I. Introduction

Researcher Richard Stiggins and colleagues at the Northwest Regional Educational Laboratory estimate that teachers spend a quarter to a third of their time in efforts to assess students—and their research also shows that on average teachers receive very little support, in preservice or inservice training, in assessment. Stiggins makes a strong argument for bringing teachers and principles together for professional development and cooperative work on strengthening assessment practices. (See Stiggins, 1988.)

The past decade has seen a growing interest among teachers of mathematics in learning the professional craft of assessment, in order to become knowledgeable about and adept at "the process of gathering evidence about a student's knowledge of, ability to use, and disposition toward mathematics and of making inferences from that evidence for a variety of purposes" (National Council of Teachers of Mathematics [NCTM], 1995).

Major shifts are underway in the world of assessment, which imply increased roles and responsibilities for teachers and motivate teachers' growing interest in assessment. As documented in NCTM's Assessment Standards for School Mathematics (NCTM, 1995), there are shifts

  • away from basing inferences on single sources of evidence and toward basing inferences on multiple and balanced sources of evidence;

  • away from reliance on comparing students' performance with that of other students and toward reliance on comparing students' performance with established criteria;



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Learning About Assessment, Learning Through Assessment I. Introduction Researcher Richard Stiggins and colleagues at the Northwest Regional Educational Laboratory estimate that teachers spend a quarter to a third of their time in efforts to assess students—and their research also shows that on average teachers receive very little support, in preservice or inservice training, in assessment. Stiggins makes a strong argument for bringing teachers and principles together for professional development and cooperative work on strengthening assessment practices. (See Stiggins, 1988.) The past decade has seen a growing interest among teachers of mathematics in learning the professional craft of assessment, in order to become knowledgeable about and adept at "the process of gathering evidence about a student's knowledge of, ability to use, and disposition toward mathematics and of making inferences from that evidence for a variety of purposes" (National Council of Teachers of Mathematics [NCTM], 1995). Major shifts are underway in the world of assessment, which imply increased roles and responsibilities for teachers and motivate teachers' growing interest in assessment. As documented in NCTM's Assessment Standards for School Mathematics (NCTM, 1995), there are shifts away from basing inferences on single sources of evidence and toward basing inferences on multiple and balanced sources of evidence; away from reliance on comparing students' performance with that of other students and toward reliance on comparing students' performance with established criteria;

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Learning About Assessment, Learning Through Assessment 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

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Learning About Assessment, Learning Through Assessment mathematical performance, then both learning and performance can suffer. Assessment-based professional development can be a stimulus for teachers to improve their instruction and to change their classroom materials accordingly. Many of the educators we interviewed related versions of the same story from their experience. Over time, when a group of teachers carefully analyze student work and use the evidence to improve classroom instruction, they become clearer and more explicit about the support they need from curricular and instructional programs in their schools and districts. For example, as teachers begin to value the student evidence drawn from using tasks that invite multiple solutions, it is natural for them to develop a desire for curriculum or supplementary materials that will allow them to incorporate such activities regularly into their instruction. The reference list for this publication is a good place to start looking for resources. For mathematical tasks, you may want to explore references 2, 10, 12, 19. 26, 30, 38, and 40; for scoring rubrics, consider 2, 10, 12, 23, 26, 30, 31, and 42; for student work samples, consider 2, 10, 12, 26, 29, 31, and 42; and for descriptions of multiple sources of evidence, consider 12, 19, 23, 28, 29, 30, 40, and 42. Much of the attention given in the past decade to assessment reform has arisen from the need to end inequities, especially in high-stakes student testing and evaluation. Often, students have been penalized for apparent lack of mathematical understanding when, for example, difficulty with language makes it impossible for them to demonstrate their understanding. Similarly, an important reason to focus on assessment in professional development is to foster equity in learning mathematics—i.e., to increase the chances that each student's mathematical power will be developed to the fullest. Arguably, there will be no real equity until, as part of the fabric of teachers' lives, they work together on regular bases, sharpening their skills in making valid inferences about student evidence to help them identify what appropriate actions are necessary for each student to learn mathematics. In the sections following this Introduction, we cite some of the characteristics and special challenges of assessment-based professional development; highlight a set of learning challenges for teachers that have become apparent in assessment-related work, with examples of how these challenges can define the content of teacher work on assessment; describe principles that are important in planning and organizing professional development;

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Learning About Assessment, Learning Through Assessment provide a set of sample activities from our own experience in planning and organizing professional development with an assessment focus1; describe a range of teacher concerns about changes in assessment and a framework for understanding and managing the concerns, and apply the framework to the teacher concerns identified in our interviews; and make a set of suggestions that we think district and school administrators should heed in order for their teachers to gain the maximum benefit from assessment-focused professional development. The document is not intended to provide a comprehensive description of the phenomenon that has come to be called ''alternative assessment.'' However, to assist the reader, a number of terms that are used in this document are defined here. (See also NCTM, 1995.) Additional works on alternative assessment are included in the list of references. Classroom assessment comprises the actions that teachers take (e.g., observations, documentation, quizzes, tests, interviews) to gather evidence in order to monitor progress, diagnose difficulties, assign students to groups, or certify achievement. (See, e.g., Wilson, 1995; Neill, 1995.) Inferences are conclusions or assertions derived from evidence; deductions. (See, e.g., NCTM, 1995.) Mathematical Power includes the ability to explore, conjecture, and reason logically; solve nonroutine problems; communicate about and through mathematics; connect ideas within mathematics and between mathematics and other intellectual activities. (See, e.g., NCTM, 1989.) A Performance standard is a statement of expected performance quality that can be used to make judgments about performances that are central to the curriculum. Performance standards answer the question "How good is good enough?" with performance descriptions and with work samples and commentaries. (See, e.g., New Standards Project, 1995.) A Rubric is a set of clearly defined rules to give direction to the scoring of assessment tasks or activities. (See, e.g., NRC, 1993b.) 1   It should be noted that the mathematics activities used in this document do not represent the full range of assessment tasks that teachers will need to use. Because we have found that teachers are most challenged by what are termed "alternative assessments," there is a high representation of these in the staff-development activities we describe.