A game is presented in which computation by a stepping-stone method is used to solve minimax problems. An additional application of this game is used for finding the Pearson correlation coefficient by non-parametric techniques. The game provides considerable computational practice as well as a motivational problem solving situation. (JP)

Four procedures are stated which are inherent in problem solving: (1) understanding the problem; (2) planning to solve the problem; (3) solving the problem; and (4) reviewing the problem and the solution. Each of the four procedures is illustrated using problems appropriate for elementary school children. These illustrations are accompanied by…

This appendix to the Mathematical Problem Solving Project "Module Development and Formative Evaluation" contains quizzes for trials 1 and 2 for the module entitled "Using Guesses to Solve Problems." Teachers' comments from these trials are included. (MP)

This problem deck is designed for use after having covered the material in an accompanying skills booklet. It provides for further use of the skills with problems involving four skills at five levels of difficulty. The four skills involve using guesses as a strategy in solving computation problems, two-step problems, situations that require…

This problem deck contains over 150 problems related to the module "Using Tables to Solve Problems." The problems are presented at five levels of difficulty and contain four basic types of two-dimensional tables: (1) constant sum; (2) constant differences; (3) constant quotient or ratio; and (4) constant product. (MP)

One of the implicit goals of the Mathematical Problem Solving Project, MPSP, was to increase the teachers' awareness of what problem-solving is and of different ways of solving problems. The problem solving sort task was developed to assess change due to involvement with MPSP in the teachers' perception of what problems they would use to teach…

This study investigated the effectiveness of teaching sixth-grade students to use diagrams, sketches, and pictures in solving arithmetic word problems. Three instructional groups were formed from a pool of 362 subjects. Group 1 practiced solving problems using only verbal statements; group 2 practiced on problems presented in word form, sometimes…

This booklet was written to help the mathematics teacher introduce computers through an easy, problem-oriented language. In Section I, a problem is selected and solved in a manner that builds up the use of the language. In Section II, the language is applied to three sample problems to illustrate further the programming techniques presented in…

Provided is an introduction to the properties of continued fractions for the intellectually curious high school student. Among the topics included are (1) Expansion of Rational Numbers into Simple Continued Fractions, (2) Convergents, (3) Continued Fractions and Linear Diophantine Equations of the Type am + bn = c, (4) Continued Fractions and…

The purpose of this study was to determine whether a greater increase in problem-solving ability of capable but poorly prepared college freshmen in a modern mathematics program occurs when students are taught to use discovery techniques. Two experimental and two control groups were formed from 70 college freshmen; two instructors were each…

The existence of inductive and deductive learning styles and their effect on mathematics achievement were investigated. On the basis of achievement scores on two tests, 298 eighth grade students were chosen, stratified by sex and previous mathematics achievement, and randomly assigned to one of four instructional sequences. No significant…

Using the "How to Solve It" list developed by Polya as a vehicle of comparison, research findings and key concepts from the psychological study of problem solving are applied to mathematical problem solving. Hypotheses concerning the interpretation of psychological phenomena for mathematical problem situations are explored. Several areas…

The author gives a method for involving students in developing and verifying elementary number theory hypotheses by studying areas and perimeters of primitive pythagorean triangles. (MN)

The opportunity for students to develop formulas that involve tangent lines to a circle and the Pythagorean Theorem and to use approximation and common sense is provided in a suggested distance-to-horizon problem. (MN)

Reviews the mathematical properties of algorithms and problems which can not be resolved by present methods in mathematics. (SL)