Probabilistic Teaching Research From The Perspective Of HPM

The birth of probability is regarded as a mathematical achievements which is an epoch-making product. Since the 21 st century, probability teaching has entered a new time, and the probability is introduced into the high school mathematics course in the countries of the world. In China,the ministry of education promulgated "the ordinary high school mathematics curriculum standard(experiment)" in 2003.The probability is included in the curriculum standard as one of the elective course.HPM mainly studies how to promote education of mathematics in the mathematical history, which is the main component of mathematics education research. The current mathematics education researchers are aware of the importance of history of mathematics in mathematics education. Not only it can promote students’ classroom learning efficiency, but also can increase the students’ mathematics history and mathematics cultural knowledge, which is the effective practice of the new curriculum standard.In this paper, based on the theory of HPM, I will probe into the history of mathematics teaching design of the probability in the high school. First of all,I analyzes the historical development of probability, the brewing period of nearly half a century that from Jacob Bernoulli(1654-1705) created probability to 18 th century mathematicians until Andrey Nikolaevich Kolmogorov(1903-1987) and others who committed to the development of process that probability to strict. Secondly,according to the investigation and study, I design two teaching cases for the concept of probability and implement in the classroom. Then I analysis the result of the implementation. Last but not least, I investigated two groups students, who are the grade one students in high school. Through this investigation, I studied that whether the design of the course under the new curriculum standard is good for the students to understand the idea of probability deeply. To understand the problem of teachers in the teaching of probability content and how to design reasonable teaching cases, I also interviewed the teachers who come from the high school.