| Summary: | 碩士 === 國立臺南大學 === 應用數學系碩士班 === 105 === The purpose of this study was to understand the effects on linear inequality of one unknown performance, learning sttitude, and how to solve problem until by the teaching Mayer problem solving theory for grade seven students. Meanwhile, we want to find out the differences of learning achievements between students of different levels. This study adopted a quasi-experimental method. The samples are two grade seven classes for total of 41 students. One of the classes is experimental group to process the Mayer problem solving theory, and the other serves as the control group to process traditional instruction. Both quantitative and qualitative methods were applied to collect and analyze the data. In order to investigate the studerns’learn effects, using the data collected, the researcher carried on quantitative analysis for the “linear inequality of one unknown learning achievement test”designed by the researcher, and the “Scale of Mathematics Learning Motivation”adapted from Tuan, Chin and Shieh（2005）. The researcher interviewed six students of different levels according to their scores. The researcher made use of quantitative analysis with descriptive approach, One-way ANCOVA, and paired-sample t-test in this study. The semi-structured interview was adopted to analyze the performance of the problem-solving among and different achievers. Through this analysis, The findings were in the following:
1. There are no significantly differences in learning achievemeny of arithmetic operation for the seventh graders between the experimental group with Mayer problem solving theory and control group with “Traditional Expository Instruction”.
2. After applying of Mayer problem solving theory, students in the experimental group have significantly differences in learning motivation.
3. By comparing problem-solving skills in commom and in differences among students of different levels in learning achievement, the study shows that high-level students have more concepts in problem-solving skills, and middle-level students grasp only some concepts that the high level students have, and low-level students can not totally get the concepts in general.
4. Most students believe Mayer problem solving theory can help them （1）Understand problem. （2）Find conditions.（3）Curious in question and concentrate in class. （4）Solve problem Step by step.
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