Establishing and maintaining the desirable kind of balance between meaning and computational competence is the subject of this reprint from a 1956 issue of the journal. Sources of the dilemma and suggestions for solution are discussed. (MNS)

The history of mental computation in the elementary school curriculum is briefly described, followed by discussion of the benefits of mental computation. How thinking skills are enhanced is then illustrated. (MNS)

Mastering the basic number combinations involves discovering, labeling, and internalizing relationships, not merely drill-based memorization. Counting procedures and thinking strategies are components, and it may be that using stored procedures, rules, or principles to quickly construct combinations is cognitively more economical than relying…

The author first corrects Baroody's description of the network retrieval model for basic number facts, in which facts are stored in memory and retrieved as needed. He then indicates weaknesses in Baroody's argument. (MNS)

Discusses four ways in which subtraction is more difficult than addition: (1) verbal solutions do not always parallel object solutions; (2) methods may interfere with each other; (3) special problems exist with subtraction on the number line; and (4) subtraction has multiple situational interpretations. (MNS)

Suggestions are given concerning the use of the pocket calculator for computations that are too trivial to be processed by a computer but too time-consuming for manual calculation. Several examples from arithmetic, algebra, trigonometry, and calculus are included. (DT)

This critique focuses on Gagne's attempt to apply information-processing theory to mathematics education, noting that this distorts what it means to learn mathematics. This is discussed with specific illustrations. (MNS)

Lessons are suggested which involve dice in the instruction of various number concepts. Activities are presented under: (1) Early Number Concepts; (2) Meaningful Addition and Subtraction; (3) Place Value Practice; and (4) Extensions for the Intermediate Grades. The primary advantage of dice is their adaptability to student ability levels and…

It is noted that defining subtraction independently of addition through use of physical objects can help one to illustrate the non-commutativity of this operation. Lack of awareness of the importance of the order of the digits may be a primary cause of errors in compound subtraction. (MP)

An exploration approach with calculators that promotes student investigation and development of mathematical processes and concepts is highlighted. The presentation helps to highlight the enormous potential of calculators to facilitate new and imaginative approaches to certain areas of number work, and shows how student interest is promoted. (MP)

Pupil difficulty with understanding mathematical sentences is viewed as a problem with reading comprehension. Suggestions are made for ways to help children over the "missing-addend hurdle." The focus is on an educational game that has been used successfully to get students to focus on the meaning of mathematical sentences. (MP)

A subtraction algorithm that does not involve borrowing is presented and called the residue method. It has been taught in junior and senior high school classes and preservice and inservice classes for teachers. The method has helped in classes where arithmetic in other bases is presented. (MP)

The use of graph paper to outline arrays of multidigit multiplication problems is promoted. (MP)

The article describes the Mental Mathematics System, a number of formulas designed to develop mathematical skills in elementary and junior high school gifted and talented students. Formulas are provided for multiplication. The formulas for mental mathematics are noted to promote student interest in the subject. (SBH)

It is suggested that the reasons for teaching the standard written algorithms for calculations are not out of date. Alternative algorithms, such as mental algorithms, calculators, and nonstandard written methods, are discussed. (MP)