A Study on the Proportional Reasoning Abilities of Students in Grades Six to Eight

• Main Authors: Hung, Meiling, 洪美玲
• Other Authors: 羅素貞
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/54073681565232408778

碩士 === 國立屏東教育大學 === 教育心理與輔導學系碩士班 === 101 === The purpose of this study was to explore the students’ proportional reasoning abilities by accessing the problem-solving performance of students on the qualitatively proportional tasks. This study also tried to understand the proportional concept of students, as well as the correlation between the responses on the qualitatively proportional task and the routine proportional task. According to the studies of Lamon (2006), Harel et al (1992), and Lamon (1993), and referencing to the mathematics textbooks of primary and junior high school, the researcher composed a proportional test as a research tool. The target of this study is 570 students in Pingtung County, which include 213 sixth grade students, 178 seventh grade students, and 179 eighth grade students. Data analysis used descriptive statistics, multiple regression analysis, three-factor analysis of variance, two-factor analysis of variance. This stud y came to the following findings: 1.The problem-solving performance of students in grades six to eight on the proportional test are well in general. 2.The problem-solving performance of students on tasks of "speed questions", "fruit questions", "cookie questions", and "fullness questions" has a significant predictive effect to the problem-solving performance of students on the routine proportional task. 3.As the values presented in the contexts of the qualitatively proportional task, the performance of the students in the proportional type of questions are superior to the performance on the inversely proportional type of questions; on the contrary, the performance of the students in the inversely proportional type of questions are superior to the proportional type of questions when the values is not presented in the contexts of the qualitatively proportional task. 4.In the problem type of proportional, the performance of the students in the numerical questions outperformed the non-numerical questions; on the contrary, the performance of the students in the numerical questions outperformed the non-numerical questions when the problem type is the inversely proportional. 5.The problem-solving performance of students has no obvious differences on grades six to eight for the qualitative proportional task. 6.In the nine job change types of qualitative proportional task, the most difficult types of problems for students are the two variables increased at the same time (i.e., the (+ +) type) and the two variables decreased at the same time (i.e., (-, -) type); the problem-solving performance of students has no obvious differences on grades six to eight for the nine job change types of qualitative proportional task. Finally, some recommendations based on the above findings are also proposed.