacher noticing in representations (a) drew attention to distinct conceptions that children required to represent counting; (b) increased the number of mathematical ideas that participants perceived in students’ thinking; and (c) helped participants perceive different levels in, and their own uncertainties about, students’ understanding. This study suggests that teacher noticing in children’s representations of counting can deepen teachers’ understanding of students’ mathematical thinking.

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Footnotes

The author wishes to thank Deborah Stipek, Hilda Borko, Jennifer Langer-Osuna, Michael Jarry-Shore, Cathy Humphreys, Kim Bambao, and MERGe for their invaluable support and feedback.

Note: Appendices for this article are available online only at https://pubs.nctm.org/view/journals/jrme/51/3/article-p268.xml?tab_body=supplementaryMaterials

Contributor Notes

Madhuvanti Anantharajan, Graduate School of Education, Stanford University, 485 Lasuen Mall, Stanford, CA 94305; madhuvan@stanford.edu

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