Designing Standards-Setting for Levels of Mathematical Proficiency in Measurement and Geometry: Multidimensional Item Response Model

Abstract

This study intends to design and verify the quality of a model that measures mathematical proficiency and aims to set the standards in measuring levels of proficiency in the subjects of measurement and geometry. Construct modeling was employed to design a mathematical proficiency measurement model which consists of the mathematical process and the dimensions of a conceptual structure. A total of 517 Secondary Year 1 students were selected from the big data to participate as test-takers. Design-based research encompassing four phases was used to verify the quality of the mathematical proficiency measurement model. A Multidimensional Random Coefficient Multinomial Logit model was used to examine the standards-setting of the mathematical proficiency measurement model. The results indicated that the two dimensions of mathematical proficiency can be further divided into five levels, from non-response/irrelevance to strategic/extended thinking and extended abstract structure for mathematical process and conceptual structural dimensions, respectively. The assessment tool covers 18 items with 15 multiple-choice items and three subjective items in measurement and geometry. Moreover, the results also demonstrated that the validity evidence associated with the internal structure of the multidimensional model is fit. Besides, reliability evidence, as well as item fit, is compliance with the quality of the mathematical proficiency measurement model as illustrated in analysis of the standard error of measurement and infit and outfit of the items. Finally, the researchers managed to set standards for the mathematical proficiency measurement model based on the assessment criterion results from the Wright Map. In conclusion, the standards-setting of the mathematical proficiency measurement model provides substantial information, particularly for measuring those students who are above the lowest level of mathematical proficiency because the error for estimating proficiency was low.