Elementary school mathematics teachers' subject matter knowledge and pedagogical content knowledge: Their relationship to classroom instruction

What professional knowledge is required for expert teaching? How must it be understood and held so that it is available for use in classroom? Such questions have been central to both teachers' professional development and instructional improvement. The present study therefore examined differences in subject matter knowledge and pedagogical content knowledge between elementary mathematics expert teachers and no-expert teachers, and in particular how the differences affected the teachers' teaching behaviors and then students' learning.;The study recruited 30 elementary mathematics teachers (15 expert and 15 no-expert teachers) and 1691 students from the thirty classrooms where the teachers taught. Three measures were used to assess the teachers' subject matter knowledge and pedagogical content knowledge of elementary mathematics. Fifty-three sessions of classroom instruction were videotaped and then were coded in terms of cognitive demands of learning tasks the teachers used and the ways they led classroom discourse. Each teacher was interviewed before and after the class being videotaped. Measures of student learning outcome included a mathematical belief questionnaire and their mathematical term examination scores. A nonverbal intelligence test was also administrated to the students for the purpose of control for the confounding effects of students' intelligence with the teacher variables on students' learning.;Results indicated significant differences in subject matter knowledge (SMK) and pedagogical content knowledge (PCK) between the two groups of teachers. Compared to the no-expert teachers, the expert teachers had profound understanding of mathematical knowledge with explicit and well-organized knowledge package. The expert group tended to hold a problem-solving view, whereas the no-expert group to hold a knowledge view, about learning mathematics. The expert teachers knew significantly more than their counterparts about students' misconceptions and difficulties for the particular topics about fractions. The expert teachers were also more likely than the no-expert teachers to confront students with misconceptions and to focus on developing students' conceptual understanding.;The differences in SMK and PCK had an effect on the teachers' teaching behaviors. Both groups set up mathematical tasks of different cognitive demands. However, the expert teachers could maintain high-level cognitive demands of tasks in their implementation, whereas the no-expert teachers tended to reduce the tasks to the mere utility for procedure acquisition without making use of the tasks to enhance students' understanding. In the expert teachers' classrooms, the classroom discourse showed a pattern of student statement-teacher questioning-student explaining (student-teacher-student). In contrast, in the no-expert teachers' classrooms, the discourse was typically showed to be a pattern of teacher initiation-student response-teacher evaluation (teacher-student-teacher).;Using the method of multilevel data analysis, the study explored the relationship between teachers' SMK and PCK, classroom instruction and students' learning. The results indicated that the teachers' SMK and PCK significantly affected their teaching behaviors including the ways they implemented mathematical tasks and led classroom discourse, and then the teachers' behaviors in turn had significant effects on students' learning. However, teachers' SMK and PCK did not have a direct influence on students' learning. Their influence on students' learning was mediated by teachers' classroom instruction.