國小學生數學自由擬題困難之初探

本研究旨在了解數學自由擬題活動所遭逢的困難。數學自由擬題是藉由人工品輔助擬題，並以合作氛圍下多次進行同儕互評，依同儕建議內容修改題目。然而，在數學自由擬題的歷程會遇到哪些學習困難？本研究嘗試從擬題、給題目建議和修改題目看三類的學習困難。採質性取向的研究；研究場域為北台灣一間國小；研究對象為兩班五年級學生，共56位學生。施測時間總計長達十堂課，共計400分鐘。資料蒐集有題目卷、建議卷、田野筆記以及訪談。資料分析以逐字稿為主，輔以相關文件；逐字稿的編碼系統採紮根精神的開放性編碼。研究結果有三：一、擬題困難：國小學生知易行難，難以將想法和數學概念組織成一個題目。二、建議困難：難掌握複雜型的題目。數字大、計算困難、題目字數多、步驟數多等造成給建議上的困難。三、修改困難：建議多不易採納。自認能力不足而無法將題目修改得更完善，如不確定建議內容、不理解數字概念等增加修題目困難。這些發現建議：擬題活動涉及的困難不單純是題目完整性與可解性，仍有情意面的困難，值得後續探究擬題鷹架的設計。

關鍵字

困難；數學自由擬題；同儕互評；建議；修改

並列摘要

The purpose of this study was to explore students' difficulties of free math problem-posing in elementary school. Students were problem-posing via artifacts, several peer reviews during the cooperative atmosphere, and modify a topic with peer review. However, what were they learning difficulties of free math problem-posing? There were three tasks in free math problem-posing, including problem-posing, suggestions, and modifies. A qualitative approach to the study. The research field was an elementary school in northern Taiwan. The subjects were two fifth-grade classes (56 students). The total time of the test is up to ten lessons for a total of 400 minutes. Data collection included topic volumes, suggested volumes, field notes, and interviews. Data analysis was mainly an interview transcript and secondary relevant document. Three major results were found: 1) Difficulties of problem-posing: Easier said than done. generating questions based on mathematical concepts and ideas; 2) Difficulties of making good suggestions: take the reins. These includes given a large numbers, word descriptions, solving steps, or calculations, which makes the suggestions difficult to understand; 3) Difficulties of making the modifications. These include problems such as self-doubting of one's ability in making the modification, uncertain on the correctness of the suggestions, confusion of incomprehensible digital concepts, etc. These findings suggest: the difficulties involved in the proposed activity are not simply problem-posing and problem-solving, but also affective factor to be considered. It is, thus, important to explore how ＂scaffolding＂ unfold in the free math problem-posing. Finally, three kinds of difficulties found in this study could be important indicators for future free math problem-posing research.