Depth of teachers’ knowledge: Framework for teachers’ knowledge of mathematics

  • Vicki-Lynn Holmes
Keywords: teacher knowledge, pedagogical content knowledge, depth of knowledge, mathematics frameworks


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 Blooms Taxonomy (1956); Skemps (1976) Instrumental and Relational Understandings; Hiebert and Carpenters (1992) Procedural and Conceptual Understandings; Webbs (2002) Depth of Knowledge; and Porters (2002) Cognitive Complexities. Content knowledge for teaching frameworks includes Schulmans (1986) Type of Teachers Knowledge and Balls (2000) Mathematical Knowledge for Teaching. The article concludes with examples of quantitative assessments of teachers mathematics knowledge based on these teacher knowledge frameworks.