Studies five-year-olds' relative number judgements of small and large number displays with and without perceptual aids. Children were found to respond to local rather than global density differences and to benefit from the provision of perceptual aids on both small and large number displays. (Author/AS)

The importance of teaching computational estimation is discussed, with note of its increased significance because of widespread use of calculators and the need to develop number sense. The reason for its failure to be taught is traced to the multiplicity of methods, and some detailed suggestions are therefore presented. (MNS)

Activities are suggested for using the hand calculator as a complement to any mathematics program. The activities focus on developing skills for using the calculator, exploring basic arithmetic operations, understanding algorithms, mental calculation and estimation, and problem solving. (DT)

The teaching and learning in algebra has been much debated. Traditionally early algebra has relied heavily on arithmetic. Recently our focus has changed to teaching algebraic thinking with arithmetic thinking. This paper explores the models that assist young students generalise the patterns of arithmetic compensation. A teaching experiment was…

A first grade teacher in a rural elementary school in upper East Tennessee observed that her students needed a better way to improve their computation skills than those of traditional instructional methods. The school system's new Mathematics textbook was correlated with commercial Mathematics software. The teacher wanted to find out if using this…

Magic squares are used both as a vehicle for arithmetic drill and the development of mathematical concepts for second-grade students. By searching for patterns within the squares, additional number concepts are developed along with the concept of symmetry. (JP)

The Cockcroft Report on English Schools recommends that all schools design their syllabuses and examinations on the assumption that all students will have access to calculators. How to use calculators sensibly to improve what is taught and how curriculum content may change are discussed. (MNS)

The subtraction ideas presented are designed for elementary and junior high school children, yet are felt to be flexible enough to offer some challenge for high school students, particularly in algebra. (MP)

Four basic types of student errors in computation are noted and described. These are: (1) mechanical, (2) careless, (3) conceptual, and (4) procedural. It is felt many teachers deal with all errors as if they were of the unhabituated procedural type, with not enough attention given to other possibilities. (MP)

This essay discusses the possible types of uses of calculators in the elementary school, citing several publications, articles, and research studies. (MP)

Factors suggested as accounting for poor problem solving are inadequate programs for teaching problem solving, choice of operation, and the number of problems. (MP)

This article offers specific strategies to diagnose and remediate difficulties students may have in learning multiplication facts. Analyzes strategies students use to go from a known fact to an unknown fact. The point is made that, for many students, the order of interpretation of a number fact may affect accuracy. (DB)

Discussed are the background and implementation of a method of teaching fractions to primary children referred to as "The Visual Concept of Fractions." The advantages and criticisms of the use of this method are stressed. (CW)

Seven junior high students with educable mental handicaps were trained to solve four-column subtraction problems involving regrouping. Results in performance favored calculators over pencil and paper, with rehearsal and visual cues influencing performance for only one student. With calculators, subjects' performances were equivalent to a…

Activities that illustrate a problem-solving approach to teaching grouping symbols, such as parentheses and brackets, are described. Suggested exercises, answers to those exercises, and variations of this activity are included. (KR)