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,…

Different methods of subtracting are described; the equal additions and the decomposition methods are discussed in detail. (DT)

Four algorithms for subtraction are described: borrow and pay back,'' equal additiions, shopkeepers' subtraction,'' and decomposition. (DT)

This article explains the generation of Kaprekar's constant in terms that upper elementary pupils can understand. The procedure is explained and the result proven. This is an example of a new, interesting problem for students that gives them drill in subtraction at the same time. (LS)

An outline of the way that fractions might be presented in ninth grade algebra is given, and implications for elementary school instruction are noted. (DT)

The author advocates the classroom consideration of new algorithms as a means of leading students to make original hypotheses. He discusses a multiplication algorithm based on the differences between squares. (SD)

The study's purpose was to investigate the differential effects on the achievement of second-grade students that could be attributed to three instructional sequences for the learning of the addition and subtraction algorithms. One sequence presented the addition algorithm first (AS), the second presented the subtraction algorithm first (SA), and…

The long division algorithm approached as repeated subtractions is explained. (DT)

Using negative digits in writing numerals and in calculation is explained. This is the second article in the series; for the first, see Vol. 1, No. 7, Nov., 1972, pp. 8-9. (DT)

An analysis is made of the extent to which specific division skills are retained from fourth to fifth grade, with results showing a significant loss in ability during the summer. Implications for instruction are included. (DT)

The purpose of the study was to compare the results obtained from a group of fourth-grade students taught to add and subtract rational numbers through the use of field postulates and other properties of whole numbers with fourth-grade students taught by a standard method using objects and the number line. Eight classes of 30 students each…