In this article, the third part of a series, the results of ab initio polymer calculations presented in part 2 are discussed. The electronic structure of polymers, symmetry properties of band structure, and generalizations are presented. (CW)

The article includes a discussion of counting and counting strategies. In addition, there are eight problem sets appropriate for use with groups of different age and ability levels. Suggestions are given for finding variations of the problems. (PK)

A training experiment with 30 mentally handicapped children tested two models of mental-arithmetic development. Children's initial responses to a mental-addition task appeared to be the product of a mechanical prescription. Errors appeared to be more errors of method than of recall. (MNS)

Presented is a rationale for the importance of estimation. Strategies used by good estimators, and teaching strategies for computational estimation are considered. (PK)

Argues that calculator activities, even in the early grades, can present situations in which basic mathematical thinking processes come into play. The activity described involves developing efficient calculator guess-and-test strategies and requires only an introductory notion of the four basic operations of arithmetic. (PK)

Describes an algorithm that provides more rapid convergence for more complicated forms of phase separation requiring the use of a digital computer. Demonstrates that this "inside-out" algorithm remains efficient for determination of the equilibrium states for any type of phase transition for a binary system. (CW)

The first aim in school might be to help children become more aware of the algorithmic processes they use; then, ensure that they can devise algorithms and define them. Many examples of how these aims can be met are given, including the use of calculators and computers. (MNS)

Five-frames are proposed as manipulative material to increase children's ability to identify the number of objects without direct counting. How to use frames and beansticks to construct basic facts without counting is discussed. (MNS)

Four worksheets for levels one-eight are included. Practice on addition, multiplication, fractions and decimals, and integers is provided through activities involving puzzling patterns. (MNS)

Presents concluding remarks to a symposium, "The Social Organization of Knowledge and Practice." Focuses on high aptitude of persons in everyday situations to solve problems and make decisions. Addresses three questions: (1) What happens when a problem-solver reaches a situation involving calculation? (2) How does learning transfer take place? and…

Forty-six junior high students were administered six tests after a variety of instructional units using PLATO and classroom instruction. Twenty-seven procedural errors in signed-number arithmetic problems were classified into two groups to facilitate investigating error changes at different times and designing remedial instruction. (BS)

This study added extraneous information and increased syntactical complexity to determine the relative importance of computational and reading abilities in solving arithmetic word problems. Analyzing tests of 200 sixth graders indicated the combined abilities accounted for 54 percent of the variance in solution accuracy. (BS)

Discussed are the roles played by anticipation, belief, and motivation in two young children's problem-solving activity. It is argued that a solver's beliefs and motivations are intimately related, and that the discussion of the two children's behaviors may have some generality. (Author/MNS)

The abacus method for instruction on addition, subtraction, and multiplication with integers is explained. How to represent the integers for each operation is detailed with words and illustrations. (MNS)

This section contains four worksheets for games on estimation. Impact, Crossfire, Fire One, and Fire Two each require the use of calculators to focus on place value, multiplication, or division. (MNS)