Objectives In this study, the understanding of sequences and concept images using formula and graph were analyzed for second-year high school students. Methods Based on previous studies, a test tool was developed and applied to 73 second-year high school students, and some students were interviewed. Based on this, statistical analysis was conducted to investigate the difference in understanding according to the expression and sex of sequences for all students, and concept images were analyzed by applying concept definition and concept image model. Results First, the understanding of the graph expression of the sequence was higher than that of the formula expression, and significant differences were found. Second, female students' understanding of the sequence was higher than that of male students, and significant differences were found. This difference was due to the branching general term for the sequence, the recurrence relation expression of the sequence, and the graph expression that diverges while vibrating. Third, from the perspective of the concept image, a sequence was recognized as a list of numbers or a function in which natural numbers are the domain. In the case of recognizing it as a list of numbers, it was recognized that the sequence was specifically a list of simple numbers, that there were certain rules, that there was an equally spaced sequence or that there was a certain interval between terms, etc. Conclusions Implications related to how second-year high school students choose problems to develop sequence tasks by level based on the expression of sequences representing difficulties were provided.
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