數學教育裡，機率課程占了重要的一席之地，在我國九年一貫課程綱要中，機率課程一直都是被安排在九年級下學期，但機率問題遍佈於日常生活中，且在數學教育裡扮演著非常重要的角色，九年級才學習顯得太晚，研究者希望探究提前學習機率的可能性，使其自發性的概念與生活及學習作更完整的連結，以貫徹數學作為一種語言的真正意涵。
本研究先探究七年級學生在未接受正式機率課程之前，機率自發性概念的狀況，發現已形成直觀地機率概念。但因為操作機率所需之比例計算在七年級才完備，所以本研究藉由機率課程教學活動，探究機率課程在八年級的學習成效。因此欲探討：1 )透過國中機率教學，八年級學生是否有能力可學習國中機率課程？2 )若使用樹狀圖作為機率教學的唯一方法，機率學習成效是否提升？3 )透過機率教學後，八年級與九年級的學習成效差異為何？
本研究之田野學校共有四所國中約三百五十名學生，且分為兩大部分，分別施以「機率學前診測」及國中機率後測與延後測。研究工具分為四部分，分別為機率學前診測、國中機率教學教案、國中機率後測以及國中機率延後測。研究方法使用獨立與成對樣本t檢定及單變異數分析（ANOVA），用來分析各項測驗的分數顯著性，及探討各試題的答對率。
根據研究結果顯示，第一，學生在尚未學習國中機率的課程之前，其實已具備一定的主觀機率與古典機率概念。第二，依照國民中小學九年一貫課程綱要教學，八、九年級學習機率課程之學習成效無差別。第三，八年級學生經過樹狀圖教學後，其機率學習有達到成效。最後再根據研究結果於未來機率課程提出若干建議。

In mathematics education,the probability course takes an important place. In our national syllabus of Grade 1-9 Curriculum Guidelines, probability courses have always been scheduled for the second semester of the ninth grade. But the problems of probability is everywhere in daily life, and they play a very important role in mathematics education. It’s too late to study in the ninth grade, and researchers hope to explore the possibility of learning ahead. We also wish to make the concept of spontaneity more complete with life and learning, and to show the true meaning of implementing mathematics as a language.

This study first explores the situation of the seventh grade students' chances of spontaneous conception before they have accepted the formal probability course. We found that the concept of intuitive probability has been formed. However, because the skills of proportion required for the probability of operation is not completed in the seventh grade, this study explores the effectiveness of the expedition course in the eighth grade by experimental teaching activities.Therefore, the three research questions are: 1) Through the probabilistic course teaching, do eighth grade students have the ability to learn the national probability course? 2) If the tree diagram is used as the only method of probability teaching, is the probability learning effect improved? 3) What is the difference in learning outcomes between the eighth grade and the ninth grade after the probability teaching?
The samples of this study has about 350 students from four schools and are investigated by three tests, namely, "Pre-experience Diagnosis of Probability" and posttest and retentive test of the probability. The research tools are divided into four parts, which are pre-experience diagnosis of probability, teaching plan of probability, posttest and retentive test of the probability. The study used independent and paired sample t-tests and single-variant analysis (ANOVA) to analyze the significance of the scores of each test and to explore the correct answer rate for each test.

According to the research results, first, students have a certain concept of subjective probability and classical probability before they have taken the course of the probability. Second, according to the Grade 1-9 Curriculum Guidelines of the national primary and secondary schools, there is no difference in the learning outcomes of the eighth and nineth grade students on probability materials. Third, after the eighth grade students have experienced the tree diagram teaching, their probability learning has achieved results. Finally, basing on the research results, some suggestions are made in the future probability course.

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