In this study, 218 highschool mathematics teachers were surveyed to identify their perceptions and reading of curriculum materials. As a result, the majority of teachers emphasized the agency of teachers in enacting the curriculum and regarded conceptual understanding as crucial in teaching conditional probability. Nevertheless, the analysis of reading of the 2015 revised mathematics curriculum showed the lowest frequency of responses using the teachers’ knowledge and experience. Among the major changes in the 2015 revised mathematics curriculum related conditional probability, teachers mentioned in the order of attitude and practice, information processing, reducing the burden of learning, improving evaluation methods, and reasoning. When teachers mentioned reasoning, they were more likely to evaluate or interpret the curriculum materials using their knowledge and experience. But most of teachers stated that the other changes as particular features were included. Thus, opportunities must be provided to improve teachers’ professional development based on the concrete methods that can enact the intention of the 2015 revised mathematics curriculum.

Using the raven’s advanced progressive matrix, this study investigated the figural reasoning ability of 30 mathematically gifted students in middle school and analyzed the figural reasoning process using eye-tracking method. As a result of the study, mathematically gifted students showed a large individual difference in figural reasoning ability. Almost all subjects were able to solve the items that require simple visual manipulation, but there were individual differences in the accuracy of visual items involving complex rules or items with two or more rules. As a result of analyzing the patterning process, there were many differences in thinking ability or characteristics such as information searching method, structure grasping speed, mental flexibility, meta-cognition, and analytical thinking, which influenced the success or failure of figural reasoning. It was confirmed that the selected mathematically gifted students' individual thinking ability and characteristics were measured and that differentiated instruction was needed to strengthen their thinking ability.

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Currently, the number of low-achievers in mathematics is constantly increasing. PISA results manifest this tendency, and it is noticeable that the proportion of low-achievers in mathematics has been growing sharply since the introduction of PISA 2015, which adopts computer-based test. In an attempt to figure out the reasons of this phenomenon, this study compares the characteristics of low-achievers and high-achievers on PISA 2018 results, supplemented by PISA 2015 results. The analysis shows that the two groups distinguish from each other in the areas of response time, the number of action, and the time to the first action. In the end, this study suggests some teaching implications for the changes caused by computer- based test environment.