Middle school mathematics teachers' subject matter knowledge for teaching in China and Korea
The purpose of the study was to investigate the reality of middle school mathematics teachers' subject matter knowledge for teaching. The specific goals of the study were to develop a conceptual framework for the structure of mathematics and enhance Ma's conceptual model describing the depth of teachers' conceptual understanding of mathematical topics. Making use of the conceptual framework and model, the study focused on investigating teachers' conceptual structures of understanding a mathematical topic in context. Data in the study were collected through interviewing nine Chinese and ten Korean middle school mathematics teachers. The teachers responded to four interview questions that were designed in the form of scenarios that presents teaching tasks related to specific mathematical topics. The teachers' oral responses were audiotaped and transcribed, and their written notes were collected. The results of the study were compared to the analysis of American and Chinese elementary and secondary teachers' responses to the same task in Ball (1988) and Ma (1999). The findings of the study suggested that the properties---depth, breadth, and connectedness---of teachers' understanding of elementary mathematics present in Ma's (1999) study were also found in the middle school teachers who successfully completed the given teaching tasks in this study. An especially interesting finding of the study was that teachers' approaches to explaining and demonstrating a mathematical topic were significantly influenced by their knowledge of learners and knowledge of the curriculum they teach. One of the practical implications of the study is that teachers should recognize the advantages of learning the conceptual structure of a mathematical topic. It allows the teachers to have the flexibility to come up with meaningful mathematical approaches to teaching the topic, which are comprehensible to the learners whatever the grade levels they teach, rather than rule-based algorithms.