Pedagogical Content Analysis

should be coherent; furthermore, the different topical strands of mathematics are highly interconnected. Last, knowledge of instructional strategies are representations for teaching a concept or topic allows teachers to possess a collection of various explanations, metaphors, analogies, and activities. Similarly, Smith and Neale (1989) characterized pedagogical content knowledge as consisting of four components: knowledge of students’ concepts, including students typical errors and developmental paths; knowledge of strategies for teaching content that enable students to conceptually understand a concept by eliciting students’ preconceptions, asking for clarification and explanation, encouraging debate, and discussion, and clearly presenting

They defined pedagogical content knowing as a teacher’s integrated understanding of four components of pedagogy, subject matter content, student characteristics, and the environmental context of learning. According to this definition, pedagogical and subject matter knowledge should be developed in the context of teachers’ understanding of students and of the environmental context learning. Consequently, Cochran et al. characterized pedagogical content knowing as follows: teachers’ understanding of students, such as abilities, learning strategies, ages, developmental levels, attitudes, motivations, and prior conceptions of a subject; teachers’ understanding of the environmental contexts of learning, which encompass social, political, cultural, and physical environmental contexts that affect teaching and learning; pedagogical understanding, which involves knowledge of curriculum and knowledge of educational goals and purposes; and knowledge of subject

Marks indicated that the categories of pedagogical content knowledge could be almost equally derived from subject matter knowledge and pedagogical knowledge; for instance, learning activities, understanding students’ misconceptions, and the use of teaching strategies. Magnusson (1999) viewed pedagogical content knowledge as the transformation of several types of knowledge for teaching. Therefore, pedagogical content knowledge is a teacher’s understanding of how to help students understand specific subject matter. More to point, they adopted Grossman’s (1990) work in pedagogical content knowledge as the result of transformation of content, pedagogical, and contextual knowledge. They modified Grossman’s model to include five additional components for the case of science teaching: orientation to teaching science, referring to teachers’ knowledge and beliefs about the purposes and goals for teaching science; knowledge and beliefs about science curriculum, consisting of mandated goals and objectives and specific curricular programs and materials; knowledge and beliefs about students’ understanding, including knowledge of requirements for learning and knowledge of areas of student difficulty; knowledge and beliefs about instructional strategies for teaching science that contain knowledge of subject-specific science learning to assess and