Investigation And Research On The Derivative Knowledge Of Normal School Students From The Perspective

In 2013, the Ministry of Education of the People’s Republic of China issued ’Interim measures for primary and secondary school teachers’ qualification examinations", marked that the normal students’priority for getting a teacher’s qualification had been broken. Do the normal students get ready to compete with the common citizen in the battle of winning a teacher’s qualification? Can the normal students win out from this invisible battle by using their current subject matter knowledge and pedagogical knowledge? By deeply and in detail investigation on the present situation of normal students, we can understand the real situation as the starting point of problem solving, meanwhile, decisions on teaching and education has important reference value.Take this question, the author referred to a lot of literature on the topic of "Teachers’ Knowledge" from China and abroad. Finally, the author chose American Professor Ball and her team’s framework MKT (Mathematical Knowledge for Teaching) which was established in 2008 as the theoretical framework of this study. Compared with PCK and MPCK theory, MKT framework covered the largest extent of the knowledge which was needed for a mathematics teacher. Through the study of the testing system called "Mathematical Knowledge for Teaching (MKT) Measures" which was developed by Ball’s team, the author learned to imitate the designing style for setting problems.In the aspect of the content of the questionnare, the author chose the derivative knowledge, there were two main reasons. First, normal students had learned the derivative knowledge in senior high school, they would do their further derivative knowledge study in the university. Second, derivative knowledge was regarded as one of the fundamental research tool when studying a function, at the same time, derivative knowledge occupied a very important position in high school and college mathematics knowledge system.In the process of the study, the author chose the MKT theoretical framework of the two big dimensions (Subject Matter Knowledge of mathematics, SMK as well as Pedagogical Content Knowledge for mathematics, PCK) with five aspects of general content (Common Content Knowledge, CCK; Specialized Content Knowledge, SCK; knowledge at the mathematical horizon, HCK; Knowledge of Content and Student, KCS; Knowledge of Content and Teaching, KCT), finally compiled the questionnaire named " Investigation of Normal Students’Derivative Knowledge from the MKT perspective" and through two pre-tests and a formal test, the author ensured the reliability of the questionnaire step by step. Based on the results that the questionnaire revealed, the author chose normal students in high, middle and low levels to do further interview in order to check the real situation of the normal students’ derivative knowledge in the perspective of MKT.Questionnaire and interview results show that:1)the normal students forgot derivative subject matter knowledge in different degrees;2) the understandings of derivatie knowledge for normal students were neither deep, nor solid;3) the normal students have a preliminary teaching knowledge of derivative knowledge;4) the normal students’ teaching knowledge for derivative had climbing space; (a. identify the students’ errors’ ability remains to be improved; b. normal students’ KCS need to develop in a deep direction; c. identify students’ speaking ability remains to be training; d. forecast students’ more than a problem solution is insufficient; e. normal students’ ability to design a teaching case is lacking; f. normal students’ reading level is still having rising space.)5) the origins to enhance normal students’ level of derivative MKT were various; (a. experiences of participating normal students’ competition, teaching experience, tutor experience, reading professional books can promote the normal students’ MKT level to some certain extent; b. competition experience for HCK, tutoring experience for KCT, reading books and periodicals for HCK and total score, interaction of attending competitions and teaching experience for HCK, interaction of tutoring experience and reading books for CCK and KCT are significant at 0.05 level; c. in the aspects of SCK, KCS, though the statistical result showed that the competition experience etc. were not promoting the MKT level significantly, normal students with normal students competition experiences, teaching experience, tutoring experience and reading professional books were performing better than the students without those experiences.6) normal students with different levels of derivative MKT had significant differences in subject matter knowledge, but not obvious in the perspective of pedagogical knowledge.Normal students should further solid their derivative subject matter knowledge, enhance their mathematics pedagogical knowledge through various channels, meanwhile, pay more attention to the balance of the five aspects of knowledge within the framework of the MKT. Only by doing that, can the normal students better improve the level of their own professional development, thus, stand out from many competitors.