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Using Coordination Classes to Analyze Preservice Middle-Grades Teachers’ Difficulties in Determining Direct Proportion Relationships

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Research Trends in Mathematics Teacher Education

Part of the book series: Research in Mathematics Education ((RME))

Abstract

Numerous studies, primarily conducted with school children, have reported the misapplication of direct proportion reasoning strategies to situations in which two quantities do not covary in a fixed ratio relationship. In the present study, preservice middle-grades mathematics teachers (N = 28) evidenced similar difficulties in a content and methods course. In particular, they correctly explained relationships between quantities that were not direct proportions but still tried to solve problems involving those quantities using direct proportions. To understand how this could occur, we used the coordination class construct (diSessa and Sherin, International Journal of Science Education 20(10):1155–1191, 1998) to analyze knowledge resources that the preservice teachers used before, during, and after a unit on proportions. Where past research has often characterized the misapplication of direct proportion reasoning strategies as the result of intuitive or impulsive responses to familiar missing-value problem presentations, our analysis suggests that recognizing directly proportional relationships is more complex than carefully interpreting problem statements.

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Notes

  1. 1.

    Context as used in Van Dooren et al. (2010) has the same meaning as in Wagner (2006): the cover story of a word problem. In the rest of the chapter, we italicize other terms from Wagner that have a narrower definition than may be typical.

  2. 2.

    All names are pseudonyms.

  3. 3.

    Alice did not participate during the second interview due to a family obligation.

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Author information

Authors and Affiliations

  1. Department of Curriculum and Instruction, Indiana University, Bloomington, IN, USA

    Erik Jacobson

  2. Department of Mathematics and Science Education, University of Georgia, Athens, GA, USA

    Andrew Izsák

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  1. Erik Jacobson
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  2. Andrew Izsák
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Correspondence to Erik Jacobson .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Western Michigan University, Kalamazoo, Michigan, USA

    Jane-Jane Lo

  2. Department of Mathematics Education, Brigham Young University, Provo, Utah, USA

    Keith R. Leatham

  3. Department of Mathematics, Western Michigan University, Kalamazoo, Michigan, USA

    Laura R. Van Zoest

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Jacobson, E., Izsák, A. (2014). Using Coordination Classes to Analyze Preservice Middle-Grades Teachers’ Difficulties in Determining Direct Proportion Relationships. In: Lo, JJ., Leatham, K., Van Zoest, L. (eds) Research Trends in Mathematics Teacher Education. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-02562-9_3

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