數學自由擬題之設計與評量－一個合作的取徑

解題能力是正式數學課程主要培養的能力，而擬題能力常被忽略。本研究關切融入合作精神以設計自由擬題課程模組之規劃與實施。合作擬題模組共計約400分鐘，國小四年級學生不受課程單元侷限進行自由擬題，歷經同儕給予建議、出題者修改、同儕試答、出題者批閱後再修改、通過班級與專家檢驗等歷程，在多回合的建議修正之合作氛圍下，完成擬出一個題目的活動。本研究針對自由擬題的題目特徵，發展一份包含四個向度的自由擬題品質規準：可解性、可讀性、生活性、與精緻性；在自由擬題的同儕建議方面，在前述四個向度以外又辨識了四個向度：完備性、情意面、雜類與誤導性。結果顯示，在同儕給予建議的幫助下，擬題品質的版本一與最終版本相比，進步達顯著，其中以精緻性進步最多；同儕給予的建議也以精緻性與題目的進步最為相關，其次是情意面的幫助。這些發現建議：擬題活動涉及的面向並不單純只用到數學能力，值得後續更多的探索。本研究對提升擬題能力的課程設計、評量，以及提高學生對於數學活動的興致皆有所探討。

關鍵字

合作；同儕互評；評量規準；數學；擬題

並列摘要

Problem-posing is usually dwarfed by problem-solving in school mathematics curricula. This study attempted to design a free-form problem-posing curricular module that incorporated collaborative strategies into the activities. The module took about 400 minutes to implement. The 4th grade participants were invited to pose a word problem free of any constraints on subjects or contents. Each initial problem would be evaluated through peer comments, trial work-outs, peer and expert inspections, and back-and-forth revisions, before it was considered a collectively owned asset. In order to evaluate the quality of the activities in each phase, this study developed a set of rubrics for the freely posed problems and the comments given by the peers. Dimensions of the rubrics were solvability, readability, reality, and sophistication. There were four types of comments: completeness, emotionality, misleadingness, and miscellany. According to the results, all posed problems were significantly improved through the revisions across all four dimensions of the rubrics, especially in the dimension of delicacy. As for the contribution of peer comments, the type of delicacy helped most, and that of emotionality followed. Findings of this study suggested that problem-posing involves abilities other than those in Mathematics, and is worthy of further investigation. This work also addressed the curriculum and rubrics design that might raise the ability of problem-posing and the enthusiasm of students on mathematical activities.