| Algebraic formula is an important part of elementary mathematics.Trigonometric function Sum Angle Formula,Difference angle formula,Double angle formula and Half angle formula(abbreviated as TFSDDH)is one of the most important categories of algebraic formulas in high school mathematics.It plays an important role for students in mastering trigonometric identity transformation.Through the investigation and research on the academic achievement of algebra formula learning of senior students in key senior high schools in Y City,and combination with the interview between students and teachers,this thesis attempts to understand the current situation on learning TFSDDH.This thesis makes an in-depth analysis on the problems found in this study,and provides suggestions for the teaching of teachers and formula learning of students in senior high school.The formula academic achievement evaluation model used in this study draws lessons from the existing international large-scale academic evaluation projects,such as PISA,TIMSS and other evaluation projects,and is further improved in combination with the particularity of algebraic formula.The two key questions in this thesis are:(1)How do senior one students master TFSDDH?What is the specific mastery of the three dimensions of understanding,connection and application?(2)What are the learning obstacles and causes of TFSDDH of senior one students?This study discloses four findings:(1)The overall situation of senior high school students learning TFSDDH is general,and only a few students in sampled group have excellent mastery,and only a few students are very weak in learning;(2)In the understanding dimension,the scores that students obtained in each secondary dimension are significantly unbalanced,indicating that the understanding of mathematical formulas of senior high school students needs to be strengthened.For example,approximately one fifth of the students can correctly write down required formula,and moreover the ability of formula derivation is shown to be very weak,and nearly 90%of students do not fully master the cosine formula derivation of sum and difference of two angles;(3)In the connection dimension,the situation of drawing concept map is not optimistic,either,students do not even establish a clear connection between concepts and formulas,which is mainly because they don't understand the hierarchical relationship between concepts;(4)In the application dimension,the overall performance of high school students is better than in the first two dimensions.However,students' mastery of the inverse use of formulas varies greatly and their ability to solve problems related to real life is relatively weak.In the dimension of deformation and use of formulas,their performance in solving problems is unstable.By sorting out and analyzing the errors in the test questionnaire completed by students,it is found that senior one students show five learning obstacles in the learning process of TFSDDH,that is,obstacles in writing and using common formula,obstacles in formula derivation,obstacles in ideological method,obstacles in memory and obstacles in calculation.Through interviews with teachers and students and literature analysis,it is concluded that the causes of students' learning disabilities can be understood as follows.From the viewpoint of students:(1)Mechanically memorization the form of formula;(2)Pay great attention to the application of the formula,but ignore the importance of formula derivation,and students are not familiar with the deformation use of the formula;(3)The consciousness of mathematical application is weak;(4)Not fully understand the concepts and relationship of trigonometric functions;(5)Lack of deep understanding of the problems to be solved,and lack of reflection process after problem-solving.From the viewpoint of teachers,there are three main reasons:firstly,largely adopt the traditional teaching methods and do not fully keep pace with newly emerging methods;secondly,focus on the application of formula but ignore the formula derivation;thirdly,largely ignore the structure of knowledge for students to learn in the process of teaching.To improve the above mentioned problems,this thesis raises the following suggestions:(1)Students should strengthen their understanding of formulas and the internal relationship between formulas,abandon mechanized learning and carry out meaningful learning;(2)Both teachers and students need to pay more attention to formula derivation.Formula derivation is as important as formula application.We should fully understand the value and significance of formula derivation;(3)Teachers should improve the teaching of concept map,make full use of concept map in daily teaching,understand and grasp mathematical concepts from various aspects and levels,such that students can master a complete and systematic knowledge system. |
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