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Scale Invariance from a Three-Dimensional Graphical Perspective: Visualizing an Eigenvector

Boston College

This article reports on one aspect of a multifaceted inquiry into the attitudes and anxieties prospective elementary school teachers may have toward teaching mathematics. At the beginning, midterm, and end of one semester, student teachers were asked to respond to an Attitudes Towards Mathematics and Its Teaching (ATMAT) Scale. The Rasch model of item-response theory was employed to estimate the difficulty level of the ATMAT items at the three different time periods. This article addresses the invariant characteristics of the scale. In addition to standard approaches taken to determine the extent to which the scale remained invariant over time, various three-dimensional graphical analyses were undertaken. These latter analyses portrayed scale invariance in ways not possible through static numerical summaries. One noteworthy consequence, in particular, highlights the pedagogical significance of these analyses: the graphical representation of an eigenvector.

Educational and Psychological Measurement, Vol. 58, No. 2, 166-178 (1998)
DOI: 10.1177/0013164498058002002


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