Teaching Research Of Probability In The New Mathematics Curriculum Of Senior High School Based On Historical-genetic-principle

It gets support from more and more educational experts and teachers that the history of mathematics is great valuable to mathematics teaching, and the Historical-genetic-principle (HGP.) which the scholars will follow the same way as their ancestors at a certain extent is also used for guiding schooling. While making a comprehensive study of the scarce researches on probability teaching, few people thought over the current probability teaching from the history perspective. Nowadays, the latest curriculum reform attaches considerable importance to the knowledge of probability, and gives probability teaching in senior high school many new chances as well as requests. Accordingly, how to teach probability through an effective way comes to be a disquisition with the worthiness both in theoretic and realistic.Based on a nice bit of literature review about HGP., the further understanding is brought up from the longitudinal and horizontal aspects: on the one hand, the cognitive development of students is similar to the historical evolution of mathematical concepts in the longitudinal aspect, corresponding to the genetic development theory from psychology; and that on the other hand, the same thinking methods may emerge as the ancestors by the students, and some similar cognitive obstacles are also possessed. And then using the resemblance way, from the longitudinal and horizontal aspects, the thesis reviews the historical facts about probability, settles the development skeleton by the timetable, and discusses some details about the probability as well.After those aforementioned working, three nonrestraint tractate questionnaires were conducted to senior high school students on the understanding of probability, and the final questionnaire was confirmed after the trail-test. Three topics are chosen for case study: the definition of probability, the solution of the problem of points, the order of probability and statistics which the students confirmed by themselves with some difficulties engendered hereby. Then the survey was conducted to 241 senior high school students in grade 2 from six different classes, which belong to three high schools in different levels in order to comprehend their cognitive development on probability, and that much more ideas were gathered by interviewing with the students. Then the outcomes of the survey were compared with the history of probability, which proved that the cognitive development of students on probability notion and solution are similar to the historical evolution forsooth, and the hypothesis that the HGP. is tenable.Depending on the theory which proved hereinbefore, the thesis starts to do some instruction attempt, still from the longitudinal and horizontal aspects: reflects on the rationality of the new course standard of math for senior high school and several new edition textbooks from the HGP. perspective, gives an overall arrangement to the probability teaching in the senior high school, brings forward some teaching conceptions, and chooses a segment, respectively from the required course and elective course, to do some teaching designing with more particular, shows the different methods in using the different types of historical material.In the end, we summarize the research process, abstract the course for theory applying that named three phases with five tasks mode, and make the teaching appliance of the theory that the HGP. to generalize. At the same time, four more suggestions are given about the instruction of the theory as follow: 1 .taking the history as a guide as well as the logicality; 2. using the history as stuff combine with the actuality; 3. syncretising the historical fact but not stacking; 4. eying on the entire knowledge but not the single section.