| Summary: | 碩士 === 國立彰化師範大學 === 科學教育研究所 === 92 === The main purpose of this study is to put the theory of analogy into the learning unit of one order function of junior high school Mathematics in order to use geometric relation graphics as analogs to help the second grade junior high school students learn the knowledge of one order function of junior high school Mathematics and analyze their thinking process of analogy. This study adopts quantitative and qualitative data to explain the learning activities, learning achievement and thinking process of students. The conclusions of data analysis are as follows:
1. The correlation coefficient testing of the basic knowledge, the logically reasoning ability, the single rule of one order function, the bilateral rule of one order function, the multiple rule of one order function and the summation of one order function have reached the prominent level which means students’ basic knowledge and logically reasoning ability are the main factors affecting the learning achievement of one order function.
2. If the case students’ test score of the learning achievement of one order function is higher than the average, their test score of the basic knowledge is also higher than the average. This explains that the basic knowledge is the main factor affecting the learning achievement of one order function.
3. Using geometric relation graphics as analogs to learn through group discussion is helpful to arouse students’ math learning interest.
4. In the four learning topics, all students are able to identify and retrieve the source domain knowledge. The most difficult parts for students are the steps to map and evaluate in the thinking organism of analogy; moreover, the correspondence of geometric relation graphics of（one order function：y=ax, a＜0）and （one order function：y=ax＋b, a＜0, b＞0） are harder than the other two topics.
5. Using the geometric relation graphics as analogs in the analogical learning is not only an effective way to promote the understanding of one order function of abstract algebra of students but also a good way to break the misconceptions of one order function and lower students’ difficulties of thinking.
6. The logically reasoning ability and the basic knowledge are the factors affecting students’ utterance quality in the group discussion.
7. Using the geometric relation graphics as analogs in the teaching of one order function is advantageous to change the misconceptions of the basic knowledge and the one order function students had before.
Key words：Analogical learning cycle, Pictorial analogies, basic knowledge, logically reasoning ability
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