因數概念不管對教師或學習者而言，都是困難且複雜的學習內容。因此本研究希望以不同教學順序的觀點，探究何種教學順序對國小五年級學習者因數概念的學習較有幫助。並以準實驗研究法的方式，分別介入「活動後教學」以及「教學後活動」，再以質性與量化的方式分析學習者的表現，用以釐清何種教學順序對於因數學習較有幫助。
透過量化分析發現，接受「活動後教學」和「教學後活動」的學習者，在因數事實性知識的表現並無差異。但接受「活動後教學」的學習者，相較起「教學後活動」的學習者，在較困難的第三部份與第四部份題目上，進步狀況較好，且前後測總分的進步幅度顯著優於「教學後活動」的學習者。
在此同時，接受「活動後教學」的學習者的課堂表現以及學習單紀錄，較接受「教學後活動」的學習者，更能發現並解釋因數概念的知識要素。
因此，針對因數概念的學習，透過本研究的分析結果證實，先給予學習者活動，再給予正式講述教學，對於因數學習較有幫助。

Students find it difficult to learn the concept of factors. It is equally challenging for teachers to impart factor concepts to their students. This study aimed to test an inverted teaching sequence in teaching factor concepts to 5th grade students to ascertain whether they would find the factor concept easier to grasp through the proposed arrangement. The study used a quasi-experimental design and applied the methodology of an activity followed by instruction in one section and instruction followed by activity in another. The qualitative and quantitative data obtained from the experimental classes were subsequently analyzed to decipher the differences between the two teaching sequences for students to learn factor concepts.
The quantitative data analysis revealed no difference between the two experimental groups with regard to the fundamental comprehension of factors. However, the activity before teaching group progress more than the teaching followed by activity section on the third and fourth part of questions that required the grasp of complex factor concepts. Moreover, the degree of the total score progress was found to be significantly more advanced in the activity before teaching group.
The learner reactions and learning sheets submitted by the two sections also evidenced that the activity before teaching group understood factor concepts better and that this unit could explain factor concepts in a more lucid manner than the teaching followed by activity group.
Thus, the study data confirmed that factor concepts are better grasped by learners by undertaking an activity before receiving direct instruction.

摘要……………………………………………………………………………………ⅰ
誌謝 …………………………………………………………………………………ⅲ
目次 …………………………………………………………………………………ⅳ
表目次 ………………………………………………………………………………ⅵ
圖目次 ………………………………………………………………………………ⅶ

第一章、緒論…………………………………………………………………………1
第一節、研究背景與動機………………………………………………………1
第二節、研究目的與待答問題…………………………………………………5
第三節、研究範圍與限制………………………………………………………6
第二章、文獻探討……………………………………………………………………7
第一節、活動對教學的影響與意義……………………………………………7
第二節、教學順序對學習的影響 ……………………………………………13
第三節、因數定義 ……………………………………………………………27
第三章、研究方法 …………………………………………………………………32
第一節、研究架構與設計 ……………………………………………………32
第二節、研究程序 ……………………………………………………………37
第三節、研究對象 ……………………………………………………………44
第四節、研究工具 ……………………………………………………………44
第五節、資料處理與分析 ……………………………………………………64
第四章、研究結果與討論 …………………………………………………………66
第一節、因數學習成效之比較 ………………………………………………66
第二節、因數學習歷程表現之比較 …………………………………………75
第五章、討論 ………………………………………………………………………83
第一節、研究討論 ……………………………………………………………83
第二節、研究小結 ……………………………………………………………92
第六章、結論與建議 ………………………………………………………………93
第一節、結論 …………………………………………………………………93
第二節、建議 …………………………………………………………………96
參考文獻 ……………………………………………………………………………99
附錄…………………………………………………………………………………104

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