國中機率課程：設計與實驗;Probability Curriculum for the Junior Level: Design and Practice

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題名:	國中機率課程：設計與實驗;Probability Curriculum for the Junior Level: Design and Practice
作者:	許哲毓;Hsu, Che-Yu
貢獻者:	學習與教學研究所
關鍵詞:	主觀機率;頻率機率;古典機率;樹狀圖;獨立性;概念詮釋結構模式;subjective probability;frequency probability;classical probability;tree diagram;independence;interpretive structural modeling
日期:	2020-07-28
上傳時間:	2020-09-02 18:53:57 (UTC+8)
出版者:	國立中央大學
摘要:	過去十多年，臺灣國中階段機率課程內容顯得較為獨尊「古典機率」而缺乏豐富度，學習時程亦較同儕國家的國民教育階段為晚，故本研究提議為此階段設計新式機率課程內容。研究團隊將自編教材《許氏機率I》和《許氏機率II》並進行教學實驗，實徵檢驗學生的學習成效與新課程之適切性。本研究為自身檢驗之兩年期縱貫研究，國中階段學生接受前述兩份機率教材的實驗教學，從八年級延續至九年級，並分別施以學習成效測驗與延宕測驗。研究證實我國八、九年級學生可理解主觀、古典與頻率機率之觀點，並處理進階機率概念之問題，如獨立性。研究亦發現藉由樹狀之結構，學生可由圖像理解、使用同階層樹枝上的機率相加、不同階層路徑樹枝上的機率相乘之運算規則。此外，本研究並從機率概念構圖中，發現樹狀圖與獨立性是學習進階機率之基礎。不過，從學生的作答文本中，本研究發現樹狀結構的學習，可能有兩項錯誤類型。（1）機率值誤植與運算規則之混淆：學生在解讀題意時，未能聯結文字語意與機率間的關係，導致機率值誤植，以及加法、乘法算則時之誤用。（2）無法繪製多組獨立、成對樣本的樹狀圖：學生對於辨識、歸類多組獨立、成對樣本產生困難，導致無法繪製正確圖形。最後，本研究建議我國國中階段之數學課程設計，可調整機率內容。在教材設計上，多以「生活經驗」連結機率概念，設計不同情境之例題。在教法設計上，可一致利用樹狀圖建立概念並發展算法。在教學活動的設計上，宜讓學生有口語詮釋機率概念的練習，提升學生機率思考。本研究設計的兩份實驗教材，可作為前述課程設計的初步參照；此教材亦為機率概念與圖形思維之連結、機率迷思概念之預防，提出一份基本的設計方案。;Over the decades, the probability curriculum at junior high stage in Taiwan has been characterized exclusively by "classical probability" which misses the richness of probability concepts. Comparing with the national curricular plan of peer countries, the introduction of probability in Taiwan is scheduled relatively late. Therefore, this research proposes to design a new probability course for the secondary stage. The research team will compile textbooks "Hsu′s probability I" and " Hsu ′s probability II" and conduct teaching experiments, so as to test the students′ learning effectiveness and suitability of the new course. This study is a two-year longitudinal study justified by self-examinations. Junior high school students received experimental teaching according to the forementioned texts from grade 8th to grade 9th, followed by a performance test and a delay test. The results verified that students in grades 8th and 9th can understand the subjective, classical, and frequency probabilistic viewpoints. They can also deal with advanced probabilistic concepts such as independent events. The research also found that with the tree diagram, students can understand and use the principles of adding branches at the same level and multiplying branches on a path of different levels from the tree diagram. In addition, from interpretive structural modeling, it can be seen that tree diagram and independence are the basis for learning advanced concepts in probability. However, from the students′ texts, this study found that students learning tree diagrams might have two types of difficulties. (1) The confusion between probability value misplacement and operational rules: Students fail to connect the relationship between literal meaning and probability when interpreting the meaning of the question, resulting in probability value misplacement and misuse of addition and multiplication principles. (2) Graph-text conversion of drawing multiple independent and paired sample tree diagrams: Students have difficulties in identifying and classifying multiple independent and paired samples, resulting in the inability to draw correct tree diagrams. Finally, this study suggests that the curriculum design of junior high school mathematics can be adjusted to include probability content. In the design of teaching materials, the concept of "daily experience" is often used to link the concept of probability and design examples of different situations. In the design of teaching method, the concept of tree diagram can be established and the algorithm can be developed consistently. In the design of teaching activities, it is advisable to allow students to practice oral interpretation of the probability concepts, so as to improve students′ probability of thinking. The experimental texts designed for this study also proposes a basic design plan for the connection between the concept of probability and graphical thinking, and the prevention of the misconceptions of probability.
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