| 摘要: | 本研究之目的為分析臺灣與香港七至十二年級中學數學教科書的機率統計主題，以瞭解兩地區的教材編寫脈絡。研究的方法為內容分析法，其中量化分析分為機率及統計兩部分。機率部分參考單維彰 (2018) 的機率學前診測雙向細目表與許哲毓 (2019) 的《許氏機率II》，擴編成「機率雙向細目統整表」作為本研究機率分析工具;統計部分則參考楊凱琳、李健恆 (2012) 統整的統計認知分析表，視其為「統計知識類型分類表」，作為本研究統計分析工具。在質性描述方面，透過質性內容分析對兩地區教科書及課程綱要進行比較，以瞭解機率統計單元編寫脈絡的異同。
量化分析結果顯示，在機率教學例的「機率類型」向度上，臺灣與香港都以古典機率為主（分別占80%及87%），比例遠高於其他機率類型，且兩地區均未涉及主觀機率的討論;在「機率概念層次」向度上，兩地區都以單一事件為主（分別占50%及58%）。針對統計教學例的分布，臺灣與香港皆以統計知識為大宗（分別佔98%與83%），而香港在統計推理及統計思考的比例共佔整體的17%，臺灣卻只佔2%，這一點值得吾人注意。
在質性描述方面，兩地區在頻率機率、幾何機率、期望值、條件機率與貝氏定理等機率內容，具有教材編排脈絡的差異;而兩地區的統計內容，在國中並無明顯差異，但在高中階段卻有明顯不同。研究者認為臺灣未來在高中統計主題的修訂，能參考香港延伸更多統計應用情境，以臻於學生的統計實用能力。本研究之結果提供未來中學機率與統計課程設計者參考，並期望對中學數學教科書中機率統計單元的教材設計有所助益。
;The purpose of this study is to analyze the subject of Probability and Statistics in the middle school mathematics textbooks of seventh grade to twelfth grade in Taiwan and Hong Kong, so as to understand the context of teaching materials in the two regions. The quantitative analysis is focusing on Probability and Statistics. In the part of Probability, referring to the pre-diagnostic two-way specification table of Probability by Wei-Chang Shann (2018) and “Hsu’s probability II” by Che-Yu Hsu (2019), the “Two-Way Specification of Probability Integrated Table” was expanded to be used as the Probability analysis tool in this study. In the part of Statistics, it refers to the “Statistical Cognition Analysis Table” organized by Kai-Lin Yang and Kin Hang Lei (2012), which is regarded as the “Classification Table of Types of Statistical Knowledge” as the statistical analysis tool of this study. In terms of qualitative description, the textbook and curriculum outline of the two regions were compared through document analysis to understand the similarities and differences in the writing context of Probability and Statistics.
The quantitative analysis results show that in terms of the sample question named “Probability Types” of Probability, the Classical Probability is dominant in Taiwan and Hong Kong (accounting for 80% and 87% respectively), the proportion is much higher than other Probability Types, but the discussion of subjective Probability is not involved in the two regions. In terms of the “Probability Concept Level”, the single events dominate in Taiwan and Hong Kong (accounting for 50% and 58% respectively). In terms of the distribution of Statistical sample questions, Taiwan and Hong Kong both focus on Statistical Knowledge (accounting for 98% and 83% respectively), while the proportion of Statistical Reasoning and Statistical Thinking in Hong Kong accounts for 17% of the whole; however, it only accounts for 2% in Taiwan, indicating that Taiwan still has a lot of teaching content to be added to enrich students’ Statistical literacy ability.
In the aspect of qualitative description, it shows that the two regions have the differences in the content of Frequency Probability, Geometric Probability, Expected Value, Conditional Probability and Bayes’ theorem. However, there is no significant difference in the content of Statistical between the two regions, but there is a significant difference in the senior high school. The researcher believe that someday in the future, the revision of Statistics in senior high school in Taiwan can refer to Hong Kong that will extend more Statistical application situations, so as to improve students’ Statistical literacy ability and make up for the regret of compulsory Statistics in senior high school in Taiwan. The results of this study provide the reference for the course designers of Probability and Statistics in middle schools in the future as well as it is expected to be helpful for the textbook editing of Probability and Statistics unit in middle school mathematics textbooks. |
