| Summary: | 碩士 === 高雄師範大學 === 工業科技教育學系 === 97 === In the current mathematics curricula for high school students, there are too many rules, concepts, test item patterns, and formulas. Often is the case that students can memorize the formulas thoroughly, but when they are faced with questions items, they simply don’t know what to do, which leads to their resistance to math learning and their low achievement. But as achievement in math learning plays a very important role in academic learning, career choice, and professional success, these low achievement students in math learning should not be given up. Thus, this study hopes to improve these students’ math achievement and make it progress back to normal level as their peer students by “applying expert system into mathematical remedial instruction.”
This study adopts non-equal group pre- and post-test experiment design. The testees, altogether 73 students, are sophomores from a public high school in Kaohsiung City. The selection criteria pick out students whose junior math scores rated below PR25 of the whole school, excluding students of mental retard, learning retard, and other physical retards. 20 of them form the Experimental Group, receiving experimental course from the researchers; Control Group A consists of 22 students, receiving regular remedial instructions from a student teacher from the same school as one of the researcher; Control Group B consists of 31 students, receiving no remedial instructions from this study ay all. All students from these three groups are given post-test as soon as the remedial instructions come to an end, and the data are under statistical analysis. Later, according to the post-test scores, students are further divided into another three groups—high-score group, average-score group, and low-score group. Any two students are picked randomly out from each group to put to thinking aloud method in mathematical problem-solving process.
The results of this study can be divided into two major parts: Part 1 is the quantity analysis of the effects of remedial instructions, while Part 2 covers the quality analysis of mathematical problem-solving process. The results are as follows:
A.The quantity analysis of the effects of remedial instructions
1.The features of strategy tree can be used to carry out the writing and teaching of remedial instruction materials.
2.There is no conspicuous difference on the co-variance analysis of the learning effects between Experiment Group and Control Group A.
3.The value of the learning effects co-variance analysis of Experiment Group is conspicuously higher than that of Control Group B.
4.There is no conspicuous difference on the co-variance analysis of the learning effects between Control Group A and Control Group B.
5.Mathematical remedial instructions offer great opportunity for students of low math achievement to catch up with their peer students’ regular learning level.
B.The quality analysis of mathematical problem-solving process
1.A complete mathematical problem-solving process should include five stages: item reading, item analyzing, strategy choosing and plan drafting, problem solving, and answer review and recheck.
2.Few students carry on answer review and recheck. In contrast, students with better math ability often proceed with the stage of answer review and recheck, so that they grab higher percentage of hitting the right answers.
3.When students with better math ability solve their math problems, they use a more complete mathematical problem-solving process.
4.Students with better math ability and those with average math ability from time to time skip the stage of strategy choosing and plan drafting and directly move into problem solving stage.
5.Students with better math ability are capable of linking the question items with their past experience and figuring out the key and proper strategy to solving the questions. Moreover, they are also able to correctly and effectively transform abstract concepts into graphs to bring on desired problem-solving thinking.
6.Math knowledge, metacognition, and attitude toward math learning all have influence on successfully solving the question items.
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