| 摘要: | 本論文通過分析比較中國大陸某一版本初、高中數學教材（簡稱中版）與臺灣國中、高中各一版本（簡稱臺版）數學教材之平面幾何與坐標幾何的內容，嘗試找出中學階段兩地教材的異同以及各自的特點，以期為兩地教材的編寫和使用提供彼此參考與借鑒的機會。（中國大陸與臺灣簡稱兩地。）
本研究主要應用文獻研究法、內容分析法及比較研究法，探討中版與臺版平面幾何與坐標幾何內容之編排順序、單元數、頁數、布題數和教學活動數、布題認知需求層次、概念引入方式，以及定理證明方法之差異。此外，並整理未完全對應的章節，也特別討論函數與圖形知識結構上的銜接之情形。
通過比對研究，本論文有以下幾點發現。
其一，在編排順序方面，中版章節間知識編排較為分散，臺版章節間知識編排較為集中。且章節編排順序的不同將導致同一性質、公式之證明方法的不同。
其二，在教材比重方面，在初中階段，中版的相關單元數和頁數之分布比例、相關內容的教學活動數，以及總教學活動數，都比臺版高，而平均每頁布題數則兩者相差不多。在高中階段，兩版相關單元數和頁數之分布比例相差不多，臺版的平均每頁布題數比中版多，中版的相關內容教學活動數、總教學活動數，以及相關分布比例均比臺版多。
其三，在布題認知需求層次方面，兩版教材之布題皆集中在特定題型：不論從整體還是大部分內容類目來看，都集中在無聯繫的程序性問題。
其四，針對本論文研究範圍內的課題，造成兩版教材之章節未完全對應的原因是：知識點之設立與否不影響課程結構，或者相關知識點被安排於教材敘述或例題中，並未設立獨立的章節。
其五，在概念引入的方式上，兩版教材對同一概念的定義敘述大致相同，但對同一概念的引入方式還是區別較大的。其中中版多以數學問題和溫故知新的方式引入，臺版則多直接引入概念。
其六，在定理證明方面，定義的敘述不同和章節編排順序不同，都會導致章節內的性質、判定和公式的證明方法不同。
其七，在函數與圖形知識結構的銜接方面，中版教材於「一次函數與直線知識結構的銜接性」相較於臺版略感不足，而兩版教材於「二次函數與拋物線知識結構上的銜接性」則各有千秋。
最後，基於兩版教材的差異和各自的特點，可以相互參考借鑒的建議如下。
1.中版教材可借鑒的做法：增強數學知識內在的完整性；增加例題量，注重知識形成的過程性；增加有聯繫的程序性問題和做數學的問題的習題設置，提高認知需求層次；注重幾何圖形的直觀性；重視資訊技術與教材的融合，培養學生的探究精神和實踐能力；優化初高中數學教材知識結構銜接。
2.臺版教材可借鑒的做法：增加例習題情景化設置，提高學生解決實際問題的能力；增加教學活動數，提高學生的動手操作能力；增加有聯繫的程序性問題和做數學的問題的習題設置，提高認知需求層次。;This thesis analyzes and compares the areas of plane geometry and plane analytic geometry in junior and high school mathematics textbooks from one publisher of Mainland China (hereinafter referred to as the China edition) and two publishers of Taiwan (Chinese Taipei, hereinafter referred to as the Taiwan edition). Find out the similarities and differences of the textbooks in both editions, and find out their respective advantages and disadvantages, in order to provide reference and reference for the compilation and use of the textbooks in the two places.
This research mainly uses literature research method, content analysis method and comparative research method to explore the differences between Chinese edition and Taiwanese edition in the contents of plane geometry and coordinate geometry in terms of arrangement order, number of units, number of pages, number of topics and teaching activities, level of cognitive needs of topics, concept introduction method, and method of theorem proof. In addition, the chapters that are not completely corresponding are sorted out, and the connection between the function and the figure knowledge structure is also discussed.
Through comparative research, this paper has the following findings.
First, in terms of arrangement order, knowledge arrangement between Chinese edition chapters is more scattered, while knowledge arrangement between Taiwan edition chapters is more concentrated. The different order of chapter arrangement will lead to different proof methods of the same property and formula.
Second, in terms of the proportion of textbooks, in the junior high school stage, the distribution ratio of relevant units and pages, the number of teaching activities related to the content and the total number of teaching activities in the Chinese edition are higher than those of the Taiwan edition, while the average number of questions per page is similar. In the high school stage, the distribution ratios of relevant units and pages in the two editions are similar. The average number of questions per page in the Taiwan edition is more than that in the Chinese edition, and the number of related content teaching activities, total teaching activities and related distribution ratio in the Chinese edition are more than that in the Taiwan edition.
Thirdly, in terms of the level of cognitive needs for the distributing questions, the distributing questions of the two editions of the textbooks are all concentrated on specific question types: regardless of the overall content or most of the content categories, they are concentrated on unrelated procedural problems.
Fourthly, the reason why the chapters of the two editions of the textbooks are not completely corresponding to the topics within the scope of this thesis are: the establishment of knowledge points does not affect the course structure, or the relevant knowledge points are arranged in the textbook narrative or sample questions, and there is no independent chapter.
Fifth, in terms of the way of concept introduction, the two editions of textbooks have roughly the same definitions and descriptions of the same concept, but the ways of introducing the same concept are still quite different. Among them, the Chinese edition mostly introduces in the way of mathematical problems and reviewing old knowledge, while Taiwan edition mostly introduces directly.
Sixth, in terms of theorem proving, the different descriptions of the definition and the different order of chapters will lead to different methods of proving the properties, judgments, and formulas in the chapters.
Seventh, in terms of the connection between the function and the figure knowledge structure, compared with Taiwan edition, the Chinese edition of "the connection between linear function and linear knowledge structure" is slightly insufficient, while the two editions of "the connection between quadratic function and parabola knowledge structure" have their own strengths.
Finally, based on the differences and characteristics of the two editions of textbooks, the suggestions for mutual reference are as follows.
1．The Chinese textbooks can be used for reference: To enhance the inherent integrity of mathematical knowledge; increasing the number of examples and focus on the process of knowledge formation; increasing the set of related procedural problems and mathematical problems to improve the level of cognitive needs; paying attention to the intuitiveness of geometric figures; paying attention to the integration of information technology and textbooks, cultivate students′ inquiry spirit and practical ability; Optimizing the knowledge structure connection of mathematics textbooks in junior and high schools.
2．Taiwan edition of the textbook can be used for reference: Increasing the situational setting of example exercises to improve students′ ability to solve practical problems; increasing the number of teaching activities to improve students′ operational ability; increasing the set of exercises related procedural problems and mathematical problems to improve the level of cognitive needs. |
