| Summary: | 碩士 === 臺中師範學院 === 教育測驗統計研究所 === 91 === The Study of the Relationship Between Problem Representation and Problem-solving Ability
Abstract
The research is based on Lesh’s five representation systems to explore students’ abilities on the translating relationship among word representation, pictorial representation and equation representation. The subjects of the study are 201 students of 5th and 6th graders. The research process is divided into three stages. First, the pictorial representation test is used to assess the students’ abilities on translating word representation into pictorial representation. Then, the equation representation test is used to assess the students’ abilities on translating word representation into equation representation. At the final stage, the mathematical problem-solving test is used to assess the students’ abilities on synthesize-problem-solving and explore the correlation between them.
The main results of the study are as follows:
Both the level of students’ preference for the problem-solving representation type and the degree of difficulty of test questions do have influence on the types of problem-solving representation the students choose. When dealing with ordinary word problems, students frequently adopt equation representation. However, when dealing with non-routine or more difficult problems, they usually adopt pictorial representation.
Both mathematics pictorial representation and equation representation can help to promote students’ abilities of problem-solving. However, most students do not equip these abilities at the same time.
Math teachers’ classroom operation modes do have influence on students’ choices of problem-solving representation types during problem-solving activities. Students in the discussion classroom type and open classroom type tend to choose pictorial representation problem-solving. On the other hand, students in the traditional classroom type tend to choose equation representation problem-solving.
According to the results above, researcher suggests that when teaching math, teachers should be open-minded and encourage students to try to use different representations to represent the meaning of the questions. Also, for assessment, teacher should look after all kinds of test items to cultivate students’ diversified problem-solving abilities.
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