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,…

An algorithm for long division is presented that involves only addition and subtraction. (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)

The author describes a new graphing algorithm for computing probabilities, and presents problems for these algorithms for use in the classroom. (SD)

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)

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)

In spite of current sentiment to the contrary, the wellsprings of mathematics are not utility and relevance, but creativity, imagination, and an appreciation of the beauty of the subject. This has implications for the teaching of mathematics. (PK)

A method is described for working multiplication problems by counting on fingers. (DT)

How graph paper has been used to illustrate the algorithm for division of fractions is presented. The combined use of graph paper and an overhead projector can make the presentation even more convincing. A review of whole number division is recommended prior to the lesson. (MP)

After an introduction including a brief history of measurement, conversion of units within the customary system, within the metric system, and from customary to metric and vice versa are discussed. A fraction/multiplication system is introduced to teach correct alignment of units of measurement and to direct proper multiplication and division of…

Advantages of using flow charts are listed. Flow charts for adding and subtracting fractions and for polynomial division are provided. Rules for constructing flow charts are given. (DT)

Activities are described in which number patterns in two-digit multiplication exercises are investigated. (DT)

More mental computation and organized and enjoyable activities to practice such skills are advocated. Suggestions for brief sessions involving challenging questions and quick recall of number facts are presented. The author presents and comments on several sample lessons designed for a wide range of student abilities. (MP)

Algorithmic and investigative approaches to mathematics are compared and discussed. Their mutually contradictory spirit is explored. Examples of the application of each method to a mathematics problem are presented. (CW)