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Making sense of double number lines in professional development: exploring teachers’ understandings of proportional relationships

Journal of Mathematics Teacher Education volume 15, pages 381–403 (2012)Cite this article

Abstract

This study presents a qualitative analysis of the knowledge teachers in one professional development course used to reason about proportional relationships with double number lines. We work from the knowledge-in-pieces perspective to consider the existing knowledge the participants did or did not invoke when learning to reason with this new-to-them representation. We analyzed videotaped sessions of a group of urban middle-grade teachers across five class meetings. Our findings include discussion of the two pieces of knowledge that emerged as important for reasoning about proportions with the representation and three knowledge pieces that deterred meaning making. Implications for professional development are discussed as are the implications for conceptualizing teachers’ understanding through a knowledge-in-pieces lens.

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Notes

  1. We use “coordinate” rather than composed unit throughout this paper to indicate instances in which it is clear that the teacher is reasoning about the quantities in a related way. We lack data necessary to determine whether these teachers were able to fully reason about the quantities as composed units (Lamon 1995).

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Acknowledgments

Work on this project was supported by the National Science Foundation (DRL-0633975 and DRL-1036083). The opinions expressed here are those of the authors and do not necessarily reflect the views of NSF. The authors wish to thank Gunhan Caglayan for his work on the data analysis as well as the Does it Work team, the participating teachers, and the facilitator for their support with data collection.

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Authors and Affiliations

  1. University of Massachusetts Dartmouth, Dartmouth, MA, USA

    Chandra Hawley Orrill

  2. Knowles Science Teaching Foundation, Moorestown, NJ, USA

    Rachael Eriksen Brown

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  1. Chandra Hawley Orrill
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  2. Rachael Eriksen Brown
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Correspondence to Chandra Hawley Orrill.

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Orrill, C.H., Brown, R.E. Making sense of double number lines in professional development: exploring teachers’ understandings of proportional relationships. J Math Teacher Educ 15, 381–403 (2012). https://doi.org/10.1007/s10857-012-9218-z

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  • DOI: https://doi.org/10.1007/s10857-012-9218-z

Keywords

  • Middle grades
  • Professional development
  • Proportional reasoning
  • Drawn representations
  • Teacher knowledge