Developing Measures of Teachers’ Mathematics Knowledge for Teaching

In this article, we discuss efforts to design and empirically test measures of teachers’ content knowledge,for teaching elementary mathematics. We begin by reviewing the literature on teacher knowledge, taking special note of how scholars have organized such knowledge. Next we describe survey items we wrote to represent knowledge,for teaching mathematics,and results from factor analysis and scaling work with these items. We found that teachers’ knowledge,for teaching elementary mathematics,is multidimensional, and includes knowledge of various mathematical topics (e.g., number and operations, algebra) and domains (e.g., knowledge of content; knowledge of students and content). The constructs indicated by factor analysis form psychometrically acceptable scales. 3 In the past two decades, teachers’ knowledge of mathematics has become an object of concern. New theoretical and empirical insights into the work of teaching (e.g., Shulman, 1986, 1987; Wilson, Shulman, & Richert, 1987) have spurred greater attention to the role played by such knowledge in teacher education and the quality of teaching itself (e.g., NCTAF, 1996). Other studies have documented the mean and variation in teachers’ knowledge of mathematics for teaching (e.g., Ball 1990; Ma 1999). Results of these efforts have been reflected in teaching standards published by Interstate New Teacher Assessment and Support Consortium (INTASC), the National Board for Professional Teaching Standards, as well as by many other states, localities, and professional teaching organizations (e.g., NCTM). Concerns that teachers possess necessary knowledge and skills for teaching mathematics,have also led to the development,and use of teacher licensing exams, such as PRAXIS, an assessment developed by the Educational Testing Service and now administered in 38 states. Other states and testing firms have developed and administer similar assessments. Given the development of such standards and assessments, one might conjecture that there is substantial agreement around the knowledge,needed for teaching children mathematics. However, a closer look at released items from the elementary mathematics