Four three-year-old girls were studied in seven sessions during a three-month period for their performance on rote and object counting tasks. Two exhibited behavior consistent with underlying stable-order and uniqueness principles. (MNS)

A card trick that can be explained and justified using first-year algebra is presented. It illustrates the power of mathematics to unmask seemingly complex situations. (MNS)

The lesson details an approach to teaching positive and negative numbers which uses number pairs and generates inverses that initially avoid any mention or use of negative signs. The material moves pupils from development of key concepts to the use of more standardized notation for number operations. (MP)

A series of problems is presented that (1) focus on certain kinds of numbers or (2) emphasize a specific concept of number theory. Several are appropriate for extensive investigation with a computer. (MNS)

This study is an examination of developmental changes in children's use of pointing gestures to achieve an accurate count. Based on the data gathered, it is argued that the functional relation between the recitation of number names and children's pointing gestures in counting changes over the course of development. (Author/AL)

The National Assessment of Educational Progress (NAEP) has completed its second mathematical assessment. This article focuses on the results from the second assessment of 9 year olds and 13 year olds; major results of the content areas are summarized and examples of the data are given to support the conclusions. (Author/MK) Aspect of National…

Critics assert that Piaget's tests seriously underestimate operational thinking by failing to consider experimenter and presentation variables. This experiment studied the impact of these social influences on number conservation performance. Subjects viewed videotapes in which the task was presented by an adult or by puppets. Presentation mode…

Included are nine brief notes on various aspects of infinity. These are an attempt to stimulate and organize the thinking of teachers and others who acknowledge the role notions of infinity play in mathematics and in children's thinking. (MK)

Attention is drawn to an ancient Greek method for finding the least common multiple (LCM) of two numbers. A link is established between this method and a well-known method of obtaining the highest common factor (HCF) numbers. This leads to consideration of some relationships between HCF and LCM. (Author/MK)

The theory of unary and binary operations are discussed and illustrated with examples from school mathematics. Presentations of selected inverse operations are made and attention is drawn to certain "typical" problems that occur during instruction and learning of these concepts. (MP)

Activities designed to aid pupils explore the Fibonacci sequence are presented in worksheets. (MP)

Novel practice exercises for addition and subtraction using a special number puzzle called a number chain are suggested. (MK)

An experimental program using the calculator in third, fourth, and fifth grades is described. Three example lessons are included, on (1) subtraction with regrouping, (2) estimation, and (3) number theory: Quadratics. (MK)

Examples given for uses for the calculator exchange key include: generation of the Fibonacci sequence and geometric series, determination of square roots, and the chief use of the function, which is to interchange the numerator and denominator of a fraction. (MK)

Presented are suggestions for teaching absolute value using five different definitions of the concept. (MK)