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Towards validation of a rational number instrument: An application of Rasch measurement theory


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Title Towards validation of a rational number instrument: An application of Rasch measurement theory
Creator Maseko, Jeremiah Luneta, Kakoma Long, Caroline
Subject Mathematics Education; Education; Mathematics fractions; equivalence; decimals; Rasch model; teacher education; percentage; compare; conversion
Description The rational number knowledge of student teachers, in particular the equivalence of fractions, decimals, and percentages, and their comparison and ordering, is the focus of this article. An instrument comprising multiple choice, short answer and constructed response formats was designed to test conceptual and procedural understanding. Application of the Rasch model enables verification of whether the test content was consistent with the construct under investigation. The validation process was enabled by making explicit the expected responses according to the model versus actual responses by the students. The article shows where the Rasch model highlighted items that were consistent with the model and those that were not. Insights into both the construct and the instrument were gained. The test items showed good fit to the model; however, response dependency and high residual correlation within sets of items was detected. Strategies for resolving these issues are discussed in this article. We sought to answer the research question: to what extent does this test instrument provide valid information that can be used to inform teaching and learning of fractions? We were able to conclude that a refined instrument applied to first-year students at university provides useful information that can inform the teaching and learning of rational number concepts, a concept that runs through mathematics curricula from primary to university. Previously, most research on rational number concept has been conducted on young learners at school.
Publisher AOSIS Publishing
Date 2019-12-05
Type info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion — Exploratory Research
Format text/html application/epub+zip text/xml application/pdf
Identifier 10.4102/pythagoras.v40i1.441
Source Pythagoras; Vol 40, No 1 (2019); 12 pages 2223-7895 1012-2346
Language eng
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Coverage South Africa — older than 17; male and female; Black, White, Coloured and Indian
Rights Copyright (c) 2019 Jeremiah Maseko, Kakoma Luneta, Caroline Long