Binomial Theorem In HPM Field Of Vision

Binomial theorem is one of the basic content of algebra, which plays an important role in the history of mathematics; it is the basic content that should be familiar by learners of mathematics. History of Mathematics has an important reference for the education of mathematics, Relations between History and Pedagogy of Mathematics(referred to as "HPM") has become an important research field of mathematics education. The " Mathematics Curriculum Standards of senior High School(Experimental)" also sets up the special topic of "History of Mathematics Selected", and requires mathematics curriculum should reflect the history, applications and development trends of mathematics appropriately. This paper will study teaching of the binomial theorem in perspective of HPM.In this paper, we shall reveal important historical content and the ideological content of binomial theorem by collecting, sorting mathematics historical materials related to the binomial theorem, and analyzes the historical enlightenment to mathematics teaching in high school mathematics. Teaching of binomial theorem is inseparable to combinatorial number. Firstly, we combed the forming process of combinatorial number formula, including the combinatorial number formula in China’s development has carried on the special research. Secondly, we review the development history of the binomial theorem, and focus on the work of Jia Xian, B.Pascal, Isaac Newton and other key figures, analyzing the revelation of mathematical thought in the process of they found the binomial theorem to the teaching of mathematics in middle school. Finally, we proposed four advice to teaching of mathematics education, combined the development of mathematical context and the reality of teaching, designed teaching cases of binomial theorem by reflecting on the teaching of current status of the binomial theorem.The study of this paper will give historical reference of mathematics for math teacher in middle school, provide material of mathematical history. Teachers can combine teaching practice, selecting the appropriate historical data into the teaching of mathematics in order to improve the quality of teaching effectively. The teaching cases based HPM binomial theorem can provide a reference for mathematics teacher to choose a reasonable historical material of mathematics in teaching process, provide a reference for the teaching of binomial theorem.