Two transcripts of children exploring and solving problems presented by computer programs are given. The transcripts show the insight that occured. (MNS)

How the author moved from concern about research to development of prescriptive models of heuristic problem solving and the exploration of metacognition and belief systems is discussed. Student beliefs about problem solving, and their corollaries, are included. (MNS)

The method of finite differences is discussed with some applications. The method is described in detail, with illustrative sequences, and several problems are presented. (MNS)

A noncredit course in a workshop format is described, with sessions focusing on recognizing and defining problems; organizing information and using modeling techniques; analyzing data, recognizing trends, and making decisions; being flexible and thinking creatively; and generalizing and consolidating. (MNS)

Given is an example of the solution of maximum-minimum problems by replacing differentiation techniques with microcomputers and simple BASIC programs. (MNS)

An application of trigonometry in weather forecasting, dealing with cloud height, is discussed. (MNS)

An investigation of the cost of homeownership by constructing a mathematical model with refinements illustrates an important type of problem solving with calculators. (MNS)

A problem on speed of travel is stated in general terms to provide practice in algebraic manipulation while maintaining a sense of real-world usefulness. A computer program is listed. (MNS)

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)

A problem concerning the ratio of the area of a hexagon and a triangle is presented, with the emphasis on possible extensions of the problem. (MNS)

Two problem-solving skills, guess-and-test and simplification, are introduced and reinforced through a variety of motivating problem situations. Solutions of sample problems and extensive directions for the teacher encourage the use of Polya's four-step model of problem solving. (MNS)

The use of logical reasoning is illustrated with a problem and its solution process. Other suggestions for teaching problem solving are included. (MNS)

A realistic problem is presented, computing the probability of winning a sports playoff series if the probability if winning a single game is known. Only simple permutation formulas and some basic logic are required to solve the problem. Two computer programs and a discussion of solution methods are included. (MNS)

An interest inventory was administered to 99 fourth-graders and used to personalize a pool of word problems previously selected by experts. Subjects were then administered tests with standard and personalized problems. Results indicated that personalization improved performance in selecting the correct process but not in computation of correct…

Evaluates 25 software packages (consisting of more than 40 individual programs), all aimed at one or another facet of mathematics learning. Title, source, current price, and detailed review (indicating the educational quality of the package) are included for each entry. (JN)