摘 要
本文進行的是的是兩岸國中數學教科書幾何證明機會的比較分析，研究對象是台灣康軒版和大陸人教版國中數學教科書中的幾何部分；研究架構是根據Otten, Males, 與Gilbertson(2014)的幾何證明教科書分析架構改編而成；分析教科書幾何部分中發展活動中提供給學生性質定理講解的講解題和性質定理應用的應用題，以及練習活動中學生獨立完成的練習題；研究單位以發展活動的性質定理為單位，應用題和練習題的小題為單位。以題幹表徵、題目問句和證實過程三種類型做同一活動版本間和版本內不同活動的對比分析。
在經過兩岸教科書的對比研究後發現：
(1)題幹表徵部分兩個版本都多數以圖形題的形式提供學生幾何證明的機會；
(2)題目問句部分兩個版本在都是以只與主張相關的問題提供學生幾何證明的機會，在此類型中，講解題多數是要求提出命題或判斷其真偽，應用題和練習題多數是要求幾何數學計算，在只與證明相關和與主張+證明相關的表現也不盡相同，康軒版缺少反例的類型。
(3)證實過程類型兩個版本講解題都是演繹性證明比重最高，且在練習題中最低，應用題和練習題是隱含的證明需求比重最高；兩個版本在應用題和練習題大多都缺少操作性證明的類型。


關鍵詞：幾何證明、教科書分析、內容分析法

Abstract
The study is a comparative analysis of the middle school mathematics textbooks providing students geometric proof opportunities. The research object is the geometry part in the middle school mathematics textbooks of is Kang Xuan edition and Ren Jiao edition. The research framework is adapted from the analytic framework made by Otten et al. (2014). This paper analyzes the exposition which explains properties or theorems and the examples which to apply of them in the development , and the exercises completed independently by students in the exercise activity. The research unit takes the properties or theorems of development activities as the unit, and the small problems as unit of the examples and exercises. Contrastive analysis of different activities between and within editions of the same activity is made in three types:statements, questions and the process of the proof .
After a comparative study of textbooks from both sides of the Straits, it is found that:
(1) About statements, both editions provide students with geometric proof opportunities are most illustrated with a figure;
(2) About questions,most questions are mostly only related to claims to provide students with geometric proof opportunities, in this type, exposition mostly requires students to make a statement or determine its value, examples and exercise to calculate with numbers, only to proof and related to claims and proof performance are also different, Kang Xuan edition lacks a counterexample type.
(3) About the process of the proof, the proportion of deductive proof is the highest, and the lowest in the exercise. The proportion of implicit is the highest in examples and exercise; Both versions lack the type of empirical proof in the examples and exercise.

Key words:Geometric proof, textbook analysis, content analysis

第一章 緒論10
第一節 研究背景與動機10
第二節 研究目的與問題13
第三節 名詞解釋13
第四節 研究範圍與限制14
第二章 文獻探討15
第一節 幾何證明的意義及重要性15
第二節 教科書及其研究方法18
第三節 數學教科書幾何證明分析的理論架構20
第四節 數學教科書幾何證明實證研究38
第三章 研究方法40
第一節 研究方法與分析架構40
第二節 研究對象與分析內容44
第三節 研究流程45
第四節 內容分析之類目建構46
第四章 研究結果與討論71
第一節 不同活動類型的幾何證明機會的分析與比較73
第二節 題幹表徵類型的分析與比較75
第三節 題目問句的分析比較85
第四節 證實過程的分析比較117
第五章 結論與建議126
第一節 結論126
第二節 建議131
第三節 反思於不足132
參考文獻133
壹、 中文部分133
貳、西文部分135
附錄141

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