| Summary: | 碩士 === 國立臺南大學 === 應用數學研究所碩士班 === 101 === The purpose of this study was to understand the seventh graders’ problem-solving performance on linear equation by different representations (graphs (G), numbers(N), equations(E), and verbal(V)), investigate the relationship within the reciprocal concept of representation question, and analyze the differences of different gender and mathematical ability in the students’ overall problem-solving performance and three different dimensions (visual (visual), numbers (numeric), abstract (abstract)) problem-solving performance. The participants were 32 boys and 44 girls, coming from one junior high school in Tainan City. They completed the linear equation examination designed by the author. Descriptive statistics, Pearson-product moment Correlation, Independent-Sample T-Test, ANOVA were then employed to analyze the collected data, and Semi-structured interview was adopted to analyze the differences of the problem-solving strategies and the representation fondness among the students with different levels of mathematical ability.
The research results are as follows:
1. The participants’ average correct rate on the questions of linear equation presented by different representations: higher correct rate on EN, VG, and GE, but lower correct rate on VE. Overall, students’ performance on graphs representation was the most centralized, but students’ performance on verbal representation was relatively scattered.
2. There was significantly positive correlation within the reciprocal concept of representation question (GN v.s. NG, GE v.s. EG, NE v.s. EN).
3. There was no significant difference between different genders in the overall problem-solving performance presented by different representations and three different dimensions (visual (visual), numbers (numeric), abstract (abstract)) problem-solving performance.
4. There were significant differences among students with different levels of mathematical ability in the overall problem-solving performance presented by different representations, where there were significant differences in the numeric and abstract dimension problem-solving performance, but no significant relation in the visual dimension problem-solving performance between high mathematical ability and low mathematical ability.
5. There were differences on the problem-solving strategies and the representation fondness among the students with different levels of mathematical ability. The fondness among students with high mathematical ability is most consistent, which graphs representation was most preferred and equation representation, numbers representation and verbal representation followed in sequence, while bigger fondness differences occurred among students with middle and low mathematical ability.
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