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Erschienen in: Technology, Knowledge and Learning 3/2011

01.10.2011

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

verfasst von: Walter M. Stroup, Thomas Hills, Guadalupe Carmona

Erschienen in: Technology, Knowledge and Learning | Ausgabe 3/2011

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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.

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Fußnoten
1
Of course other similar network tools can be used. We’ve also found the activity works well with students making a white-board sized histogram using adhesive notepads (e.g. Post-It™ Notes) with the value written on the front-facing side and the computing method written on the back.
 
2
There is not a sense in which this shortcoming in the use of this average might be appreciably improved by having a larger sample or by carrying out many more trials.
 
3
We set aside for now issues related to replacement. Humorously, one of our student suggested this aspect of the model might represent students who would freely elect to retake the course, “just for the fun of it,” in subsequent semesters.
 
4
In the history of intelligence research, the ascription of significance to the emergence of distinct “bell curves” has given rise to some rather incendiary racist claims (c.f., Herrnstein and Murray (1994).
 
5
Such relative ordering of responses “better … characterized” as reflecting “discrete classes or types of understanding” is discussed in a book titled Knowing What Students Know published by the National Research Council (NAP 2001, p. 126) as an instance of an ordered latent class model (p. 127). Using this kind of model, each class or mode of response “can be viewed as a point on a continuum” of performance (p. 127) or as a “quantitative parameter” reflecting a relative “degree of proficiency” (p. 151). At an even more basic level, simple dichotomous coding (“1” for a correct response and “0” for any of the wrong responses) also does exactly this (and most item response theory also assigns fine-grain significance to expected values between 0 and 1 for students of varying abilities). Mitchell (2009) discusses this move to assign such quantitative significance as the “psychometricians’ fallacy” that he says “occupies a central place in the paradigm of psychometrics” and consists of the tendency to conclude “that an attribute is quantitative from the premise that it is ordinal.”
 
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Metadaten
Titel
Computing the Average Square: An Agent-Based Introduction to Aspects of Current Psychometric Practice
verfasst von
Walter M. Stroup
Thomas Hills
Guadalupe Carmona
Publikationsdatum
01.10.2011
Verlag
Springer Netherlands
Erschienen in
Technology, Knowledge and Learning / Ausgabe 3/2011
Print ISSN: 2211-1662
Elektronische ISSN: 2211-1670
DOI
https://doi.org/10.1007/s10758-011-9187-9

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