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)

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)

Basic rules of test construction are detailed to provide teachers with ways to improve the validity and reliability of teacher-made tests and worksheets. Designing the test, writing the items, and scoring the test are each discussed. The critical need for good instruments is promoted. (MP)

Procedures enabling teachers to diagnose and analyze a child's ability to understand and memorize basic facts are described. (JT)

Described and compared are two approaches for evaluating student problem solving skills at the elementary school level. One model was developed by Charles and Lester; the other model was developed by Woods. (RH)

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)

Alternative identification and instructional procedures are discussed. Instructors are warned against assuming an equivalence between the quantity of mathematical work a child demonstrates and the quality of that child's thinking. A need to integrate qualitative information is seen. Two types of activities for gifted pupils are detailed. (MP)

Mathematics success or failure is noted as possibly related to the way in which material is presented rather than to the subject itself. Teachers are encouraged to have pupils complete a questionnaire that is designed to measure their mathematical "state of health." Instructors are told to identify learning styles. (Author/MP)