Matrix had been deleted from the national curriculum of Korea due to the reduction of learning burden, but it was recently suggested that matrix should be included again in the national curriculum as a part of restructuring future-oriented learning contents for the age of intelligence in the course of the research for 2022 revised mathematics curriculum. In relation to this suggestion, the items involving matrix in the past college scholastic ability tests of Korea were pointed out as a problem. As the matrix items have been criticized for the high level of difficulty due to demand of specific operation of matrix and overfull calculation proficiency, the need for discussion on improvement of assessment of matrix was proposed. The purpose of this study is to compare matrix items from various countries and find a way to improve assessment of matrix with focus on whether the mathematical thinking and mathematical modelling ability could be considered in the assessment of matrix in a balanced way. To this purpose, the cognitive levels of matrix items in college scholastic ability tests of Korea, and exams for senior secondary certificate of Australia, England, France were investigated and compared with each other. The result show that Korea has the highest percentage of the Connection item while the Reflection item accounts for the highest percentage for the other three nations. It was also found that most of Reflection items of Korea focused on the assessment of performing calculation process, but Reflection items of Australia, England and France assessed a variety of cognitive elements containing Integrating, Justifying and Modeling. The results suggest a way in which matrix could be assessed meaningfully in a variety of cognitive levels and cognitive elements as an alternative to calculation-focused assessment.

The national mathematics curriculum revision process is underway in the background of the era where rapid technological development, uncertainty and volatility are expanded. In this process, consideration of matrix as a learning content emerged as one of the key issues, and conflicts among diverse educational participants are escalating. This study attempted to obtain implications for revising the presentation of matrix in textbooks by comparing the perspectives reflected in mathematics textbooks in Korea, Singapore, and Australia. First, the study compared and analyzed the learning contents, concept introduction and contents development methods in the textbooks from the three countries, and found that Korean textbooks cover more learning elements and tend to focus on calculation, while the other two textbooks from Singapore and Australia value the meaning of matrix as a useful means of expressing data. In addition, the results of comparing tasks based on the cognitive level framework developed by integrating the TIMSS cognitive domain and Jan de Lange’s framework showed that more than 80% of the tasks included in the Korean textbooks remained at the level of reproduction and connection, while Singapore and Australian textbooks provided various opportunities to learn such as making conjecture, justification and mathematical modeling through 70% and 45% of the tasks at the level of reflection, respectively. Drawing on the implications from the analysis, it is suggested to have fewer focus on content elements and more emphasis on conceptual understanding, mathematical reasoning, and mathematical modeling rather than calculation.