Diagnostic evaluation is a major way to help students overcome errors. How such evaluation can be done is discussed, with comments on what should be checked and recorded by the teacher. (MNS)

Two successful procedures for evaluating problem-solving performance in the classroom are shared. Five goals for teaching problem-solving are noted, followed by a discussion of evaluating a child's performance through joint use of: (1) analyzing written work; and (2) observing and questioning students. (MP)

Discussed are "moves" in teaching mathematics that can serve as a basis for defining understanding. How to characterize and use moves is discussed, with specific examples and research evidence. (MP)

Performance assessment, a method that makes possible the assessment of multiple dimensions of students' progress, including dispositions, is described. Criteria for good performance tasks are given, and their structure is illustrated through an example. A list of 10 dispositions toward mathematics and a self-evaluation group-performance rating…

Presents the elementary-level formative evaluation method of functional diagnosis that gives students immediate feedback on completed assignments. Gives three examples of the method as observed in the classrooms of master teachers: putting red dots next to problems needing attention; paired learning, and student answer keys. (MDH)

Presented are practical methods exemplifying principles of assessment that involve minimal disruption of the instructional process and not impose additional work on the teacher. Informal assessment methods include annotated class lists and student work folios. Formal assessment methods include practical tests, student-constructed tests, and…

Presented are assessment techniques to help improve instruction. Included are the formative assessment techniques observation and questioning, diagnostic interviews, and problem-solving-based investigations and the summative assessment technique of performance-based tasks. Examples of these methods are provided together with at-home activities…

Examples are presented in which students are able to answer test items requiring manipulation of numbers for such topics as reducing fractions, but lack understanding of the operation. In addition to paper-and-pencil test, interviews are recommended for evaluating a student's understanding. (JP)

Many teachers use cooperative learning methods during instruction but face the problem of aligning evaluation techniques with that instruction. Described are methods to include cooperative problem solving in evaluation, including strategies to identify possible grading schemes, to make appropriate problem choices, and to evaluate individual versus…

This article suggests that the choice of instructional materials be guided by children's needs. (MM)

Several ideas for questions and settings for interviews are presented. It is noted that although subtraction is used as an example in each case, most of the material can be easily adapted to the other basic operations. Many problems are noted with standard diagnostic tests and use of them is discouraged. (MP)

Two perspectives that frame the aspects of the debate on assessment issues are analyzed. The "count-everybody" perspective calls for national standards over which all students would be tested. The "everybody-counts" perspective favors assessments that are developed from multiple perspectives. (MDH)

Recommendations and assessment procedures are provided to help decision-makers choose the best metric materials available. (JT)