Case Study on Vocational High School Students’ Performance for Average Problems

• Main Author: 林志聰
• Other Authors: Shiang-Tung Liu
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/73174430633531197580

碩士 === 國立嘉義大學 === 數理教育研究所 === 101 === This study aimed to investigate 271 vocational high school students’ ability of solving average problem and the percentage of the types of problem solving by using a self-designed “Average Problem Worksheet”. According to the analysis of resources, heuristics, and control of 3 case students’ performance of problem solving, the research findings could be found. Problem solving could be divided into three types when the students dealt with the familiar average problems: 75% students chose to use “total sum divided by the number”; students of using error type were 9% due to the lack of considering “weighted”; 11% students did not have procedural knowledge. When facing unfamiliar questions of average speed, most students solved the problems by the assumption of the distance in between two locations (4%); when facing “restoration average problems”, most students used the method of “work backward” (3%). In terms of the average problems of arithmetic progression, students had difficult solving it possibly because they did not have prior knowledge of arithmetic progression’s median. Referring to the averaging problems of “seeking the total sum of each number and the minimum number of the sum of the difference”, the students tended to use ‘intuitive method’. Regarding the performance of the case students who failed to solve the average problems, Hsiao-Wei solved familiar and abstract problems by using the method of error type. The results were close or far from the average problems because he did not control the used numbers. Next, Hsiao-Chi solved unfamiliar and concrete problems due to the lack of control towards the answer. Finally, Hsiao-Cheng solved unfamiliar and abstract problems such as “restoration average” because he had insufficient resources and did not identify the extra message.