研究生: |
丁斌悅 |
---|---|
論文名稱: |
國二學生學習線型函數時的概念表徵發展研究 |
指導教授: | 曹博盛 |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
論文出版年: | 2002 |
畢業學年度: | 90 |
語文別: | 中文 |
論文頁數: | 189 |
中文關鍵詞: | 概念發展 、表徵 、認知發展 、線型函數 、二元一次方程式 |
論文種類: | 學術論文 |
相關次數: | 點閱:425 下載:127 |
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本研究之主要目的在探討國二學生學習線型函數時,三個主要表徵(『表列』、『代數式』、『圖形』)的認知發展情形;並試圖瞭解這三個主要表徵的認知發展情形彼此之間的關係。以期能夠提供數學教師們,作為函數與線型函數單元教學之時,使用表徵的參考依據。
本研究以台北市大同區某公立國中二年級一個普通班的學生為研究對象,樣本數為25名。主要是以Anna Sfard的概念發展理論為依據,將二元一次方程式與線型函數概念,依三個主要表徵分成「內化」、「壓縮」、「物化」三個層次,首先利用自編之二元一次方程式測驗卷(前置施測卷),以瞭解學生在線型函數教學之前的先備知識,接著藉由自編之線型函數測驗卷(後置施測卷),調查學生的線型函數概念,在每個表徵的認知發展情形,輔以訪談來深入瞭解學生填寫測驗卷時的想法。同時也依表徵來研究國二學生在二元一次方程式與線型函數上的解題策略、迷思概念與錯誤類型。
本研究的主要發現如下:
1.國二學生在學習線型函數概念時,三個主要表徵的認知發展情形並不相同。
2.學生在表列、代數式、圖形三個表徵層次上的發展速度,並沒有太大的關聯。
3.由於線型函數命名的特性,『圖形』表徵在幫助學生其他兩個表徵,發展至較高層次時,扮演一個很重要的角色!
4.學生在線型函數的概念表徵發展上,凡是在『代數式』表徵上能達到物化層次的學生,在其他兩個表徵上也必能達到。
5.學生在前測(二元一次方程式)時,三個主要表徵表現上的優劣(以魏氏考驗作檢定):
a.『表列』表徵的整體表現與『代數式』表徵沒有顯著差異。
b.『表列』表徵的整體表現優於『圖形』表徵,且達顯著水準。
c.『代數式』表徵的整體表現與『圖形』表徵沒有顯著差異。
6.學生在後測(線型函數)時,三個主要表徵表現上的優劣(以魏氏考驗作檢定):
a.『表列』表徵的整體表現優於『代數式』表徵,且達顯著水準。
b.『表列』表徵的整體表現與『圖形』表徵沒有顯著差異。
c.『圖形』表徵的整體表現優於『代數式』表徵,且達顯著水準。
7.學生在「線型函數」教學之後,『表列』、『代數式』、『圖形』三個表徵,後測的表現都優於前測,且都達到顯著水準(以魏氏考驗作檢定)。
最後根據本研究的一些缺點提出檢討,並對數學教師與未來研究作出若干的建議。
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