Freudenthal's Theory Of Mathematics Education In The Application Of Trigonometric Functions

With the development and improvement of the new curriculum reform,teaching materials and content on trigonometric functions are stable and united,which has promoted the teaching and made teachers more adaptable to the contexts.However,there are also some barriers needed to be handled when teachers implement their methods.After going through literature review,I have found some interesting discoveries.In the first place,after the new curriculum reform of trigonometric functions with more to learn,high school students have more difficulty memorizing the teaching materials.Secondly,trigonometric functions learned by senior school students are very different from the knowledge studied by junior ones.Thus they find it not easy to transfer and understand the true nature of the math concept,let alone learning to use them in reality.In order to solve all these problems,we can not simply make up some naive doggerel or just fill the students' brains with equations,but get to the heart of the problem.And to distinguish the differences and links of trigonometric functions gained in senior school and junior school,more explanation is necessary.Some studies based on the principle of students oriented have been made so as to deal with the issues above.In this dissertation,we are going to analyze Freudenthal's mathematics education theory and the existing research results of teaching on trigonometric functions and then make a summary of the history of it.Hence some relative conclusions will be drawn and solutions will be given.The detailed descriptions of this thesis are as follows.Firstly,citing Freudenthal's mathematics education theory as the foundation and with accordance to the given knowledge of the graduates of junior school,I going to offer some teaching tactics on how to guide the high school students to make the transition from ratio method to unit circle definition method and integrate the knowledge of the trigonometric functions.based on the sine and cosine function,for example,inscribed Angle of the triangle function as the breakthrough point and the turning point,we first exam acute Angle trigonometric function in the original cognitive level and under thelateral expansion of acute triangle function difference Angle formula of knowledge points,and then extend the cognitive according to "conflict-looking for a new method of resolving contradictions" by acute Angle trigonometric function longitudinal expansion to arbitrary Angle trigonometric function and at any Angle method defined by the triangle function line explain the unit circle to summarize trigonometric function and the teaching design.And finally we summarize and reflect on the teaching design.