以電腦遊戲為情境支援非例行性數學問題解決的類推與核證

A computer game as a context for supporting generalization and justification in non-routine mathematical problem solving

李俊儀(Chun-Yi Lee)

指導教授 ： 陳明溥

國立臺灣師範大學/教育學院/資訊教育學系/博士(2009年)

摘要

本研究的目的是要探索不同種類的解答方式演練範例與問題提示策略對於國中三年級學生例行性問題解決與非例行性問題解決得分表現、類推表現與核証表現之影響，並分析學生在例行性問題解決與非例行性問題解決的類推策略。活動之教學設計以蛙跳遊戲為情境並提供相關電腦工具用來支援例行性與非例行性問題解決的類推與核證。本實驗共分兩個階段，在例行性問解解決任務階段，將學習者分為多解答方法演練範例組與單解答方法演練範例組，多解答方法演練範例組提供學生的範例中都有2個以上的解答方法，並要學生比較分析多種解答方法的優缺點;單解答方法演練範例組，所提供的範例則只提供一種較為常見的解答方法。兩組都有提供學生自我解釋解答步驟的學習單，以記錄學生的學習過程與思考策略。在非例行性問題解決任務階段，則將學習者分為精緻化反思問題提示組與專家解題程序問題提示組，精緻化反思提示組提供了三層的提示，由一般策略提示到特定策略提示，讓學習者有機會將思考過程更加精緻化並提供更多反思的機會; 專家解題程序提示組則是提供學習者專家的解題程序提示，希望學習者能模仿專家的解題行為與思考模式順利解決任務。本研究根據上述兩個階段的分組，採不等組前後測二因子之準實驗設計，選取台灣桃園縣某縣立國民中學國三學生四個班共120人為實驗研究對象，該校採常態男女合班的模式教學，隨機將四個班分別指定為多解答方法演練範例-精緻化反思問題提示組(M-R)，單解答方法演練範例-精緻化反思問題提示組(S-R)，多解答方法演練範例-專家解題程序問題提示組(M-P)與單解答方法演練範例-專家解題程序問題提示組(S-P)。學習單依照上述四組分別設計並於蛙跳問題教學網站提供相對應的網路學習教材。
經由統計與實徵資料分析所得主要結果如下: 1.先備知識與數學態度可以有效預測例行性問題解決之得分表現、類推表現與核證表現。2.精緻化反思問題提示組學生，在非例行性問題解決的得分表現、類推表現與核證表現，都顯著高於專家解題程序問題提示組。3.多解答方法演練範例，雖然在一開始的例行性問題解決階段，看不出任何優於單解答方法演練範例的效果，但在非例行性問題解決階段的類推與核證表現上，卻發現多解答方法演練範例教學的好處。4.類推與核證的關係是非常緊密的，發展較好的類推策略會影響到後續的核證品質，而發展較好的核證策略則會影響到後來的類推層次。5.多解答方法演練範例組的學生在科技輔助教學意見的看法上，比單解答範例演練組學生更為正向，特別是在情感方面與知覺易用性這兩個層面上。
最後根據研究結果與發現，提出若干建議以做為教師教學改進與未來研究之參考。

關鍵字

多解答方法 ； 非例行性問題解決 ； 類推 ； 核證 ； 樣式推理 ； 電腦遊戲

並列摘要

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.

並列關鍵字

Multiple solution methods ； Non-routine problem solving ； Generalization ； Justification ； Pattern reasoning ； Computer game

參考文獻

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