Academic scholars face a difficult challenge when attempting to grasp the intricate world of mathematics. The complexity of mathematical concepts often lies hidden beneath layers of formulas and procedures, obscuring their true essence. Traditional educational resources often fall short in conveying the profound meaning behind these concepts,…

Suggestions are given for teaching flowcharting at the elementary school level. A short list of sources for free materials on computers is included. (DT)

The method described here converts a given problem in a base other than ten to a related problem in base ten, solves the related problem in base ten, and converts the answer back to the original base. Limitations are discussed. (MP)

Outlines various subtraction methods, such as the decomposition method, equal-addends method, and low-stress algorithm. Describes a subtraction method by addition of complements. Discusses the advantages and disadvantages of the method. (YP)

Described are two methods of calculating developed by the Dutch WISKOBAS Project: addition and subtraction with a loop abacus and multiplication using a grid model. (MP)

Renaming fractions with the dot method is described with illustrations. It can be used to introduce renaming at the manipulative level in a meaningful way prior to moving to a more abstract level where prime factorization will be involved. (MNS)

This article discusses the use of concrete materials as conceptual models which serve as references for later learning of algorithms. (DT)

Three alternative methods of finding averages of two numbers are presented. (MP)

These three brief articles concern problems students encounter in solving simple linear equations, children's conceptions of number, and the distinction between adding objects and adding numbers as illustrated by students' problems with Euler's formula. (SD)

An algorithm is provided for generating as many desired digits in the decimal representation of a rational number on a calculator. It may be used whenever the number of digits displayed on the calculator exceeds the number of digits in the denominator. (JT)

Students who were unsuccessful in performing long division were taught to use a successive subtractions algorithm. (SD)

The author argues that secondary-school teachers need to be more aware of the content of primary level mathematics work. Citing an algorithm, he discusses the issue of basic skills in relation to the increasing use of calculators. (SD)

Various algorithms used in addition, subtraction, and division problems were identified. The percentages of people in the National Assessment survey populations using each method are reported, as are the percentages of those using the most popular methods who answered correctly. Implications for instruction are discussed. (SD) Aspect of National…

The author develops a four-stage model for concept-internalization. The stages are: (1) concrete structure; (2) linguistic structure; (3) algorithm; and (4) mastery. The model is related to teaching methods and the teaching of long division is examined in detail. (SD)

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…