The message of this article is that there are many types of problems ordinarily requiring advanced techniques or special insight to solve which can now be done as simple programming exercises on inexpensive programmable calculators. Several examples appropriate for the secondary school curriculum are given. These are: (1) evaluating polynomials;…

The abstracts and critical analyses of research in this document were prepared and compiled to add to the fund of information on the effects of hand-held calculators on achievement and learning. Since many persons find it difficult to secure original copies of all research studies, the expanded abstracts should provide specific information…

Many problems and activities which can be worked with a calculator are contained in this booklet. The problems include: pattern recognition, combinations of operations, estimation, squares and square roots, rate problems, area, and volume. Chapter topics include: getting to know the calculator, single-step problems, using formulas, and…

The twenty-two essays on problem solving included in this publication give ideas and examples for use in the classroom at all levels of instruction. Topics discussed in the essays include but are not limited to: problem posing, clues from research, story problems, calculators, textbook problems, and measuring problem solving. Polya's heuristics as…

This report is concerned with the observation that many teenagers and adults are unable to apply arithmetic even when they know how to perform the operations. It is speculated that this is probably due to not having been taught when to use the fundamental operations. Examples of types of "real" problems which require the various…

The norm-referenced score scale used by the National Foundation for Educational Research (NFER) is described. The usefulness of standardized scores is explained by a simple numerical example, and the formulas and computations are shown for calculating a mean, a standard deviation, and a deviation or z score. The need for a representative sample is…

This paper is divided into three parts. Part I connects the reality of the classroom with the idealism which arises from some of the problem solving literature. It is argued that a broader concept of problem solving is needed to provide a perspective for bridging the gap between the conceptions of problem solving in the literature and typical…

This collection of reprints from the IDEAS section of the "Arithmetic Teacher," has been selected from those activities appropriate for students in grades 4 through 8. The selections have been reprinted just as they originally appeared in the journal. The ideas are grouped under the headings computation, fractions, problem solving, geometry, and…

The statistical methods presented in this workbook focus on the display of central tendency, statistical tests, and correlation. Chapters 2, 3, and 4 consist of worksheets, each of which provides step-by-step instructions for calculating and interpreting a particular statistical method. The introduction to each worksheet explains how and when to…

Presented is a budgetary decision model developed to aid the executive officers in arriving at tentative decisions on enrollment, tuition rates, increased compensation, and level of staffing as they affect the total institutional budget. The model utilizes a desk-top programmable calculator (in this case, a Burroughs Model C 3660). The model…

An analysis of the quantitative processes underlying conservation of quantity is presented. Models of three quantitative operators--subitizing, counting, and estimation--are derived from adult performance in quantification tasks, and some features of the operators are described. The emergence of conservation is described in terms of the…

Research on error patterns associated with whole number computation is reviewed. Details of the results of some of the individual studies cited are given in the appendices. In Appendix A, 33 addition errors, 27 subtraction errors, 41 multiplication errors, and 41 division errors are identified, and the frequency of these errors made by 352…

Two questions were investigated in this study: (1) How did the computational proficiency of sixth graders who had one year's experience with Developing Mathematical Processes (DMP) materials compare with an equivalent group of students who used the usual textbook program; and (2) What occurs when sixth graders study algorithms as sequences of rule…

The construction of tables of numbers is discussed as a learning activity that involves work in such things as reciprocals, calculators, formulas, patterns, discovery, prime numbers, and other types of numbers. (MP)

A problem from number theory is used to illustrate the use of the computer and programable calculators in solving problems. Programs are included. (MP)