A multiple habituation paradigm was used to determine whether 10- to 12-month-old infants were able to discriminate between visual arrays differing only in their numerosity. (Author/RH)

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…

A reply by Macnamara to Brainerd's criticism of the Macnamara (1975) article analyzing Piaget's theory of number. (JMB)

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)

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…

A study is conducted to prove Kaprekar's conjecture with the help of mathematical concepts such as iteration, fixed points, limit cycles, equivalence cases and basic number theory. The experimental approaches, the different ways in which they reduced the problem to a simpler form and the use of tables and graphs to visualize the problem are…

Recent work has investigated children's developing understanding of the anatomical locus of identity. In two studies, we extend this work by exploring the role of the mind as opposed to the brain in children's conceptualization of identity. In Experiment 1, an analysis of natural language indicated that adults use the term mind more frequently…

Seven studies explored the empirical basis for claims that infants represent cardinal values of small sets of objects. Many studies investigating numerical ability did not properly control for continuous stimulus properties such as surface area, volume, contour length, or dimensions that correlate with these properties. Experiment 1 extended the…

In this note, using the theory of Pell equation, the authors discuss the integrity of certain series involving generalized Fibonacci and Lucas numbers.

A whimsical mathematics event for children and adults, derived from Lewis Carroll's Alice's Adventures in Wonderland, was held at the Providence Children's Museum in Rhode Island. NCTM's Standards were the basis of all the activities. (Contains 10 figures and 1 table.)

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

This article describes how the story of Alice in Wonderland helps students understand the operation of multiplying by a rational number less than 1 and related aspects of ratio and proportion. Included with this article is a "How Tall Is Alice?" Worksheet. (Contains 1 table and 6 figures.)

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…

Children's literature can play a significant role in integrating math and science concepts into real-world applications. One particularly delightful selection is "Cucumber Soup" (Krudwig, 1998). This book can create a context--making cucumber soup--for weighing and for a real-life on adding fractions. This kind of learning context takes children…

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…