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

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Technology, Knowledge and Learning Volume 16, Number 3, ISSN 2211-1662


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.


Stroup, W.M., Hills, T. & Carmona, G. (2011). Computing the Average Square: An Agent-Based Introduction to Aspects of Current Psychometric Practice. Technology, Knowledge and Learning, 16(3), 199-220. Retrieved August 21, 2019 from .

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