本研究是描述一名國小教師進行六年級比與比值教學的行動研究歷程，內容主要呈現研究者在實踐行動時所遭遇的問題，與透過不斷反思，尋求解決策略的歷程。
本研究採行動研究法，以研究者本身任教的六年甲班為研究場域，研究者在進行文獻探討與參考學生前測中的表現後，以能力指標與本單元的教學目標為主軸，與諍友討論並形成教學活動設計，接著才進入現場教學。論文內容呈現本單元中「比感」、「比的意義」、「比值」三個教學主題的行動歷程。研究過程中，研究者透過以下方式做為行動策略的來源：閱讀文獻、分析教材、蒐集並分析學生的解題記錄與數學日記、撰寫教學反思日誌、與諍友們討論，以及在跨校教師成長團體中與本單元相關的的教室觀察和討論會。
在本研究中，研究者主要透過布題的設計，幫助研究者分別達成預期的目標，包括題目語意結構的選擇、題型的改變、情境的設計以及數字的調整。研究發現學生會受數字影響而忽略情境，透過課堂布題討論以及進行分類活動確能逐漸形成學生比感，也由於比例情境多元，比感教學需在不同情境不斷延續。而比的意義可以利用「關係的集合」語意結構，幫助學生查察到情境中有配對關係的兩數量，而利用差數規律題目的對照能夠突顯比例問題中的兩數量為乘除關係。因此在情境可類推，兩配對數量為乘除關係且具有意義時，此兩數量才能用比「：」來記錄其關係。比值概念則在多個對象比較的情境能突顯比值的需求感，並可發展至某項為1的自然想法；再透過教師課堂提問與適當情境，引導學生至後項為1的路徑以學習比值，數字設計上以前項為後項的整數倍為佳。依問題中兩數量的單位相同或相異，比值有不同意義，均需做介紹。利用九頭身美少女與黃金比值情境可以提升學生至比例關係中的兩數量可放大縮小的比例運思層次。
雖然九頭身美少女、黃金比值與放大縮小相類似，但本研究中只探討一維（長度）的改變，建議後續研究可朝向放大縮小語意結構方向進行。

This study demonstrated action research process of an elementary math teacher teaching “ratio and proportion” to the 6th graders. The study was mainly to present the problems the researcher met while practicing activities and the procedure of seeking strategies to solve problems.
This action research took class A ,where the researcher herself was the teacher , as the research subject . All the teaching activities were designed according to National Math Curriculum Guideline, textbook teaching targets, students pretest and the discussion with teachers in a mathematical professional group.
The references of strategies used in this research are as follow: literature review, students pretest, textbook analysis, students performance evaluation such as the observation of solving questions and students mathematics diary, as well as teacher’s log,and frequent discussions with other teachers in a mathematical professional group. The teaching strategies included the chosen of semantic structure of questions, the types of questions, the change of numbers and situations of questions.
The study shows that
1)Students often ignored the context of questions while solving problems.
2)Students can develop their sense of ratio through practicing on compiling questions and class discussion
3)Teachers should help students build up sense of ratio by providing various contexts of questions.
4)Teachers should help students recognize two quantities has a relation of subtract and divide, that can be expressed as “a to b” or “a:b”. To help student understand better, using semantic structure of associated sets is a good tool.
5)The concept of ratio and proportion is better be built up in a multi-objects comparative context. Teachers should help students understand the relationship between antecedent (the first number) and consequent (the second number), the concept of the consequent should become 1 is suggested to teach in class.
6)In this study, there is only a change of one dimension (length), other identical dimension changes are suggested in further research.

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