Describes a study which compares the abilities of 130 first graders in responding correctly to open (Computational) addition exercises to their abilities in responding to equivalent problems stated in the closed form. No statistical difference between levels of correct responses to opened or closed exercises was indicated. (PR)

The Wechsler Intelligence Scale for Children-Revised arithmetic subtest revealed a significant difference in performance between sixth graders with learning disabilities, including arithmetic, and Ss who were learning disabled in areas other than arithmetic. A significant main effect was associated with type of presentation/response behaviors. (CL)

It is argued that Macnamara's criticisms of Piaget's theory of number do not lead to Macnamara's conclusions about arithmetic instruction. These conclusions appear to be based on misconceptions about logic and logical theories of number. The misconceptions are discussed and an empirical rationale for the conclusions about arithmetic instruction is…

Discusses flaws in the reasoning behind a "new system" proposed for rounding numbers that was published in a previous issue of this journal. Concludes that the new system should be used only for numbers in which the nonzero digits following a dropped 5 have some significance. (JRH)

Mathematics is a uniquely human capacity. Studies of animals and human infants reveal, however, that this capacity builds on language-independent mechanisms for quantifying small numbers ([less than] 4) precisely and large numbers approximately. It is unclear whether animals and human infants can spontaneously tap mechanisms for quantifying large…

Divisibility tests for digits other than 7 are well known and rely on the base 10 representation of numbers. For example, a natural number is divisible by 4 if the last 2 digits are divisible by 4 because 4 divides 10[sup k] for all k equal to or greater than 2. Divisibility tests for 7, while not nearly as well known, do exist and are also…

Multiplication and division have in general been much more difficult to perform than addition and subtraction. Perhaps, if we could find some device for reducing multiplication and division to addition and subtraction, computational loads could be lightened. One such device is that of logarithms of course. This note outlines another such device…

Investigating the relationship between fractions and their equivalent decimal representations helps clarify to students that both representations stand for a single (rational) number on the number line. Since students are taught to perform computations with fractions and also to compute with decimals, performing these computations side-by-side…

The purpose of this study was to examine executive functioning in patients with Huntington's disease using an arithmetic word-problem-solving task including eight solvable problems of increasing complexity and four aberrant problems. Ten patients with Huntington's disease and 12 normal control subjects matched by age and education were tested.…

The telescoping sum constitutes a powerful technique for summing series. In this note, this technique is illustrated by a series of problems starting off with some simple ones in arithmetic, then some in trigonometry, famous families of numbers, Apery-like formulas, and finally ending with a class of problems that are solved by computer.

This article defines the generalized mean and shows how it relates to such statistics as the arithmetic, geometric and harmonic means.