Diagnosing Teachers’ Understandings of Rational Numbers: Building a Multidimensional Test Within the Diagnostic Classification Framework

Authors

  • Laine Bradshaw,

    Corresponding author
    1. The University of Georgia
    • Laine Bradshaw and Jonathan Templin, Department of Educational Psychology, The University of Georgia, 323 Aderhold Hall, Athens, GA 30602; laineb@uga.edu, jtemplin@uga.edu. Andrew Izsák and Erik Jacobson, Department of Mathematics and Science Education, The University of Georgia; izsak@uga.edu, erdajaco@indiana.edu. The following members of the Diagnosing Teachers’ Multiplicative Reasoning project helped draft items for the test we report: Bridget Druken, Laura Giberson, Joanne Lobato, Cynthia Lopez, Jessica McCreary, Caitlin O'Connor, Chandra Orrill, Amanda Paganin, Becky Stephens, and Lauren Susoeff. We thank the many teachers who took pilot versions of the test and helped us understand how to refine our items and the anonymous reviewers who provided helpful comments on an earlier draft.

    Search for more papers by this author
  • Andrew Izsák,

    Corresponding author
    1. The University of Georgia
    • Laine Bradshaw and Jonathan Templin, Department of Educational Psychology, The University of Georgia, 323 Aderhold Hall, Athens, GA 30602; laineb@uga.edu, jtemplin@uga.edu. Andrew Izsák and Erik Jacobson, Department of Mathematics and Science Education, The University of Georgia; izsak@uga.edu, erdajaco@indiana.edu. The following members of the Diagnosing Teachers’ Multiplicative Reasoning project helped draft items for the test we report: Bridget Druken, Laura Giberson, Joanne Lobato, Cynthia Lopez, Jessica McCreary, Caitlin O'Connor, Chandra Orrill, Amanda Paganin, Becky Stephens, and Lauren Susoeff. We thank the many teachers who took pilot versions of the test and helped us understand how to refine our items and the anonymous reviewers who provided helpful comments on an earlier draft.

    Search for more papers by this author
  • Jonathan Templin,

    Corresponding author
    1. The University of Georgia
    • Laine Bradshaw and Jonathan Templin, Department of Educational Psychology, The University of Georgia, 323 Aderhold Hall, Athens, GA 30602; laineb@uga.edu, jtemplin@uga.edu. Andrew Izsák and Erik Jacobson, Department of Mathematics and Science Education, The University of Georgia; izsak@uga.edu, erdajaco@indiana.edu. The following members of the Diagnosing Teachers’ Multiplicative Reasoning project helped draft items for the test we report: Bridget Druken, Laura Giberson, Joanne Lobato, Cynthia Lopez, Jessica McCreary, Caitlin O'Connor, Chandra Orrill, Amanda Paganin, Becky Stephens, and Lauren Susoeff. We thank the many teachers who took pilot versions of the test and helped us understand how to refine our items and the anonymous reviewers who provided helpful comments on an earlier draft.

    Search for more papers by this author
  • Erik Jacobson

    Corresponding author
    1. The University of Georgia
    • Laine Bradshaw and Jonathan Templin, Department of Educational Psychology, The University of Georgia, 323 Aderhold Hall, Athens, GA 30602; laineb@uga.edu, jtemplin@uga.edu. Andrew Izsák and Erik Jacobson, Department of Mathematics and Science Education, The University of Georgia; izsak@uga.edu, erdajaco@indiana.edu. The following members of the Diagnosing Teachers’ Multiplicative Reasoning project helped draft items for the test we report: Bridget Druken, Laura Giberson, Joanne Lobato, Cynthia Lopez, Jessica McCreary, Caitlin O'Connor, Chandra Orrill, Amanda Paganin, Becky Stephens, and Lauren Susoeff. We thank the many teachers who took pilot versions of the test and helped us understand how to refine our items and the anonymous reviewers who provided helpful comments on an earlier draft.

    Search for more papers by this author

  • This research was supported by the National Science Foundation under Grant Nos. DRL-0903411 and SES-1030337. The opinions expressed are those of the authors and do not necessarily reflect the views of NSF.

Abstract

We report a multidimensional test that examines middle grades teachers’ understanding of fraction arithmetic, especially multiplication and division. The test is based on four attributes identified through an analysis of the extensive mathematics education research literature on teachers’ and students’ reasoning in this content area. We administered the test to a national sample of 990 in-service middle grades teachers and analyzed the item responses using the log-linear cognitive diagnosis model. We report the diagnostic quality of the test at the item level, mastery classifications for teachers, and attribute relationships. Our results demonstrate that, when a test is grounded in research on cognition and is designed to be multidimensional from the onset, it is possible to use diagnostic classification models to detect distinct patterns of attribute mastery.

Ancillary