A cognitive diagnostic assessment of PISA math items: What skills have Canadian student mastered?
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Date
2022-01
Authors
Zeng, Jianjie
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Abstract
The Organization for Economic Cooperation and Development (OECD)-sponsored Program for International Student Assessment (PISA) plays an essential role in encouraging educational reform and strengthening educational policy. According to recent research issued by the C.D. "Howe Institute," a Canadian think tank, Canadian students’ mathematics results have steadily dropped in foreign tests since 2003 (Richards, 2017). To investigate the declining trend of Canadian students’ mathematical literacy, this study proposes the use of cognitive diagnostic models (CDMs), which provide profiles of mastery and non-mastery of mathematical skills or attributes (e.g., quantity, change and relationship, space and figure, uncertainty and data, etc.) that are critical for students’ success in mathematics achievement. Compared to standard testing and evaluation methods such as item response theory (IRT) models, CDM is regarded as a person-centered statistical model, which provides detailed mastery of each individual’s cognitive attributes or knowledge and skills and offers important guiding information to teachers’ teaching and test writing (Leighton & Gierl, 2007). Given the fact that the Deterministic Inputs, Noisy “and” Gate (DINA) model is a widely employed CDM, DINA model is applied in this study to demonstrate specific learning outcomes of 15-year-old students across Canada, and identify differences within-Canada in PISA test. The aims of this study are to (1) examine whether the PISA data fit to the constructs or skills as stated in their manual with the DINA model, (2) explore the essential reasons causing declining Canadian scores by identifying the mathematics skills that Canadian students have or have not mastered in PISA testing, (3) examine differences in mastering mathematics skills in PISA testing across ten Canadian provinces. The results showed that (1) the DINA model is applicable to analyze the Canadian students mastering of mathematical literacy as evidenced by reasonable parameter estimates including slipping, guessing, Item Discrimination Index (IDI) and Root Mean Square Error of Approximation (RMSEA); (2) the mathematics skill, geometry (space and shape skill), has the lowest mastery rate for 15-year-old Canadian students. On the contrary, the mathematics skill, application of mathematics thinking in daily life (employing skill), has the highest mastery rate for Canadian students; (3) students in Quebec not only performed better in test but also acquire the highest mastery rate in all 11 mathematical skills defined by PISA. The t test was utilized to analysis the differences in mastery rate within-country, and the p value showed that Quebec and British Columbia had comparative better personal and occupational skills compared to the students in other provinces. The findings illuminate the mathematical abilities that Canadian students have acquired or have not entirely grasped, thereby assisting educators and policymakers in establishing and enhancing the educational curriculum for mathematics instruction in Canada.
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Keywords
Cognitive Diagnostic Model, Q-matrix, DINA, Programme for International Student Assessment, Mathematics Literacy, Mathematics Skills