診斷教學對一位小六生擬題表現之影響 －－以時間計算問題為例

The Intervention Effects of Diagnosis Teaching on a Sixth Grader’s Problem Posing Performance: Time Computation Problems as a Research Task

數學擬題乃是以數學計算式子，給學生編製數學應用問題的活動，此活動著眼於建立數學概念與生活情境相結合。學生的擬題表現是一種診斷工具，用以了解數學概念與數學句子的關係是否合理。再者，根據研究者教學經驗，時間計算問題對於高年級學生有很大的困擾，於是先做擬題活動的預試，再挑選出一位對時間計算問題有困擾的國小六年級女學童進行擬題活動及診斷教學的研究。本研究旨在探討個案關於時間計算問題的擬題表現，探討診斷教學的策略，以及診斷教學對個案擬題表現的轉變。本研究發現：在診斷教學前，個案對擬題的表現不夠理想，「時刻」與「時距」發生混淆；在診斷教學時，研究者利用提問以製造認知衝突，利用數線圖表徵等策略，幫助個案建立了時刻與時距的關係；診斷教學後，個案的擬題表現有顯著的進步。本文又根據研究結果提出五點診斷教學上的建議。

Mathematics problem posing refers to a kind of activity in which students create mathematical word problems based on time computational problems. Mathematics problem posing can also be used as a sort of diagnostic tool to detect whether students’ concepts and statements about math are reasonable. From the authors’ teaching experiences, the time computation problems are hard to upper graders of elementary school students. To examine students’ difficulty of computation problem, problem posing activities was organized for warming up their experiences and for choosing the research case from the pilot. The purpose of this study was to explore the problem posing performance and the effect of diagnosis teaching intervention of this case. This case had difficulty with computational operations when completing math problems; however, the student had no difficulties responding orally during the interview. The researcher finally monitored the student’s performance while providing diagnosis teaching intervention. The study found the student confused two terms: “interval of time and “point in time”, thus causing her to pose incorrect mathematics problems. She was successfully able to adjust some of her misconceptions after the researcher intervened by questioning. In addition, the strategy of using number lines to represent the structure of the problems she posed was found to be an effective method in adjusting her problem posing. Moreover, the strategy of asking her to solve the problems she posed drove her to understand the mistakes she had made