Preservice teachers' knowledge of content and students in geometry

Abstract

The purpose of this study was to explore what kind of knowledge of content and students preservice teachers have with respect to geometry and how they apply their knowledge to examining students’ work. The data were collected in several ways: written tasks, pre- and post-tests, interviews, and observations. The knowledge of content and student (KCS) tasks were designed to investigate preservice teachers’ knowledge of students’ thinking and misconceptions and were analyzed by applying two different frameworks: Radatz’s error analysis to describe causes of students’ errors and Shulman-Fischbein framework for analyzing preservice teachers’ subject matter and pedagogical content knowledge in mathematics. The pre- and post-tests were scored and analyzed to identify changes in preservice teachers’ knowledge and to verify the influence of the KCS tasks and the content and methods courses. The interviews and observations were used to identify preservice teachers’ backgrounds and opinions. The analysis revealed that preservice teachers had strong subject matter knowledge in geometry. When analyzing students’ thinking and misconceptions, they sometimes tended to focus on the correctness of students’ final answers and to ignore details in students’ solutions. Additionally, they tended to pay more attention to algorithmic and formal aspects of mathematical knowledge than to the intuitive aspect. The preservice teachers’ ability to propose instructional strategies to correct students’ misconceptions was narrow in that they did not apply a variety of teaching methods, activities, and manipulatives. The causes of students’ errors and misconceptions were multidimensional, whereas preservice teachers’ knowledge in this area was narrow in that preservice teachers interpreted students’ errors from only one or two perspectives. The results of the pre- and post-tests revealed that preservice teachers’ knowledge in geometry improved, which may be influenced by their course taking and the KCS tasks used in this study. These findings imply that teacher preparation programs need to provide opportunities for preservice teachers to investigate students’ thinking and misconceptions through content and methods courses in order to enhance their knowledge.