An analysis on understanding and functional thinking on quadratic function’s translation of middle and high school students

In this study, middle and high school students were analyzed for understanding and functional thinking about the translation of quadratic functions according to grade and gender.To this end, first, the test tool was reconstructed based on previous studies.The results of analyzing this by using the data applied to a total of 106 students consisting of 34 middle school students and 72 high school students are as follows.First, for middle and high school students, there was no significant difference between grades and sex in the understanding of translation in the x-axis or y-axis direction of the quadratic function.Second, the understanding of translation in the x-axis direction of the quadratic function tended to be lower than the understanding of translation in the y-axis direction of the quadratic function.However, as the grade went up, the difference in understanding of translation in the x-axis and y-axis directions of the quadratic function tended to decrease.Third, the understanding of translation in the x-axis right directions of the quadratic function tended to be lower than that of the quadratic function in the x-axis left directions, and the understanding of translation in the y-axis downward directions of the quadratic function tended to be lower than that of the quadratic function in the y-axis upward direction.Fourth, as a result of error analysis, the collision phenomenon between geometric and algebraic thinking appeared more in the translation of the quadratic function in the x-axis direction than in the y-axis direction of the quadratic function.Based on these results, this study discussed functional thinking and teaching and learning implications related to translation of quadratic functions of middle and high school students.