An example is presented that can be used to introduce the study of limits of sequences through recursive formulas yielding square roots. (MP)

A proof is given of the irrationality of the square root of 2 which depends on notions of terminating and repeating decimals. (MP)

A class's struggle with the computer solution of a nontrivial problem is related. The use of algorithms allowed a trial-and-error approach.

Topics discussed include: maximizing the volume of a box, finding different size squares on a geoboard, the angles formed by the hands of a clock, and questions related to three consecutive integers. (MP)

An argument is given for providing children with visual images for number concepts that they can internalize and which can aid understanding of numbers and their relations. (MP)

Topics discussed are: triangular numbers; three proofs of the surface area of a sphere; reverse notation; highest common factors; square roots from a graph; and clock geometry. (MP)

Activities are suggested for setting up a mathematics center for a week or more at a time. The activities relate to weight, counting, puzzles, length, graphing, and ordering. (MP)

An activity is described that is designed to give students a chance to learn about speed by calculating their own running or walking speed and the speed of cars. (MP)

This paper discusses the process of investigating a mathematical situation, making conjectures, formulating an equation, then using mathematical induction to show the result is valid. Several examples appropriate for secondary school level are given. (DT)

A procedure for recording the prime factors of a composite number is explained. (DT)

Activities are described in which the calculator is used for extending students' knowledge of place value and of basic arithmetic operations. (DT)

Conjectures about triangular arrangements of nine digits are stated and proved. (DT)

A method is given for determining what months will have a Friday the thirteenth for any given year. (DT)

Investigates the problem-posing abilities of third-grade children who displayed different profiles of achievement in number sense and novel problem solving. Concludes that children had difficulties in posing a range of problems in formal contexts in contrast to informal contexts, and children of different achievement profiles displayed different…