The Study Of The Causes Of Trigonometric Problem Solving Errors

Mathematics learning cannot be separated from the solution, the solution will appear incorrect solutions, since the error can not be avoided, timely analysis of the causes of errors and correct mistakes, reduce mistakes is particularly important, to positive attitude towards errors, and make good use of the wrong value.Trigonometric function is an important content of high school mathematics knowledge, one of the most basic functions of high school, is also one of the important contents of the high school mathematics, is the basic model of the phenomenon of the periodic phenomenon, is also a function of the mapping of the views of a model.Using the basis of existing research, through the questionnaire survey to understand the understanding of high school mathematics teachers of trigonometric function is important, difficult and error prone points, towards problem solving attitude and improved error means. Based on limited time job wrong topic sorting, error frequency error statistics, the types of classification; for students to concentrate on test papers were collected by, photo finishing papers in the error analysis, classifying and analyzing the types of errors; to participate in the limited time job for student academic level of high, medium and low divided into three categories according to, each level of the extraction of a student to "think aloud" survey, different levels of students in the major cause of the error.Through this study, the following conclusions are obtained:1. main types of triangle functions(1) in any corner of the triangle function definition and induction formula part, the error is more concentrated in the knowledge and strategic error, of course, because of the calculation and the error can not be ignored.(2) in the trigonometric function of the image and the nature of the contents of this section, the solution of the related properties of the composite function become difficult and error prone points, the problem solving strategies and knowledge mistake and become the main type of error.(3) the most common mistakes of the students in this part of the triangle identity transformation are the lack of solving strategies, which leads to the problem of solving problems, and the neglect of the angle of the angle leads to the error of the triangle function, and the lack of accurate strategy guidance.(4) according to the high, middle and low level of students' academic basis, the students of different levels of A, B and C show different types of errors:A levels of the students are more negligent errors, often because of psychological neglect or excessive tension and other factors leading to the occurrence of errors;B level of students is more of a problem solving strategy, the idea of solving the problem can not be quickly and accurately obtained.C language level of the students is more knowledge of error, due to the lack of basic knowledge, leading to new knowledge, the lack of fixation point of knowledge learning, so the students lack of confidence in mathematics learning is the lack of to learn the basic knowledge of mathematics.2. main reasons for the error of the triangle function(1) the understanding is not in place. Can not accurately understand the concept of arbitrary angle; ignore angle range of delta evaluation, angle, or is does not have the mining conditions in the title implied, lack of precise angular range strategy.(2) factors of strategy and method. Can not effectively carry out pattern recognition, thus can not find the correct solution strategy.(3) the lack of a function of the thought of the trigonometric function. The lack of functional thinking makes the problem solving and the use of the combination of several forms, but the learning process, the number and the shape is divided, can not be effectively used to solve the problem of the combination of a number of ideas to study the triangular function and solving problems.(4) the lack of the overall concept of the formation of knowledge networks. For the triangle identity transformation, it is necessary to grasp the intrinsic link of the formula, not only to pay attention to the learning of knowledge group, but also to improve the understanding of the connection between groups.Finally to the high school students' emergence of triangular problem solving, put forward effective suggestions, for the future of the teachers have targeted teaching, students have the direction of learning, better grasp the knowledge of the triangle.