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Technology, Knowledge and Learning

, Volume 16, Issue 3, pp 199–220 | Cite as

Computing the Average Square: An Agent-Based Introduction to Aspects of Current Psychometric Practice

  • Walter M. Stroup
  • Thomas Hills
  • Guadalupe Carmona
Article
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Abstract

This paper summarizes an approach to helping future educators to engage with key issues related to the application of measurement-related statistics to learning and teaching, especially in the contexts of science, mathematics, technology and engineering (STEM) education. The approach we outline has two major elements. First, students are asked to compute an “average square.” Second, students work with an agent-based simulation that helps them to understand how aspects of the central limit theorem might be integrated into a much larger conversation about the appropriateness, or validity, of current psychometric practices. We are particularly interested in how such practices and interpretive frameworks inform the construction of high-stakes tests. In nearly all current high-stakes test development, tests are thought of as being built-up from individual items, each of which has known statistical properties. The activity sequence outlined in this paper helps future educators to understand the implications of this practice, and the sometimes problematic assumptions it entails. This instructional sequence has been used extensively as part of a core course in a university-based certification program in the United States (UTeach) recognized for its innovative approaches to developing a new generation of secondary STEM educators.

Keywords

Statistics Learning theory Central limit theorem Simulation Conceptual change Psychometrics Item response theory 
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Notes

Acknowledgments

The authors wish to express their appreciation to Uri Wilensky, Andy diSessa, and Bruce Sherin for their longstanding engagement and support in the preparation of this paper, and to John Henry Newman for reminding and reassuring us that some ideas and stances need to be a long time in the world—and may indeed wait for far better advocates than ourselves—as they become “deep, and broad, and full.” Funding from the National Science Foundation: Grant # 09093 entitled CAREER: Learning Entropy and Energy Project (W. Stroup, Principal Investigator) helped support this work. The views expressed herein are those of the authors and do not necessarily reflect those of the funding institutions.

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Walter M. Stroup
    • 1
  • Thomas Hills
    • 2
  • Guadalupe Carmona
    • 1
  1. 1.Science and Math EducationThe University of Texas at AustinAustinUSA
  2. 2.University of BaselBaselSwitzerland

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