4: Assessing Teachers’ Mathematical Knowledge: What Knowledge Matters and What Evidence Counts?

For more than two hundred years, teachers—and what they know—have been objects of scrutiny. Teachers have been tested, studied, analyzed, lauded, and criticized. In short, both they and their performance have been assessed to an extent rare in other professions. Both the purposes and methods for assessing teachers have varied. With some assessments, the goal has been to evaluate individuals’ qualifications for the work of teaching, while with others, the focus has been to analyze the knowledge teachers use to do that work. Most assessments have been evaluative, either explicitly or implicitly, seeking to appraise the adequacy of individual teachers’ knowledge or the quality of their performance. Some assessments have contributed to building evidence about the knowledge needed for teaching, thus helping to establish criteria for professional qualifications and the methods for certifying them. What is assessed differs across approaches, and how it is assessed varies: Some are indistinguishable from a test that could be given to students, while others pose tasks special to the work of teaching. Teachers have been interviewed and observed; they have been queried, given tasks, and asked to construct portfolios representing their work. The variation in purposes, test content, and assessment methods has increased over the past 30 years, as teacher testing has become more commonplace and the number of teacher tests has multiplied.