擬題成品與研究結果為學術與教學現場激起許多討論與應用上之建議。擬題成品的呈現，展現了自由擬題與生活情境題的價值：使學童更投入、主動、深入地學習，並自然而然地發展數學外部連結。合作時機與建議對象帶來的不同效果與互動歷程，也提供教學現場實施之圖像。而兩規準之應用，除了加強數學內部連結之外，建議規準的應用也可使數學溝通能力更有進展。 ;Problem-posing and collaboration have been recently considered as two important issues by mathematics education researchers around the world. However, academic researchers address the benefits of collaborative learning while school teachers point out that the students’ widely varied abilities and teachers’ time constraints will have an influence on the quality of the collaborative effects. In addition, “high achievement but low interest” is still an unsolved problem in mathematics education in Taiwan. Therefore, the two research questions are: 1) To what extend do student’s problem-posing improve? 2) What collaborative effects do suggestions from peers and teachers have on the quality of students’ problems?
The major characteristic of this problem-posing activity is “one problem, many revised versions”. There are two stages: the “peer-help” stage is from the first to the fourth version, and the “teacher-guide” stage is between the fourth and the fifth version. Each fifth grader is encouraged to give suggestions to his or her classmates and to help each other pose a mathematic problem. After the fourth version is completed, the teacher will provide guidance to problems that need further improvement.
This study used a mixed method. Two sets of rubrics were generated to evaluate the quality of the problems by posers and suggestions by peers. The results were analyzed in a quantitative fashion. Problems between versions, interviews, and worksheets data were used to analyze qualitatively the progress they made.
The result shows that: 1) The free problem-posing activity produced problems presented with wordiness, inconvenient numbers, and high relations with students’ life experience or other subjects. 2) The student-posed problems made significant progress throughout the five-version process. Each received different kinds of help from the “peer-help” stage and “teacher-guide” stage. In particular, the teacher had a significant influence on solvability and readability of the problems, while peers helped on the connection to their daily life, the refinement, and the concept level of the problems.
Debates and implications for school teaching are provided. The free problem-posing has its virtues in engaging students in more active and deeper thoughts, but has its drawbacks in developing lengthy and context-rich problems which goes against the current practice among professional mathematicians. The different collaborative design and its effects on peer collaboration provide a promising picture for teacher practitioners. Future study can focus on the refinement of the two sets of rubrics. The potential of problem posing on student’s mathematics communication ability is also discussed.
