Two separate and simultaneous studies took place in middle socioeconomic schools. A considerable degree of consistency of results in problem-solving performance with and without calculators was found in the two investigations. Calculator-using groups performed significantly higher than non-calculator groups where differences occurred. (MP)

An exploration of a problem called solving quadratic congruences modulo p is detailed and is built around an alternate method of deriving the quadratic formula. Three practical pedagogical values that have been experienced by students and instructor when the material was presented to classes are noted. (MP)

A list of heuristics for elementary school children is provided. Two examples which are viewed to demonstrate the conscientious and creative use of problem-solving strategies by fourth graders are detailed. Suggestions for teachers on how to help pupils develop their problem-solving abilities are included. (MP)

Suggestions for assisting learning disabled (LD) students in decision making are given for determining what information is needed, the correct operation for solving a given problem, and whether an answer is reasonable. (MP)

Research appears to support one major conclusion: problem-solving strategies should be taught. Sections presented are: Why doesn't research tell us what to do? What do we know about problem solving? What can teachers do to help children learn to solve problems? What has recent research affirmed? (MP)

Details of a scope-and-sequence outline for problem solving in the elementary mathematics program of the Philadelphia School District are provided. The emphasis is seen to be on process rather than product. Information about the first 18 of 21 levels in the problem-solving strand is provided. (MP)

A teaching strategy for problem solving with computers is detailed. The approach provides a "midline" level of help that encourages exploratory activity yet provides enough guidance to increase chances of pupil success. (MP)

A programing language called DYNAMO, developed especially for writing simulation models, is promoted. Details of six, self-teaching curriculum packages recently developed for simulation-oriented instruction are provided. (MP)

Failure of most children to solve word problems beyond the simplest is seen to stem from two causes: failure to understand applied arithmetic and failure to relate problems to the real world. Relevant research is reviewed, and a route for new research is proposed. (MP)

The processes and perceptions of pupils in the mathematical processing of proofs are examined in clinical interviews of secondary school pupils. Analysis of the data led to the identification of clusters of characteristic response types. (MP)

Ways to incorporate student mistakes in the instruction of mathematics at the undergraduate level are discussed. A sample investigation of a pupil error with a formula from Calculus is featured. (MP)

Approaches to developing a good mathematics textbook for the junior high student are discussed, with the pitfalls and difficulties reviewed. Examples from new Polish textbooks are presented to illustrate possible solutions. (MP)

An alternative application of logarithms in the high school algebra curriculum that is not undermined by the existence and widespread availability of calculators is presented. The importance and use of linear relationships are underscored in the proposed lessons. (MP)

Providing students with realistic problems will facilitate a better understanding of and reason for computation. Specific suggestions for introducing and for increasing problem-solving skills are described. (CJ)

First-grade children's solution processes for addition and subtraction were studied. Their processes tended to represent the relationships or actions described in individual problems. (MP)