The Influence Of Mathematics Teacher Knowledge On His Teaching Design

Teachers have an important role in the educational cause of a country.Teachers’ knowledge is the solid foundation for fulfilling the duty of "educating people".From the definition of the connotation of teachers’ specialization,we can see the importance of teachers’ knowledge to teachers’ profession.To achieve the goal of cultivating "mathematics literacy" in a new round of mathematics curriculum reform,mathematics teachers’ professional knowledge also has an important role,as one of the elements of their professional quality.As teachers’ knowledge has a profound influence on their teaching.This research takes the "basic inequality" as an example,to explore the impact of mathematics teachers’ knowledge on their teaching design,and provides suggestions to improve their level of knowledge,based on the investigation of normal students and teachers’ MKT of "basic inequality".After referring to the relevant literature,the author chose the theory of "Mathematical Knowledge for Teaching(MKT)"as the theoretical basis of questionnaire,which is advanced by Ball and her teammates.The survey selects the grade 2013 students,studying Mathematics and Applied Mathematics(normal)in School of Mathematical Sciences of Yangzhou University,and the teachers in Jiangsu province middle school mathematics teachers training class organized by School of Mathematical Sciences of Yangzhou University in 2015 and 2016 as the object of the investigation to know their MKT of "basic inequality".Then the author selects a novice teacher with just two or three years of working and an experienced teacher with over 20 years teaching experience as the object of a case study to explore the influence of mathematics teachers’ knowledge on their instructional design.Concretely,the author investigates the two teachers’ MKT of "basic inequality",analyzes their teaching design of "Proof of basic inequality"(first class)from the introducing of the formula,formula proof and the examples explaination.The questionnaire results of normal students and mathematics teachers show that:(1)the mastery of the basic inequality’s subject content knowledge(SMK)of normal students is weak.They have problems on the proof of inequality and the basic knowledge of proving basic inequality.They are also in the lack of specialized content knowledge(SCK).(2)the normal students have a preliminary grasp of basic inequality’s PCK.Although they have learned pedagogy,psychology courses,their analysis of basic inequality’s teaching and understanding of the difficulties and possible causes in the process of students’ learning basic inequality seems to be mostly based on their learning experience,which may be due to their lack of teaching experience.They are not familiar with the relevant content in the textbook and have a poor knowing of materials of introducing the basic inequality.(3)the mathematics teachers’ mastery of SMK can still be improved.Although mathematical knowledge needed to teach inequality proof,basic inequality’s proof is not a problem for them,their grasp of the relationship between basic inequality and other mathematical knowledge is obviously weak,which is to say,the connectivity of their mathematical cognitive structure is not perfect.As for their SCK,although it is enough to make their teaching smoothly,the neglect of the essence of mathematics knowledge in the examination environment makes the corresponding part of their knowledge become weak.(4)teachers’ mastery of PCK needs to be improved.The long-term teaching experience makes them familiar with this part of teaching,students’ problems in learning basic inequality and the reasons.Teachers can also give the corresponding teaching measures to solve the problems,but the neglect of the essence of mathematics knowledge in practical teaching under an exam oriented environment leads to their mastery of some knowledge’s weakness.They also lack the necessary thinking and understanding of some problems in teaching and have relatively simple materials of introducing teaching.Through a case study of a novice math teacher and an experienced math teacher,the author finds that:mathematics teachers’ knowledge affects their choice of teaching content in teaching design;mathematics teachers’ knowledge level affects the quality of handling teaching content in the teaching design;mathematics teachers’ knowledge influences their teaching measures in their instructional design.Therefore,the author gives some suggestions based on the investigation of the normal students and teachers’ MKT on the basic inequality.Firstly,in the process of cultivating normal students,we should pay attention to their grasp of elementary mathematics knowledge system by setting relevant curriculum and promoting their self-reflection and compensation on mathematical knowledge.Secondly,to increase the proportion of teaching practice in the course of mathematics normal students by learning from the"U-S teacher education community" approach and setting the establishment of university contact with local schools.Thirdly,mathematics teachers should pay more attention to improving the mastery of the knowledge system of mathematics,maintain a continuous learning attitude of the new educational theory,constantly update their own teaching philosophy,and actively carry out self-reflection and peer exchanges,etc..Fourthly,the teachers’ professional development department should develop practical training programs for teachers on the basis of in-depth understanding of the actual situation.