Study On The Prospective Mathematics Teachers’ SMK And PCK On The Derivative

Recently, a growing body of research has shown that teachers’ knowledge and skillsimpact students’classroom experience and their mathematical cognitive outcome. So, whatknowledge prospective teachers should have is becoming a challenging task. This researchuses the method of qualities to study prospective mathematics teachers’ SMK (SubjectMatter Knowledge) and PCK (Pedagogical Content Knowledge) on the derivative. Thewriter expects to provide suggestions for further prospective teachers’education.The paper use Ma’s framework of “profound understanding of fundamentalmathematics (PUFM)”to research prospective teachers’ SMK on the derivative throughsurvey and concept map, and Ball’s framework of PCK in “mathematical knowledge forteaching (MKT)”to research prospective teachers’PCK on the derivative through interview.The conclusions are:(1)Prospective teachers’ inadequacy in SMK can be found in the depth, breadth andthoroughness of their understanding on the derivative. The loss of depth of understandingis means that prospective teachers can’t connect the derivative concept with those ofgreater conceptual power, such as limitation. The loss of breadth of understanding is meansthat prospective teachers have inadequacy in other topics that connect to the derivative.And the loss of thoroughness of understanding is reflected in concept map that draw byprospective teachers.(2)Prospective teachers’ inadequacy in PCK on the derivative can beseen in the following aspects: prospective teachers do not have deep understanding ofteaching materials, they can’t explaining students’misunderstanding precisely, and give theappropriate strategy to solve students’ problem. There also have some unreasonable spotsin their organization of the lesson of derivative concept.(3)The factors that affect thedevelopment of prospective teachers’ PCK are the learning experience in middle schooland college, the experience of being a practice teacher and their SMK on the derivative. The compositions of PCK also affect each other.Finally, some opinions and suggestions have given to prospective teachers andteachers’university according to the conclusions.