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？
;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.