A Comparative Study On PCK Of Slope Between Pre-service Teachers And Beginning Teachers

This research studied 4 pre-service teachers and 4 beginning teachers'PCK (Pedagogical Content Knowledge) of the slope concept through survey, interview and evaluations of videotaped mathematics lessons. This paper focuses on comparing PCK of slope between the two groups of teachers and looking for factors that affect their PCK development. The conclusions are:1. The differences between the two groups of teachers' "content knowledge" of slope are small:(1) They have comparable abilities to solve problems by using the slope concept;(2) They both have various representations of slope, with minor differences. The representations that impress the pre-service teachers most lie in the real world situations, while the representations that impress the beginning teachers most lie in the knowledge related to school curriculum; some teachers in both groups have difficulties in transferring from the physical representation to the algebraic representation; most beginning teachers cannot find the connections between the two algebraic representations, but the pre-service teachers can connect them through multiple ways and they can point out the connections to the follow-up knowledge.(3) Teachers in both groups have only a superficial understanding of the connections between slope and related knowledge. They can neither explain why slope is defined as the tangent of the angle of inclination by connecting it with the meaning of slope in the real world situation, nor solve problems about lines in three-dimensional spaces.2. Beginning teachers possess more "teaching knowledge" about slope than pre-service teachers:(1) When explaining students'misunderstandings, beginning teachers'analyses are deeper, but there is no difference in their strategy choices to solve students'problems.(2) When analyzing the organization and the way of presentation of the subject, beginning teachers' considerations are more careful and thorough. They have developed knowledge about students, thus they can analyze problems from students' perspective. Moreover, they have a deeper understanding of teaching and a broader perspective as well.3. The main factor that affects pre-service teachers'PCK development is the learning experience in middle school, including their own teachers'ideas and teaching. The second factor is their mentors'ideas and teaching in practicum before graduation. The main factor that affects beginning teachers'PCK development is the teaching experience. The second factor is the learning experience in middle school.Although the pre-service teachers have just finished college study, the influence of the college lessons seems weak. Apart from a better understanding on the connections between the different algebraic representations of slope, they do not otherwise have more "content knowledge" than the beginning teachers. On the other hand, the beginning teachers'teaching experience allows them to have more comprehensive "teaching knowledge" than the pre-service teachers, although due to the short career age, the beginning teachers'knowledge about students sometimes does not become a part of their thinking strategies.