| Teacher knowledge was an active research area in the last twenty years. It focuses on all kinds of knowledge that teacher knows related to teaching, The study explored subject matter knowledge in teacher knowledge. From the past researches on subject matter knowledge, we find that researchers often focus on teachers' understanding of mathematical concepts and procedures. This is the knowledge of "knowing that". The past researches on subject matter knowledge didn't touch on the knowledge of "knowing how". Based on the theory of problem schema in psychology, we studied teacher's problem schemas, which are related to problem solving.; To explore possible relationship between problem schema and teaching, we first identified the figure of schemas secondary school mathematics teachers have. Then we examined the differences between expert teachers and non-expert teachers to explore the relationship between teachers' problem schemas and their teaching context. In this study, secondary school mathematics teachers were chosen for case studies. Qualitative research methods, including questionnaire and interview were adopted to find out teacher's problem schemas.; The study shows that there are various types of problem schemas among secondary school mathematics teachers. They include: "schema organized by mathematics concept ", "schema organized by conclusion or unknown", "schema organized by basic figure ", "schema organized by mathematical structure", "schema organized by general mathematical problem solving strategies". Compared to non-expert teachers, expert teachers have a wider set of problem schemas. Expert teachers not only have the schemas non-expert teachers have, but also have the schemas non-expert teachers don't have. "Schema organized by mathematical structure", "schema organized by general mathematical problem solving strategies" are two of them. Generally speaking, expert teachers possess more profound problem schemas. Hence we see a relationship between problem schemas and teaching expertise.; Based on the findings above, it is recommended that the future study should explore further how teachers' problem schemas influence their teachings by means of classroom observation. The second recommendation is to study problem schema and other subject matter knowledge in one research to see a comprehensive view. It is also recommended that the development of teachers' problem schemas and subject matter knowledge should be strengthened in teacher education. |
