What students need to know in a world where most computations are done by machine is discussed. Needed changes in the mathematics curriculum are then detailed in relation to mental arithmetic, numeration, decimals and fractions, paper-and-pencil computation, order of operations, problem solving, and instruction on calculator use. (MNS)

Describes the method to solve problems called T-E-M-T-T: trial, error, and modified trial through technology. The method integrates students' skills of estimation, mental computation, and appropriate choice of calculator use. Includes 2 activities for each of grades K-4 and 5-8 that illustrate the method. (MDH)

Presents five activities focusing on mental computation and estimation for the K-3, 3-5, 4-6, and 6-8 grade levels that require the student, acting as a judge, to review solutions to problems and to pronounce and justify a verdict. Provides suggested materials, questions, possible extensions, answers, and worksheets for each activity. (MDH)

Two games and one activity designed to be used with a hand-held calculator are presented. (MK)

Five reasons are discussed for teaching estimation involving utility, problem solving, concept formation, calculations, and attitude. Specific types of estimation are analyzed and examples given. (MP)

A distinction is made between basic computational skills and skills related to applied mathematics and verbal problem solving. The advantages of using calculators for teaching the latter skills are discussed. (MP)

The focus is on multi-step problems, with suggestions on helping students understand the mathematical relations, decide which computational procedures to use, and identify the sequence in which computations should be performed. An activity to aid understanding of variables is also included. (MNS)

When the words "problem" and "answers" are used in connection with computational exercises, students think they are solving problems. Distinguishing between computational forms and problems is illustrated with a variety of topics. (MNS)

Problems and activities are presented for which "I can't do it" or "It can't be done" are the correct responses. Including problems of this type in the curriculum adds a new dimension to students' learning and helps to develop better problem solvers. (Author/MK)

A restaurant menu is used to apply mathematics to real situations. A variety of mathematical problems, as well as applications to other content areas, is suggested. (JT)

Specific instruction in different contexts provide needed background for solving addition and subtraction problems. The categories of problems and relative difficulties are presented, followed by an explanation of a successful instructional sequence. (MNS)

Pertinent findings from research on problem solving are presented to describe how primary-level children may gain an understanding of addition and subtraction as well as practice computational skills through one-step problems. Then suggestions for teaching problem solving are given. (MNS)

Students have the opportunity to verbalize relationships that demonstrate the acquisition of good number sense. They are to develop clues about the answer to a problem without computing or telling the answer, and to state or write several things they know about the answer to each problem. (MNS)

Examples from almanacs are used to provide real-life problems that involve estimating, computing, and thinking. (MP)