| Summary: | 博士 === 國立臺灣師範大學 === 資訊教育學系 === 97 === The purpose of this study was to explore the effects of multiple solution methods and elaborative reflection prompts on ninth graders’ generalizations and justifications in routine and non-routine problem solving. The Frog Leaping Computer Game was used as the context and web-based learning environment was provided for supporting generalizations and justifications in routine and non-routine mathematical problem solving.
A 2x2 (multiple solution methods: Multiple/Single; question prompts: elaborative Reflection/expert Problem-solving procedure) and factorial, quasi-experimental study was conducted to investigate generalizations and justifications of routine and non-routine problem solving performance. One hundred and twenty 9th graders from four classes in a public junior high school participated in the eight-week experimental instruction. These four classes were randomly assigned to the four groups (M-R, S-R, M-P, and S-P) to receive the one-hour weekly treatment. Worksheets and web-based learning materials were separately designed to record the four groups’ learning processes and thinking strategies.
Based on the data analysis of this study, the main results revealed that
1. Prior knowledge and mathematics attitude could significantly predict routine problem solving performance, generalization performance, and justification performance.
2. R group outperformed P group on non-routine problem-solving performance, generalization performance and justification performance.
3. In routine problem solving, M group did not outperform S group. However, M group outperformed S group on non-routine generalization performance and justification performance.
4. Generalization and justification are closed linked. Helping students develop their powerful generalizations would aid in their abilities to construct justifications. Furthermore, a focus on justification could help students develop the subsequent, more powerful generalizations.
5. M group had more positive perceptions toward the computer tools than R group, especially in the affective scale and perceived control scale.
Lastly, implications derived from these results were discussed and recommendations for both further instruction and future research were also provided.
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