A Rasch analysis of a Grade 12 test written by mathematics teachers

Abstract

There is much concern in South Africa about the low levels of mathematics achievement amongst learners. Aligned to this issue is that of mathematics teachers’ proficiency in mathematics. The purpose of this study was to explore mathematics teachers’ proficiency in the mathematics that they teach. A sample of 253 teachers’ responses to a shortened Grade 12 examination was analysed using the Rasch model. When the teachers’ proficiency and item location are represented on one scale, as is the case in Rasch measurement theory, it is expected that the teachers should be located beyond the difficulty level of the items as they teach the content to their learners. However, in this study, the teachers’ proficiency was located close to the mean of the item locations. Furthermore, the levels of almost one-third of the group were below that of all the Level 3 and Level 4 items in the test. If such a result holds across other groups of teachers, it may explain why higher levels of passes in mathematics are not achieved. A second aim of this study was to illustrate how the application of the Rasch model can be used to contribute to a more informative and fair assessment. In line with Rasch measurement theory, the test was subjected to various analyses and the results were used to improve the fit of the items and the test.