Depth of Teachers' Knowledge: Frameworks for Teachers' Knowledge of Mathematics

This article describes seven teacher knowledge frameworks and relates these frameworks to the teaching and assessment of elementary teachers’ mathematics knowledge. The frameworks classify teachers’ knowledge and provide a vocabulary and common language through which knowledge can be discussed and assessed. These frameworks are categorized into two classes: content knowledge and content knowledge for teaching. Content knowledge frameworks include Bloom’s Taxonomy (1956); Skemp’s (1976) Instrumental and Relational Understandings; Hiebert and Carpenter’s (1992) Procedural and Conceptual Understandings; Webb’s (2002) Depth of Knowledge; and Porter’s (2002) Cognitive Complexities. Content knowledge for teaching frameworks includes Schulman’s (1986) Type of Teachers Knowledge and Ball’s (2000) Mathematical Knowledge for Teaching. The Diagnostic Teacher Assessment of Mathematics and Science (DTAMS), a tool that assesses both mathematics teachers’ depth of conceptual knowledge and pedagogical content knowledge, is used to concretely connect the frameworks. The article concludes with examples of quantitative assessments of teachers’ mathematics knowledge based on these teachers’ knowledge frameworks.