德國六至九年級數學教科書機率單元之內容分析;Content analysis of the probability unit of mathematics textbooks for grades 6 to 9 in Germany

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题名:	德國六至九年級數學教科書機率單元之內容分析;Content analysis of the probability unit of mathematics textbooks for grades 6 to 9 in Germany
作者:	黃雅萱;Huang, Ya-Hsuan
贡献者:	數學系
关键词:	德國數學;機率教科書;量化分析;質性分析;素養;German Mathematics;probability textbook;quantitative analysis;qualitative research;literacy
日期:	2020-07-16
上传时间:	2020-09-02 18:45:00 (UTC+8)
出版者:	國立中央大學
摘要:	本研究針對適用於德國巴伐利亞邦的Lambacher Schweizer數學教科書中六至九年級的機率教材，進行量化和質性分析。其中量化分析採取單維彰、許哲毓與陳斐卿（2018）對於機率學前診測之雙向細目表，質性分析採用張芬芬（2010）提出的五個階段模式。量化分析結果顯示德國六至九年級教科書皆有機率課程，但七年級以統計為主，機率作為連結，因此較少被提及。對於機率教學情境問題的分布種類，在「機率類型」向度上，主觀機率占3%、古典機率占74%、頻率機率占23%；雖然以古典機率占大多數，但不偏廢其他兩類型，且有適當連結。在「機率概念層次」向度上，單一事件占79%、餘事件占4%、獨立性事件占12%、互斥和事件占5%；雖然以單一事件為主要教學內容，但是有適度延伸到其他幾項基礎概念。質性分析結果顯示德國教科書的機率課程編排模式依序為「引入」、「課程內容」、「演練」，其中每一模式所提供的教材編排方法豐富多元。且發現本研究所分析的德國教科書，亦符合鄭章華（2018）依據現實數學教育（2014）所歸納的素養導向教材六大原則。本研究屬於單維彰（2018）「建構下一代國中階段數學課綱：機率新課程」科技部計畫的一個基礎項目。研究結果以及過程中翻譯整理的德國機率單元教材，也可以提供給未來的課綱工作者、教科書編者、自編教材的教師，作為參考資源。 ;This study conducted quantitative analysis and qualitative research of the sixth to ninth grades of the Lambarcher Schweizer series probability textbooks published in the German state of Bayern. Among them, the quantitative analysis adopts Wei-Chang Shann, Che-Yu Hsu, Fei-Ching Chen (2018) for the Two-Way Specification Table of probability pre-school diagnosis, and the qualitative research method adopts the The Five Steps of Qualitative Data Analysis of Chang Fen-Fen (2010) for qualitative research steps. The quantitative analysis found that German textbooks in grades 6 to 9 all have probability courses, but grade 7 is mainly based on statistics, and the probability is used as a link, so it is rarely mentioned. The distribution types of probabilistic teaching situation problems, subjective probability accounts for 3%, classical probability accounts for 74%, and frequentist probability accounts for 23% in the "probability type" dimension, in which the classical probability is the majority. And in the "probability conceptual level" dimension single event accounts for 79%, complementary event accounts for 4%, independence event accounts for 12%, mutually exclusive event accounts for 5%, in which single event accounted for the majority. The qualitative research shows that the probability curriculum layout mode of German textbooks is "introduced", "curriculum content" and "exercise" in sequence, and each of the layout steps provides rich and diverse. Then through the six principles by Chang-Hua Chen (2018) for Realistic Mathematics Education (2014), which is based on " Mathematics in Context ". To illustrate the German probability textbooks as a literacy -oriented teaching material design concept. This study is part of the project of Wei-Chang Shann (2018) " A New Probability Curriculum for the Next National Standards on the Secondary Level", and the provision of probabilistic literacy-oriented textbooks for the 108-curriculum that is just on the road, as a reference resource for future writing of Probability textbooks, curriculum development and teaching on-site teachers.
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