國中數學教科書負數教材之內容分析比較—以負整數加減運算為例

The Comparison and Analysis on Negative Numbers in Mathematics Textbooks of Junior High School--the Addition and Subtraction of Negative Integers as the Example

蔡英如(Ying-Ju Tsai)

指導教授 ： 張英傑 ； 李武炎

淡江大學/理學院/中等學校教師在職進修數學教學碩士學位班/碩士(2013年)

https://doi.org/10.6846/TKU.2013.00012

摘要

本研究目的呈現國內各版本國中數學教科書負數概念的表徵，分析負整數加減運算的呈現方式，同時探討各版本負整數加減運算習作練習題與課本內容配合度的情形。本研究以概念圖為工具，採用內容分析法，對現有100學年度三個版本國中數學教科書負數教材內容進行內容分析，其研究結果如下：一、各版本在負數概念的表徵，以「語言表徵」和「符號表徵」所佔比例最高，其次所佔比例由高至低為「圖形表徵」、「真實情境表徵」、「具體物操作表徵」；二、各版本在負整數加減運算的呈現方式，以Ａ、Ｂ版本的題目類型呈現較為完整，Ｃ版本則是缺少「含絕對值」題目類型的呈現；三、各版本在負整數加減運算的習作練習題與課本內容配合度，以Ｂ版本習作的配合度最高，其次為Ａ版本習作，而Ｃ版本習作配合度最低。最後依據研究結果分別對教材內容、教科書的編撰及使用與未來研究提供相關建議以供參考。

關鍵字

負數 ； 整數加減 ； 數學教科書 ； 表徵 ； 習作

並列摘要

The main propose of this study was to illustrate the representation of the concepts of negative numbers in mathematics textbook of junior high school and to analyze the representations of the addition and subtraction of negative integers, as well as to discuss the condition of the compatibility between workbook exercises and textbook content in every version concerning the addition and subtraction of negative integers. With the tools of concept mapping, content analysis was applied to negative numbers in the teaching materials of three existing versions of junior high mathematics textbooks. The findings of this study were as follows. First, it is shown that within the representations of negative-number concepts, the 'spoken languages' and 'written symbols' have taken the highest percentage, followed by 'pictures', 'real scripts', and 'manipulated models', from higher to lower hierarchy. Second, within the textbook version, while the presenting methods of the addition and subtraction of negative integers are rendered, it is found out that the question types in version A and B are more complete while version C lacks the representation of 'absolute value'. Third, when researching on the compatibility between practice questions and textbook content of the addition and subtraction of negative integers, version B has the highest compatibility while version C has the worst score. Version B stands in the middle. Finally, according to the findings of this study, some suggestions were rendered to the content of the teaching materials, compiling and usage of the textbook, and future studies as references.

並列關鍵字

negative numbers ； addition and subtraction of integers ； mathematics textbook ； representation ； workbook

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