| Mathematics teachers in preparing for lessons need to be clear how to teach, but in understanding of the students’answers and determining the teaching objectives, teachers also need to be clear about subject content knowledge and enhance understanding of-mathematical knowledge.Trigonometric function as a kind of basic elementary functions is a typical teaching in high school.The research takes the trigonometric function as the carrier to survey teachers’ understanding of knowledge.The author surveyed30teachers of East Campus of Yangzhou University Affiliated Middle School and Baipu Middle School and12normal students(with teaching practice as the new teachers) of Yangzhou University.Specific research problems include:(1)How does the teacher deal with trigonometric function;(2)How does the teacher present trigonometric function;(3)How does the teacher help the students correct the mistakes.The author analyzed the survey data,found that:(1)The majority of the teachers have good understanding of trigonometric concepts,they can establish contact between knowledge effectively. Then,The minority of the teachers who are lack of teaching experience just reach the level of problem-solving,they may not establish contact.Also some teachers don’t remember the content and let alone understanding.(2)About image transformation,all the teachers can reach the level of memory and problem-solving.they describe not only the rule of the image transformation but also the key point clearly and accurately.However,only some teachers can establish the contact, construct and rich the link of the knowledge,finally reach relational comprehending.(3)Many teachers have instrumental understanding of induction formula, only a few teachers can also point out the role and nature of induction formula, they pay attention to symbolic-graphic combination in teaching,and aren’t merely content to mechanical memory.(4)Most of the teachers can combine triangle composite function with general composite function. When solving the problems,they can give the solution and the basis.(5)Experience influences the teachers’understanding,but it is not very obvious.Based on the conclusions above, the author proposes some suggestions to promote teachers’ and normal students’ understanding:emphasize teachers’ study to subject content knowledge.carry out the targeted teacher training; attach great importance to basic courses,carry out the research on elementary Mathematics from an Advanced Standpoint,get a deep understanding of the basic knowledge of mathematics.Finally it will help promote the teachers ’professional development effectively. |
