Study On Representation Of Pedagogical Content Knowledge Construction Of Primary School Mathematics Teachers

Pedagogical Content Knowledge was issued by Shulman in annual conference speech of American Education Research Association in 1985. Since 80 s of 20 th century, Pedagogical Content Knowledge has been an important concept in research and there are various teachers’ Pedagogical Content Knowledge modes like integrated knowledge, skills, understanding, teaching skills, all of which elaborate fully the importance of Pedagogical Content Knowledge as the basis of teaching knowledge. As shown in studies, Pedagogical Content Knowledge as a complicated concept includes many elements. In spite of the fact that many scholars are engaged in Pedagogical Content Knowledge research, their understanding on Pedagogical Content Knowledge development is limited. Very little is empirical research on certain teaching content, deepening into subjects, and discussion of intension included in Pedagogical Content Knowledge elements, how elements are related and influence each other. As Pedagogical Content Knowledge has become the core of teacher knowledge research and is seen in documents of education reforms, it has become a guidance kept in developing teacher education modes. The present study explores elements, types and sources of Pedagogical Content Knowledge construction of primary school mathematics teachers from the angle of Pedagogical Content Knowledge construction, and provides implications for pre-service and in-service mathematics teacher training and development.The present study aims to clarify elements, types and sources of Pedagogical Content Knowledge construction of primary school mathematics teachers. It based on the teaching deduction and action mode by Shulman, discusses the core content of primary school mathematics—number operation. The study combines both qualitative and quantitative research with emphasis on the former. The study employs instrumental case study to explore and prove elements of Pedagogical Content Knowledge construction of primary school mathematics teachers through analysis of two experienced primary school mathematics teachers. The analysis result contributes to questionnaire design. The questionnaire surveys 60 experienced and 60 new teachers. Some of the teachers are interviewed. The researcher analyzes the types and sources of Pedagogical Content Knowledge construction representation of experienced and new teachers, and as well provides implications and suggestions for in-service and pre-service teacher education. The findings of research are:There are 2 aspects and 3 dimensions in elements of Pedagogical Content Knowledge construction representation of primary school mathematics teachers. One aspect is understanding, including two dimensions: understanding the nature of teaching content, of students learning. Another aspect is representation, which is the usage of teaching representation. Teachers’ understanding on content nature and students learning influence their teaching representation to some degree.It’s found that experienced teachers’ nature understanding focuses on 3 horizontal types: Property-Proof Understanding, Use-Application Understanding, Representation-Metaphor Understanding. There are differences between experienced teachers in their understanding. New teachers’ understanding distributes to 4 horizontal types, with focus on Skill-Algorithm Understanding and Property-Proof Understanding. Two kinds of teachers both lack Use-Application Understanding dimension. As for understanding on students learning, experienced teachers focus on types of partial accuracy analysis and full accuracy analysis. New teachers focus on zero analysis and fuzzy analysis. As for usage of teaching representation, experienced teachers more focus on multi related representation and translation extend representation, while new teachers more on single representation and multi unrelated representation.There are 4 types in Pedagogical Content Knowledge construction through cluster analysis. They are Excellence, experience, lack, and singleness type. There are obvious differences in representation types of two kinds of teachers. Experienced teachers are more excellence, Experience types and new teachers more lack type. Representation types of different themes in two kinds of teacher are also different. Representation type of experienced teachers is related to their year of teaching, and that of new teachers is related to their teaching experience and education degree.Questionnaire on two kinds of teachers’ evaluation on Pedagogical Content Knowledge sources finds that there are similarities and differences in their sources of Pedagogical Content Knowledge construction. They both believe the important sources are their teaching experience, text book, curriculum standards, and analysis targeted at students.The last finding is that Pedagogical Content Knowledge construction is a series of process with complicity, but not a single direction. The three elements of nature understanding of content, students learning and usage of teaching representation are like knit of three laves in topology. They will not change relation due to our classification. The basis for Pedagogical Content Knowledge construction has been internalized, under with context, only complex analysis can disclose original elements. That is the reason why these elements are complicated and related like knit of three leaves in practice.Teachers’ pedagogy conception affects his teaching always. The hidden nature of conception is teacher’s organizational construction of concrete teaching materials like an invisible hand. It composes teachers’ methods in dealing with teaching task and functions as a basis in teacher thinking and practice.