High School Trigonometric Function Teaching Research Based On The History Of Mathematics

Under the background of new lesson mark,in order to cultivate the students’ mathematical literacy,mentioned in the mathematics teaching should be combined with the content properly into the history of mathematics,that is to say,the history of mathematics into mathematics classroom teaching is especially important.While the "radian measure" and "trigonometric function" of these two concepts through a long historical development process,many mathematicians in the history of all of them carried on the thorough research,therefore,these two concepts contains a wealth of history of mathematics.However,the contemporary most teachers did not well follow the positioning of "curriculum standard" using the related mathematics history in the teaching of mathematical concepts.In order to response to the new standard,Therefore,this paper mainly studies the teaching of "radian measure" and "trigonometric function of arbitrary angle" based on the history of mathematics.This paper mainly studies from the following aspects:1.The development history of radian measure and trigonometric functionsBy looking for radian measure and trigonometric function related development history,after careful analysis and research,found the radian is background of the system into the system is not unified,so the generation of radian measure is to unify into the system,radian measure unified string length unit arc length and quantity.The quantity analysis of trigonometry related history,can be found that acute angle trigonometric function and arbitrary angle trigonometric function the distinction that having essence,acute angle trigonometric function is a tool for solving triangle;The trigonometric function of any angle is a mathematical model to study the periodic change phenomenon in the real world.It is a periodic function.Therefore,in the teaching,the trigonometric function of arbitrary angle cannot be regarded as the extension of acute angle trigonometric function.2.Textbook analysis of "radian measure" and "trigonometric functions of arbitrary angles"In order to understand how to write the two concepts of "radian measure" and "trigonometric function of arbitrary angle" in the textbooks currently used,the authorselected the textbooks of beijing normal university edition,jiangsu education edition,hunan education edition and renmin education edition for analysis.Whether it reveals the historical background of the emergence of concepts;Whether the history of mathematics is integrated into the compilation of textbooks and in what form;Whether it has effectively implemented the requirement of "integrating mathematics culture into curriculum content" in the curriculum standard.3.Teaching case analysis based on literature and classroom teaching analysis based on front-line teachersIn order to know about the "radian measure" and "arbitrary angle trigonometric function" teaching research present situation,this article will analysis mathematics education workers,published in hownet or uploaded to baidu library of teaching cases,such as sorting out of these two concepts,their teaching methods.Based on this,will use the classroom observation method to understand a glimmer of teachers’ classroom teaching is how to expand the teaching for these two concepts.After analysis,found in these two concepts exist certain problems in the teaching,especially not well reveal the historical background and concepts in mathematics essence,failed to reflect the necessity of the concept is introduced.4.Teaching design of "radian measure" and "trigonometric function of arbitrary angle" based on the history of mathematicsBased on the research of radian measure and trigonometry history,aiming at the problems existing in teaching materials and teaching,the teaching design of "radian measure" and "trigonometric function of arbitrary angle" based on the history of mathematics is designed according to the positioning of curriculum standard and HPM theory.