OVERVIEW

This section presents eight standards for the evaluation of the teaching of mathematics organized under two categories:

The Process of Evaluation

1. The Evaluation Cycle
2. Teachers as Participants in Evaluation
3. Sources of Information

The Foci of Evaluation

4. Mathematical Concepts, Procedures, and Connections
5. Mathematics as Problem Solving, Reasoning, and Communication
6. Mathematical Disposition
7. Assessing Students' Mathematical Understanding
8. Learning Environment

INTRODUCTION

Efforts to improve the teaching of mathematics are necessarily a function of what good mathematics teaching is considered to be. Deciding which aspects of teaching need to be improved requires both information about the teaching process and a framework that suggests what we value. The previous section presents a vision for teaching mathematics based on the Curriculum and Evaluation Standards for School Mathematics. The standards in this section are intended to help teachers attain that vision by emphasizing the role that evaluation can play in teachers' professional development. In keeping with the notion that assessment is a process of gathering and interpreting information, these standards focus on how and what information should be gathered and analyzed to help teachers improve their teaching.

The assessment process described in the following standards can be used by a teacher engaged in a process of self-analysis and personal growth or by a teacher working in concert with colleagues or supervisors in an effort to improve instruction. Each standard serves as a statement about what should be observed regardless of who is doing the observing. Further, the standards can be useful in evaluating teachers with a wide range of teaching experience and expertise. They provide foci to be considered by all who teach mathematics.

Evaluation comes in many forms. Teachers improve their own teaching by reflecting on and analyzing previous lessons. Evaluation is also an activity involving peers, one supporting the other in trying to improve the quality of instruction. The vignettes in this section illustrate both forms of evaluation.

Teachers are sometimes evaluated because of district or state mandates to make career-ladder decisions or to make judgments about a teacher's competence. It is our position that such evaluations should also adhere to the following standards particularly with respect to the teacher's participation in the process and in defining the foci of the evaluation.

Teachers who strive to improve their instruction will take risks by experimenting with instructional approaches that are either new to them or that they have not yet mastered. The assessment process should not restrict a teacher's willingness to take those risks, nor should it be permitted to interfere with instruction in any other way. Teachers need freedom and support to develop professionally. For a teacher engaged in experimentation, self-analysis or conferring with a colleague may be more appropriate than evaluation by an administrator.

It is imperative that the teaching of mathematics enable every student to become mathematically powerful and that we increase the participation of all students in the study of mathematics. By "every student" we mean specifically

• students who have been denied access in any way to educational opportunities as well as those who have not;
• students who are African American, Hispanic, American Indian, and other minorities as well as those who are considered to be a part of the majority;
• students who are female as well as those who are male;
• students who have not been successful in school and in mathematics as well as those who have been successful.

Thus, an important consideration in evaluating the teaching of mathematics is whether the mathematical needs of every student are being addressed.

ASSUMPTIONS

The standards in this section are based on the following four assumptions:

1. The goal of evaluating the teaching of mathematics is to improve teaching and enhance professional growth. The teacher is the key to high-quality mathematics education for students. It is the teacher who makes decisions about curriculum and teaching methods to maximize student learning. Professional development extends and expands teachers' abilities to make good decisions by giving them access to a deeper understanding of mathematics, a greater knowledge about students' learning of mathematics, a greater repertoire of teaching strategies, and the ability to match their repertoire to the needs of all students. Evaluation helps identify the teacher's needs so that appropriate professional development experiences can be provided.

2. All teachers can improve their teaching of mathematics. These standards are intended for all teachers. Whether beginning or experienced, all teachers can find some aspect of their teaching that can be improved by considering one or more of the standards. Though experienced teachers might be more adept at self-analysis, beginning or struggling teachers can also reflect on the standards and arrive at some conclusions on how their teaching can be improved.

3. What teachers learn from the evaluation process is related to how the evaluation is conducted. The primary emphasis of the standards is on improvement through self-analysis and working in a collegial and supportive environment with peers, supervisors, and administrators. Evaluations can be conducted in many ways, and many sources of information should be used. When written evaluation reports for a teacher's personnel file are produced, a spirit of sensitivity, mutual respect, and concern for professional growth as the primary purpose of evaluation are especially important.

4. Because teaching is complex, the evaluation of teaching is complex. Simplistic evaluation processes will not help teachers realize the vision of teaching mathematics described in these standards. Teaching is a function of many activities including listening, informing, stimulating, challenging, and motivating. These and other activities should be done in ways that are responsive to students and take advantage of their knowledge and disposition to do mathematics. A particularly sensitive issue related to the complexity of evaluating teaching is whether and how information about students' understanding of, and disposition to do, mathematics should be considered. It seems only reasonable that students' progress should provide a source of information about teaching. However, student learning of, and disposition to do, mathematics should not be the only sources of information. It follows that any evaluation process that intends to help teachers achieve the vision of teaching mathematics suggested in this volume should consider numerous factors and circumstances and should have a longitudinal and cyclical perspective.

The next section contains three standards that describe the evaluation process and its contribution to a teacher's professional development. The subsequent section contains five standards that provide the foci for evaluating the teaching of mathematics.