A comparative analysis of understanding and errors in inverse functions among Korean and Chinese high school students

The inverse function is a reverse function of a given function and is an important mathematical topic where students can acquire reversible reasoning. In reviewing various previous studies, it was found that the understanding of inverse functions has been investigated from various perspectives among high school students, college students, and prospective mathematics teachers. However, there has been no study that compares and analyzes the understanding of inverse functions among high school students on an international scale. Therefore, this study compared and analyzed the level of understanding, proficiency, and types of errors related to inverse functions among 209 high school students from Korea (162 students) and China (47 stu dents) using a questionnaire task that involved finding the inverse functions and graphing six types of functions (linear functions, quadratic functions, rational functions, radical functions, exponential functions, and logarithmic functions). From the results of this study, the rate of non-response among Korean students in finding the inverse function of a given function exceeded half, while there were no non-responses from Chinese students. “Students from both countries did not use line symmetry to graph the inverse functions and showed no connection between the inverse function expressions and their graphs.