Abstract
As one of the most influential international large-scale educational assessments, the Program for International Student Assessment (PISA) provides a valuable platform for the horizontal comparisons and references of international education. The cognitive diagnostic model, a newly generated evaluation theory, can integrate measurement goals into the cognitive process model through cognitive analysis, which provides a better understanding of the mastery of students of fine-grained knowledge points. On the basis of the mathematical measurement framework of PISA 2012, 11 attributes have been formed from three dimensions in this study. Twelve test items with item responses from 24,512 students from 10 countries participated in answering were selected, and the analyses were divided into several steps. First, the relationships between the 11 attributes and the 12 test items were classified to form a Q matrix. Second, the cognitive model of the PISA mathematics test was established. The liner logistic model (LLM) with better model fit was selected as the parameter evaluation model through model comparisons. By analyzing the knowledge states of these countries and the prerequisite relations among the attributes, this study explored the different learning trajectories of students in the content field. The result showed that students from Australia, Canada, the United Kingdom, and Russia shared similar main learning trajectories, while Finland and Japan were consistent with their main learning trajectories. The primary learning trajectories of the United States and China were the same. Furthermore, the learning trajectory for Singapore was the most complicated, as it showed a diverse learning process, whereas the trajectory in the United States and Saudi Arabia was relatively simple. This study concluded the differences of the mastery of students of the 11 cognitive attributes from the three dimensions of content, process, and context across the 10 countries, which provided a reference for further understanding of the PISA test results in other countries and shed some evidence for a deeper understanding of the strengths and weaknesses of mathematics education in various countries.
Highlights
Initiated by the Organization for Economic Cooperation and Development (OECD) in 1997, the Program for International Student Assessment (PISA) is held every 3 years to assess the fundamental knowledge and critical competencies needed for students approximately 15 years old to participate in society
The participants were from the United Kingdom (GBR, 3,811), Finland (FIN, 2,661), and Russia (RUS, 1,666) in Europe; China (CHI, 1,763, including the data selected from Hong Kong, Macau, Shanghai, and other places), Japan (JPN, 1,904) and Singapore (SGP, 1,667) in Asia; the United States (USA, 1,630) and Canada (CAN, 6368) in North America; Australia (AUS, 4,342) in Oceania, and Saudi Arabia in Africa (ALB, 1,402)
PISA reports the motivation, self-confidence, learning strategies, and the environmental background information of students, including the social, economic, cultural, and educational aspects and population distribution related to knowledge and skills (OECD, 2004)
Summary
Initiated by the Organization for Economic Cooperation and Development (OECD) in 1997, the Program for International Student Assessment (PISA) is held every 3 years to assess the fundamental knowledge and critical competencies needed for students approximately 15 years old to participate in society. Mathematics, as one of the core tests in PISA, has been extensively studied; for instance, educational equity issues have been studied through assessing the opportunities of learning for students (Duru-Bellat and Suchaut, 2005; Luyten, 2017; Hansen and Strietholt, 2018), the gender differences in PISA performance (Steinthorsdottir and Sriraman, 2008; Kyriakides et al, 2014), PISA performance differences in age (Sprietsma, 2010), the relationship between PISA performance and social achievement (Knowles and Evans, 2012), the influence of language on PISA performance (El Masri et al, 2016), the heterogeneity of PISA performance (Wößmann, 2005), etc These studies have focused on either the factors that affect PISA achievements or the impact of PISA achievements on society and education. Mathematics educators, mathematicians, measurement experts, and educational statisticians have been advised to collaborate in research projects to recognize the potential values of concept discussions and secondary analyses that are directly applicable to the existing school systems (Ferrini-Mundy and Schmidt, 2005)
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