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)

The format of digits in liquid crystal displays (LCDs) on calculators and watches can motivate some simple investigations appropriate for school mathematics. Several sample problems or investigations are provided. (MK)

Samples of children in English secondary schools were given a test on integers, as part of the investigation into children's understanding of mathematics undertaken by the Concepts in Secondary Mathematics and Science (CSMS) project. This is a brief report of the performance of the third-year children. (Author/MK)

Noitcarf numbers provide a simulation activity that allows teachers or education students to gain an understanding of the feelings of students who are taught mathematics by a "rules" method. They are actually an abstract presentation of operations with fractions. (MK)

An activity is presented which provides a novel approach to number patterns, experience in following an unusual algorithmic procedure, and practice in systematic search techniques and basic facts. (MK)

Provides data incongruent with Piaget's idea of a concrete operational stage. Shows no clear-cut termination of preconceptual thinking and no simultaneous conceptual development in the three content areas (number, space, and time). (Author/RL)

The importance of place value is discussed. Examples illustrating place value in addition and subtraction are given. (MK)

An activity is described in which PI is approximated by measuring the perimeters of regular polygons inscribed in a unit circle. (DT)