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

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.

The Mathematical Proficiency Promoted by Mathematical Modelling

This study aims to investigate the mathematical proficiency promoted by mathematical modelling tasks that require students to get involved in the processes of developing mathematical models, instead of just using known or given models. The research methodology is grounded on design-based research, and the classroom design framework is supported by complexity science underpinnings. The research intervention consists of high-school students, from a grade 11 mathematics course, aiming to solve four different modelling tasks in four distinct moments. Data was collected during the intervention from students’ written mathematical work and audio and video recordings, and from recall interviews after the intervention. Data analysis was conducted based on a model of mathematical proficiency and assisted by interpretive diagrams created for this research purpose. This research study offers insight into mathematics teaching by portraying how mathematical modelling tasks can be integrated into mathematics classes to promote students’ mathematical proficiency. The study discusses observed expressions and behaviours in students’ development of mathematical proficiency and suggests a relationship between mathematical modelling processes and the promotion of mathematical proficiency. The study also reveals that students develop mathematical proficiency, even when they do not come to full resolutions of modelling tasks, which emphasizes the relevance of learning processes, and not only of the products of these processes.