An investigation of the effectiveness of modeling a mathematics activity for in-service teachers with respect to mathematical content and accuracy, students' involvement, and instructional goals.

摘要

The purpose of this qualitative study is to compare how teachers who participated in a mathematics teacher enhancement project implemented a reaction time activity in classrooms with how the activity was modeled in the project. The comparison was based on three dimensions and several sub-dimensions: mathematical content (data collection, data interpretation, coordinate graphing, statistical terms, linear regression, slope, and exponential functions) and accuracy (using accurate mathematical terminology, presenting accurate mathematical data or graphs, and avoiding computational mistakes), students' involvement (being lectured to, physically acting out the activity, participating in discussion, and doing seatwork), and instructional goals (skills, concepts, and problem solving).;The research questions are as follows: (1) to what extent and why are the mathematical content and accuracy of the model activity maintained or altered by the in-service teachers in the classroom activity? (2) to what extent and why is the level of student involvement of the model activity maintained or altered by the in-service teachers in the classroom activity? and (3) to what extent and why are the instructional goals of the model activity maintained or altered by the in-service teachers in the classroom activity?;The twelve participants of this study were one model instructor, six high school teachers, and five middle school teachers. Four instruments were employed in collecting the data for this study: one video tape of the activity modeled by the instructor in the project, eleven video tapes of the activity conducted by the teachers in the classrooms, the model instructor's interview, and the teachers' interviews.;The findings indicate that there were differences between the model activity and the classroom activity with respect to mathematical content, level of students' involvement, and instructional goals. It was evident that the model activity provided greater emphasis to linear regression, while the classroom activity provided greater emphasis to coordinate graphing. Discussion dominated the model activity time, while physically acting out the activity and discussion dominated the classroom activity time. Equal portions of the model activity time were spent addressing skills, concepts, and problem solving, while addressing skills dominated the classroom activity time for both the high school and middle school classes. The middle school teachers spent more time than the high school teachers addressing concepts and problem solving. The findings suggest that the differences were attributed to class size, students' mathematical ability, grade level, time, and the presence of the researcher with the camera.