Research On Teaching And Learning Of Probability And Statistics In Taiwan's Senior High School

Since the year nineteen eighty, probability and statistics has become the most theoretically-rich branch of researches in mathematics education, the research of teaching and learning in this subject from the western scholars has become a popular question. In studying of students' cognition to probability and statistics, both psychologists and mathematical educators focus on the wrong conception and reasoning of it.The purpose of this dissertation is threefold. First, it is to investigate the preknowledge and misconceptions held by Taiwanese high school students before they learn probability and statistics; second, it is to determine whether equiprobability bias exists among students even after the instruction of classical probability; third, through practical teaching experience, the dissertation tries to devise appropriate teaching strategies for high school students. These purposes where accomplished using the assessment of probability and statistics developed by researcher.Using both quantitative analysis and qualitative research, this study aims to answer the following three questions:1. What prekonwledge of probability and statistics do Taiwanese students possess, and what can be done to aid them in their learning of this subject ? The result of this study shows that, most of the high school students still have false comprehension in the Law of Large Numbers before learning classical probability, they think that as the number of trial times goes bigger, the chance of that the appear number of times equals to the expected average number also goes higher. After cognitive conflict teaching, students make quite a remarkable progress in the understanding of this law and overcomes representativeness bias they hold beforehand.2. Do Taiwanese students misuse Laplace's definition of probability even after learning classical probability ? Why is it required to treat identical objects as different in the calculation of classical probability ? The result of this study finds that, after learning classical probability about SOX students misuse probability definition, therefore they have equiprobability bias. For this kind of mistake, using generic example as scaffolding and through a series of cognitive conflict, it results in that the number of students who can reach to the level four of understanding increased from 29.4% to 45.8% .3. What differences exist between the probability and statistics curriculum of Taiwan and that of other countries ? What teaching strategies may be derivedfrom the testing results of this study, so that student may learn this subject more effectively ? The result of this study indicates that, there is an obvious difference in the constitution of probability and statistics curriculum of Taiwan and western countries. Probability problem grounding on permutation and combination become vexed and difficult, its content also relatively emphasizes on calculation and ignores application, thus the students' reasoning ability in this subject are generally poor. Although through short-term teaching experiment, there is no distinct difference in the increasing of this ability between experimental group and contrasting group.In the process of this research, a teaching experiment was applied to parts of participating students. The main object is to investigate how to rid students of their previous misconceptions, and to raise levels of understanding for probability and statistics. After the above teaching experiment was carry out for two weeks, the experimental group's levels of understanding is much better than the contrasting group. Thus, applying the most suitable method of teaching is indeed helpful to enhance students' comprehensibility on probability and statistics.Finally, based on the conclusions and discoveries found in this study, a suggestion is advanced for Taiwan's present teaching materials on probability and statistics, hoping that it can offer advice for all the high school mathematics teachers and curriculum developers. For the limit of study condition and time, some related problems on teaching and learning of probability and statistics for high school students still needs further research and inquiry in the future.