Research On The Status Quo Of High School Mathematics Teachers SMK And PCK

Teachers' knowledge has become an important symbol of teacher specialization,among which subject matter knowledge and pedagogical content knowledge are the core of teachers' knowledge.Many scholars at home and abroad have carried out a lot of in-depth research on the subject teaching knowledge,but the current situation of teachers' knowledge is not studied much in combination with specific knowledge points.Derivative is one of the most important concepts in mathematics,and it plays an increasingly important role in the college entrance examination.It links well with the knowledge of secondary mathematics and higher mathematics,and embodies the beauty of local linear form of function.It is an important tool for studying elementary functions.Taking derivative as an example,this paper makes an empirical study on the current situation of derivative SMK and PCK of senior middle school mathematics teachers.Through questionnaire survey and data analysis,this paper has understood the current situation of derivative SMK and PCK level of senior high school mathematics teachers,analyzed the factors that affect the knowledge level of derivative,combined with the questionnaire survey and the interview investigation,Understand the derivative knowledge that deserves attention in the teaching process.In view of the research in this paper,the main conclusions are summarized as follows:(1)Before becoming a teacher,more than half of the teachers thought that the knowledge of calculus in college mathematics analysis played a very important role in the understanding of derivative knowledge in senior high school;after becoming a teacher,more than half of the teachers thought that the knowledge of calculus played a very important role in the understanding of derivative knowledge in senior high school.The four most important derivative knowledge sources for teachers are their own teaching experience and reflection,daily communication with colleagues,case study and reading professional books.(2)Regarding the subject matter knowledge of derivative,most teachers have a good understanding of derivative limit form,but more than half of them still lack the ability of image discrimination and image representation.Some teachers have a vague understanding of the concept of function derivation in higher mathematics,which is limited to the definition of derivative in high school mathematics,and some teachers have a vague understanding of the relationship between derivable and continuous.Moreover,most teachers have forgotten the academic derivative knowledge,and lack of a higher perspective to examine the derivative knowledge.(3)On the pedagogical content knowledge of derivative,most teachers are familiar with the difficulties and mistakes that students may make in learning derivative,and can give the corresponding analysis to the mistakes that appear,and give the breakthrough strategies to the difficulties students face.Some teachers can realize that derivative can not be regarded as a rule or procedure,teaching should be combined with specific teaching content,pay attention to let students understand ideas and methods.(4)There was no significant difference in teachers' derivative knowledge in different age groups,but there was significant difference in derivative teaching knowledge among teachers of different ages.Whether there is teaching experience in grade three or not and whether there is a subject competition has a significant influence on the teachers' derivative knowledge of subject content and subject teaching knowledge.(5)Generally speaking,the average knowledge level of derivative of teachers is not optimistic,and the score rate of derivative SMK is significantly higher than that of derivative PCK.