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Measurement in physics education research with the Rasch model

As any other empirical scientific discipline physics education research needs to base its conclusions on the results of measurement. Researchers often attempt to measure student knowledge, understanding of concepts or student attitudes, entering in this way inevitably the realm of psychometrics, which is often regarded by physicists as an area in which it is difficult to achieve reliable measurements. Are there ways to bring measurement in physics education research closer to the standards of measurement in physics? The use of the stochastic Rasch model could be a step in that direction. As a means of test analysis, Rasch measurement parallels physical measurement processes by being largely concerned with the construction of linear measures along specific, unidimensional constructs. It allows users to create an interval scale of scores for both the item and person measures. The first requirement is that the variable to be measured with a test is specified and described by a set of well chosen test items. The model assumes that the test is unidimensional, meaning that each item probes only the measured variable. The location of a person along the measured variable is described by a measure called person ability, which gives the information about the intensity of the measured variable that the person possesses. Items are described by another measure called item difficulty. Item difficulties and person abilities are calculated from raw test scores for items (from the number of correct answers to an item) and persons (from the number of correct answers given by a person) and expressed on logit scale. The construction of measures is usually performed by some Rasch model software such as Winsteps. Each item and person measure comes with its Rasch standard error which indicates the uncertainty of the estimate. The analysis of distributions of item difficulties and of person abilities, as well as the analysis of the fit of data with the model can give significant information about the structure and functioning of the test. Basic elements of the Rasch model will be presented and illustrated on the example of the Rasch model based analysis of the Force Concept Inventory (FCI)1. The Force Concept Inventory (FCI) is an important diagnostic instrument which is widely used in the field of physics education research for evaluation of student conceptual understanding of mechanics. The data come from the large scale research carried out in 2006/07. which investigated Croatian high school students' conceptual understanding of mechanics on a representative sample of 1676 students (age 17-18 years) using the FCI. Most of the students were found to be non- Newtonians, as measured by the FCI standard. In addition, the FCI post instruction scores of 141 first year university students were also analyzed and found to represent a predominantly Newtonian population. The Rasch model based analysis of both sets of data provided an insight in the structure of the FCI and its different functioning on non-Newtonian and predominantly Newtonian population and suggested some possible ways for improving the test. 1 M. Planinic, L. Ivanjek, and A. Susac, Rasch model based analysis of the Force Concept Inventory, Phys. Rev. ST Phys. Educ. Res, 6, 010103 (2010).

physics education; measurement; Rasch model; FCI

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