away from relying on outside sources of evidence and toward a balance between these sources and evidence compiled by teachers; and
away from a preponderance of assessment items that are short, skin-focused, single-answer, and decontextualized, toward a greater use of tasks that are context-based; open to multiple approaches and, in some cases, to multiple solutions; complex in the responses they demand—e.g., in communication, representation, and level of generalization; and drawn from a wide spectrum of mathematics concepts and processes.
The following document addresses professional development that can support teachers in becoming more effective users of assessment. It is based on recent staff-development literature, our own experiences with hundreds of teachers in three national projects (see the Appendix for project descriptions), and the experiences of a group of ten educators we interviewed about their work with teachers in the area of assessment. In the document, we advocate for teachers' professional development in assessment to be carried on with colleagues in groups that work together over time, rather than through a set of disconnected events, a position consistent with that taken by NCTM's Professional Standards for Teaching Mathematics (NCTM, 1991). Ongoing collaborative work is particularly desirable because of the critical role in assessment played by drawing and checking inferences that are tied to standards—skills that can facilitate coordinated action among teachers, but require time to develop. However, there are other compelling reasons for teachers to work together on assessment.
Assessment has the potential to bring explicit attention to what is important to teach and learn in mathematics. Are students demonstrating that they understand percentage if they can convert a percentage into a decimal? What constitutes a convincing mathematical argument in middle school; in high school? In what ways does algebraic thinking get revealed? Many probing and critical questions like these are at the heart of assessment-focused professional development.
Teachers reflecting together on assessment can strengthen classroom assessment and help them calibrate across grades their expectations for mathematics learning outcomes. In particular, individual teachers' observational and questioning skills can be strengthened, as can their capacities to talk with students about progress toward standards. Almost every student of mathematics has had the experience of trying to determine how this year's teacher's values differ from those of last year's teacher. Individual teacher perspectives are important to nurture, but when differing teacher criteria cloud the picture for students as to what is important in