A Comparative Study On The Inadequacy Of Professional Knowledge Of Elementary Mathematics Teachers In Shanghai And Hong Kong

This research is a comparative study to explore the similarities, differences and the inadequacy of the professional knowledge of elementary teachers in Shanghai and Hong Kong - the two cities in China under the influence of Confucian heritage culture. It helps to enhance mathematics educators the understanding of the professional knowledge of oriental mathematics teachers and to provide evidence and suggestions for reflection and further development in mathematics education.The research question is, "what are the similarities, differences and the inadequacy of the professional knowledge of elementary teachers in Shanghai and Hong Kong?" The research adopted a qualitative approach, designed in two dimensions, namely, "mathematics content" and "teacher professional knowledge". The former one covered three areas of mathematics content, including geometry, algebra, data handling, and one inquiry problem related to arithmetic and geometry. The latter one covered two categories of teacher professional knowledge, namely, subject knowledge and pedagogical content knowledge. Semi-structured interviews were conducted to 12 elementary mathematics teachers from each city. Evidence of illustration in drawing and written form was also collected. The six hypothetical scenarios covered three areas of mathematics content and two categories of teacher professional knowledge in a form of matrix. Data were analyzed by the correctness of the mathematics knowledge and by categorization to form lists of the similarities, differences and inadequacy of professional knowledge of elementary mathematics teachers.The research discovered, (1) on the correctness of the concepts, Hong Kong teachers generally had some missing concepts or misconceptions in various areas of mathematics content, in particular, in geometry. On the contrary, missing concepts or misconceptions of Shanghai teachers were usually not fundamental ones. (2) On the connectedness of concepts, the connectedness of Hong Kong teachers was not as strong as Shanghai teachers. In geometry, fragmentation and contradiction among concepts were found in Hong Kong teachers. In data handling, Shanghai teachers were unable to apply knowledge correctly and meaningfully in contexts. (3) On the understanding of basic principles, Shanghai teachers mastered the principles of classification and the strategies of inquiry better and more systematic than Hong Kong teachers. However, Hong Kong teachers had greater intention to inquire than Shanghai teachers. (4) On handling with mathematics representations, the correctness and precision of language of Hong Kong teachers were weaker, and in a greater diversity, than Shanghai teachers. Hong Kong teachers imposed more restrictions on their students in the ways of representation. (5) On handling with feedback, the feedback from Hong Kong teachers did not help students much in establishing mathematics concepts and the connectedness among concepts constructively and positively. Hong Kong teachers paid more attention on the diversity of students' abilities when giving feedback while Shanghai teachers more on the students' needs for further learning.In addition to the conclusion made on the comparison and the characteristics of the professional knowledge of the elementary mathematics teachers of the two cities, the research further brought up some issues to be concerned and suggestions for follow-up action on the development of mathematics education in the two cities.