Two difficulties that students have in computing with fractions are idenfitied. Then a procedure is described, stressing the identity element, that resolves these difficulties and increases students' understanding and retention. (MNS)

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)

Described is a student-discovered algorithm for solving a problem involving division by a fraction. (RS)

Reviews the historical development of subtraction algorithms used in the United States. Discusses different algorithms used and developed throughout history that had a major impact on the way subtraction is taught today. (Contains 22 references.) (ASK)

Difficulty levels of 168 randomly generated multiplication problems were obtained by testing 238 fifth-graders. Variables concerning the number of operations, digits carried, and magnitude of the digits were defined, and a least-squares procedure was used to construct structural models accounting for 60-70 per cent of observed problem difficulty…

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…

A concrete approach to subtraction problems with minuends to 19 is presented. (MP)

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

Computational algorithms from American textbooks copyrighted prior to 1900 are presented--some that convey the concept, some just for special cases, and some just for fun. Algorithms for each operation with whole numbers are presented and analyzed. (MNS)