不同數學寫作模式與數學能力水準對國小學童分數除法學習成效之影響

The influence of different mathematic writing models and math levels on elementary school students’ learning effectiveness for learning fraction division

相關文獻已指出紙筆式數學寫作能協助教師了解學生數學概念的學習成效， 透過紙筆式數學寫作活動的練習，學生可建構出合於邏輯的數學意涵，惟紙筆式 數學寫作的成效會受個人先備知識與能力的影響，產生不同差異的學習結果。近 來，部分文獻的提倡與教育思潮的興起換來線上式數學寫作的契機，是故，本文 結合以上兩項變因（數學寫作模式與數學能力水準），透過準實驗設計法進行二因 子多變量共變數分析。研究對象有95人，研究期程配合學校教學進度以分數除法 為單元，分析學生在成就測驗總分與總解題策略量。研究發現：以高、中、低三 種數學能力面向來看，除了低數學能力的學習者外，使用線上式數學寫作的學習 者皆較紙筆式數學寫作有較佳的總分與總解題策略量之表現。再以兩種寫作模式 來看，使用線上式數學寫作的學習者，都能讓不同數學能力的學習者在總分與總 解題策略量的表現上有顯著差異，若改使用紙筆式數學寫作，則在總解題策略量 的表現上未若使用線上式寫作來得佳。據此研究結果，本文提出相關結論供學校 及教師參考運用。

Previous studies have confirmed that pen-and-paper mathematic writing facilitates teachers to understand the learning effectiveness of students’ mathematic concepts. Pen-and-paper mathematic writing practices enable students to construct logical mathematic meaning. However， the effectiveness of pen-and-paper mathematic writing is influenced by an individual’s prior knowledge and skills， which leads to varying learning results. Recent promotions in relevant literature and the emergence of education trends have given rise to opportunities for online mathematical writing. Therefore， the present study combined the two above variables (mathematical writing mode and math level) and employed a quasi-experimental design to conduct two-way multivariate analysis of covariance (MANCOVA). A total of 95 subjects were recruited. To comply with school syllabuses， the present study focused on the unit of fraction division and subsequent analyzed students' total scores and total number of problem-solving strategies. The results of this study indicated the following: In terms of the dimensions of high， medium， and low math skills， aside from learners with low math skills， employing online mathematical writing yields total points and a total number of problem-solving strategies superior to that of pen-and-paper mathematic writing. Regarding the two writing models， learners that use online mathematical writing exhibited significant differences in total points and a total number of problem-solving strategies compared to those that used the pen-and-paper method， regardless of math level. The performance in total number of problem-solving strategies of learners that switched to the pen-and-paper mathematic writing model was inferior to those who used online mathematical writing. Based on these findings， the present study offers a conclusion that serves as reference for schools and teachers.