Pedagogical content knowledge of preservice secondary mathematics teachers
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The purpose of this study was to investigate how a methods course and its associated field experience supported the development of pedagogical content knowledge for preservice secondary mathematics teachers. I also investigated what course topics contributed to that development from the preservice teachers’ perspective. The data were collected in the form of interviews, observations, questionnaire and class artifacts and were analyzed according to the pedagogical content knowledge framework developed for this study. Six preservice teachers participated in the study, and each was interviewed three times during the semester. All documents produced by the preservice teachers or distributed in the course were collected to gain a better understanding of the nature of the course topics and preservice teachers’ experiences with them. I defined pedagogical content knowledge as having four components: knowledge of subject-matter, knowledge of pedagogy, knowledge of learners, and knowledge of curriculum. Knowledge of subject-matter refers to knowing mathematical concepts, facts, and procedures and the relationships among them. Knowledge of pedagogy encompasses knowledge of planning a lesson and teaching strategies. Knowledge of learners entails knowledge of students’ common difficulties, errors, and misconceptions. Finally, knowledge of curriculum includes knowledge of learning goals for different grade levels and instructional materials such as technology, manipulatives, and textbooks. The preservice teachers’ knowledge of subject-matter was influential on the other components of their pedagogical content knowledge. The preservice teachers’ ability to make appropriate connections among mathematical concepts, to generate different solutions and representations for problems, to address students’ difficulties and misconceptions effectively, and to choose appropriate examples to teach a particular topic were largely based on the depth of their subject-matter knowledge. However, the field experiences contributed to their repertoire of examples of students’ difficulties and misconceptions as well as instructional strategies and materials. Although the preservice teachers thought that course topics contributed to their pedagogical content knowledge, they were weak in applying their knowledge when they were asked to design a hypothetical lesson or help a hypothetical student who was struggling to understand particular mathematical concepts. The findings of this study imply that teacher education programs need to offer content courses that provide preservice teachers with opportunities to review fundamental topics taught in secondary school mathematics classes.