一～九年級數學教科書中代數符號及等號概念之發展設計
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2010
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Abstract
本研究對三個版本國中、小數學教科書進行九年(共54冊)的課程分析，僅對數學教科書中的代數符號及等號概念發展，整理出一套類目歸類，進行版本間的互相比較。本研究以Ausubel(1963)的「有意義的學習論」、Küchemann(1981)的孩童文字符號使用層次理論為主要的理論架構，使用內容分析法進行分析。得到以下結果：
一、此概念之課程發展過程，三個版本主要差異性為題目數與引入時間點。
二、概念啟蒙例的呈現上，三個版本有情境佈題與描述方式上的差異性。
三、先備知識的複習上，三個版本課程內容的表現有安排與呈現方式上的差異。四、課程內容與九年一貫能力指標的對應程度，有出現教材內容與指標不相符的情況。
The purpose of this study is to analyze the design of developing the algebraic symbols and the equal sign concept in mathematics textbooks from 1st to 9th Grade. The theoretical model in my thesis is based on Ausubel’s（1963）meaningful learning theory and Küchemann’s (1981) Children’s interpretations of the letters. The objects of study include three editions mathematics textbooks which were adopted the examination of National Institute for Compilation and Translation, and the contents of these textbooks are analyzed by the content analysis method. The thesis investigates four aspects. The result of this study includes: (1) On the contents design of developing the algebraic symbols and the equal sign concept, the differences among these editions are the amount of examples and the introduced timing. (2) On the expression of generic examples of the algebraic symbols and the equal sign concept, the differences among these editions are the example posing way and the description. (3) On the design of prior knowledge of the algebraic symbols and the equal sign concept, the differences among these editions are arrangement and expression. (4) On the correspondence between the designed order of the algebraic symbols and the algebraic competence indicators, some parts did not correspond with the indicators. At last, there are some suggestion about the results of study and methodology for the future study.
The purpose of this study is to analyze the design of developing the algebraic symbols and the equal sign concept in mathematics textbooks from 1st to 9th Grade. The theoretical model in my thesis is based on Ausubel’s（1963）meaningful learning theory and Küchemann’s (1981) Children’s interpretations of the letters. The objects of study include three editions mathematics textbooks which were adopted the examination of National Institute for Compilation and Translation, and the contents of these textbooks are analyzed by the content analysis method. The thesis investigates four aspects. The result of this study includes: (1) On the contents design of developing the algebraic symbols and the equal sign concept, the differences among these editions are the amount of examples and the introduced timing. (2) On the expression of generic examples of the algebraic symbols and the equal sign concept, the differences among these editions are the example posing way and the description. (3) On the design of prior knowledge of the algebraic symbols and the equal sign concept, the differences among these editions are arrangement and expression. (4) On the correspondence between the designed order of the algebraic symbols and the algebraic competence indicators, some parts did not correspond with the indicators. At last, there are some suggestion about the results of study and methodology for the future study.
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有意義的學習論, 孩童文字符號使用層次理論, 代數符號, 教科書, 等號概念, meaningful learning theory, children’s interpretations of the letters, algebraic symbols, textbooks, the equal sign concept