The standards in this section emphasize the type of information that should be obtained in assessing classroom teaching. At times the assessment process should focus on what the teacher is doing, and at other times it should focus on what the students are doing. By focusing on the teacher, assessment can determine the teacher's command of knowledge and strategies for teaching mathematics as well as whether the teacher is providing adequate encouragement for students to learn. By focusing on the students, assessment can determine whether the teacher has provided a context and opportunity for students to be engaged in significant and appropriate activities and whether the students demonstrate a disposition to do mathematics.

To a great extent, improving the teaching of mathematics depends both on a teacher's ability to determine what individual students know and how they construct mathematical ideas and on the teacher's ability to base instruction on those determinations. Teachers must be able to analyze their students' understanding of both mathematical content and mathematical processes. Teachers must also be able to analyze how well groups of students reason and solve problems together and communicate their mathematical ideas. Such appraisal is vital to using group work in ways that foster the development of students' mathematical power within the classroom community. The teacher's ability to analyze and describe group as well as individual learning is fundamental to the following standards.