Cycles of Generalizing Activities in the Classroom

This study considers classroom situations in which students and the teacher co-contribute to promoting generalization . It specifically focuses on the ways in which students and a teacher in one classroom engage in generalizing arithmetic. Generalized arithmetic is an important route into early algebra (Kaput in Algebra in the Early Grades. Routledge, New York, 2008); its potential as a way to deepen students’ understandings of concepts of school arithmetic makes it an important focus of early algebra research. In the analysis we identified generalizations around properties of arithmetic and the actions that promoted these types of generalizations, and then considered the relationship between these actions . Analysis revealed that generalizations became platforms for further generalization.

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Acknowledgements

The research reported here was supported in part by the National Science Foundation under DRL Award #1415509 (Principal investigators: Maria Blanton and Bárbara Brizuela) and DRK-12 Awards #1219605 and #1219606 (Principal investigators: Maria Blanton, Eric Knuth, and Ana Stephens). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

1. University of Wisconsin–Madison, 1025 West Johnson Street, Madison, WI, 53706, USA Susanne Strachota
2. University of Texas at Austin, 1912 Speedway STOP D5700, Austin, TX, 78712, USA Eric Knuth
3. TERC, 2067 Massachusetts Ave., Cambridge, MA, 02140, USA Maria Blanton

1. Susanne Strachota