| Summary: | 碩士 === 國立交通大學 === 教育研究所 === 93 === Abstract
Problem solving has long been a crucial issue in mathematic education. In schools, providing students with word problems is an important way to help them become competent mathematics problem solvers. Based on the view of constructivism, this study mainly investigated the learners with different capabilities of math arithmetic and reading comprehension on their performance, error types, and the procedures for problem solving in dealing with different mathematical word problems. Moreover, the study explored the effectiveness on cooperative problem solving.
By reviewing the theoretical foundations of problem solving, there were two different mathematical word problems: traditional and narrative ones. Five steps were also proposed for problem solving: understanding the problem, matching the pattern, making a plan, carrying out the plan, and judgement. Afterward the study integrated the factors and error types in problem solving through surveying the researches on mathematical word problems.
Tests and observations were adopted in this study. The participants were 203 eighth-grade students, who were classified into four groups: having no difficulties in math arithmetic and reading comprehension (Group 1), having reading comprehension difficulties only (Group 2), having math arithmetic difficulties (Group 3), and having difficulties both in math arithmetic and reading comprehension (Group 4). All of the students were given traditional and narrative word problems individually and collaboratively. Their performance, features of solving behaviors, and procedures of problem solving were investigated.
Research findings were summarized as follows. First, students’ performance in traditional word problems was highly related to math arithmetic examination. It indicated that the traditional word problems were decontextualized and were highly coherent with their arithmetic abilities. However, students’ performance in narrative word problems was not as good as that in traditional word problems. Besides, though the students in Group 2 and Group 3 belonged to different difficulties, the performance of narrative word problems turned out no significant differences.
Second, most of the students attained high-level stages in solving traditional word problems except those in Group 4. However, except Group 1, most of the others stayed in low-level stages in solving narrative ones. Furthermore, depending on intuition or smooth working on the procedures of problem solving, most of the students did not judge their final answers. Based on the research findings, a model of problem solving was developed. Successful problem solving resulted from going through a ‘exploring belt’ and ‘the core of problem solving.’
Third, the findings also revealed that most of the students did not perform well in story-based narrative word problems. In particular, the unanswered situation of Group 2, Group3, and Group 4 students was much more frequent than that in traditional word problems. On the other hand, the students of Group 2 and Group 4 with obvious errors of linguistic knowledge may require interventions aimed at reading comprehension. The students of Group 3 and Group 4, on the other hand, may need instruction in automatic skills in mathematics.
Finally, solving problems cooperatively promoted both the scores and problem solving stages in traditional and narrative word problems. In the procedures of cooperation, the unanswered situations were greatly reduced in narrative word problems because of the affective supports from interactive conversations. Furthermore, the Group 1 students usually played a tutor role in cooperative activities with those in other groups, which were likely similar to an expert-novice relationship, while the complementary cooperative combination of Group 2 and Group 3 students was likely in a ‘equivalent plane,’ which revealed more verbal interaction.
The study indicated that cooperative problem solving may be an important research issue for mathematical problem solving. Further research was suggested to deeply investigate the effect on cooperative problem solving.
|
|---|
