Suggests that, although questions are often used to help students or stimulate student thinking, questions can also be used to help evaluate student thinking and attitudes about problem solving. Sample problems and questions are given. (PK)

How children give meaning to problems solved by multiplying or dividing is considered. After showing two cases of children's understanding of multiplication problems, six recommendations for classroom practice are presented. (YP)

Examines whether verbal problem-solving skills in a group of fourth graders would improve if they were specifically taught how to generate their own diagrams when solving word problems. Classifies textbook word problems into three general types and describes them: (1) tabular; (2) geometric; and (3) contingency diagraming. (YP)

Presents a study of 87 second graders to demonstrate that achievement tests in primary mathematics emphasize pupil's lower-order thinking by comparing answers to interview questions from constructivist and traditionally instructed groups. Results indicated that constructivist instructed students demonstrated superior higher-order thinking on tasks…

Argues that, because problem solving has two aspects, a thinking process and a final product, a good evaluation requires consideration of both aspects. A holistic scoring point system is described. (PK)

Investigates how primary-level pupils can solve word problems more effectively using computational skills in small, cooperative groups. Points out six principles for successful cooperative groups through problem solving protocol analysis: (1) teach strategies; (2) rehearse techniques; (3) involve everyone; (4) cooperate to solve problems; (5) keep…

Described is the Delaware Elementary Mathematics League; a state mathematics competition for grades 4-6. Included are specific sample test items and a discussion of how they can nurture the development of problem-solving skills. Sample tests are also discussed. (CW)

Discussed are some objections to using calculators in mathematics instruction and testing. Indicates that many commercially available tests do not permit the use of a calculator. Several steps to facilitate the use of calculators are suggested. (YP)

Explains a set of processes that teachers might use to structure their evaluation of students' learning and understanding. Illustrates the processes of setting goals, deciding what to assess, gathering information, and using the results through a measurement task requiring students to estimate the number of popcorn kernels in a container. (MDH)

Reports the third grade and seventh grade results of the fourth mathematics assessment of the National Assessment of Educational Progress. Summarizes the major results of the performance on number, operations, and word problem items. Some examples of data are given. (PK)

Discusses the use of computer spreadsheets to prepare questions from a problem. Presents three sample problems, templates, and questions. Provides a list of available spreadsheet programs. Lists five references. (YP)

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…

In 1987, Toronto Board of Education mandated the development of standards, called "benchmarks," for students' achievement in mathematics and language at the end of grades 3, 6, 8, and 10. The development and testing of benchmarks stressing higher-order thinking, problem solving, and the use of experiential approaches and manipulative…