The examination by students of the associative property of a binary operation is used to illustrate how students can be involved in mathematical discovery. (MP)

Discussed are possible lessons for teaching the algebraic concepts of variables, rational expressions, and functions. (CT)

The operation of rounding is shown to lead into an investigation of an abstract mathematical system. Properties of the system are discussed and graphs of the rounding function are drawn. Some questions for discussion are given. (MP)

Allowing students to discover a winning strategy for this game is suggested as a way to introduce modular arithmetic. (MP)

An example is given of the discovery method of instruction applied in a remedial college algebra course. (DT)

This student discussion guide is intended to accompany "Discovery in Mathematics," a text for teachers. This guide is a part of the developing curriculum program that helps students to organize their mathematical experiences in the early school years. The materials in this booklet deal mainly with fundamental arithmetic and algebraic…

An algebra in which the basic operations correspond to lowest common multiple and greatest common factor is developed through questions which can be explored by the able high school mathematics student. (FL)

An activity leading to the discovery of a property of primes is suggested for encouraging algebra students to make nontrivial conjectures. (MP)

This article extends number bases to negative integers, then to positive rationals and finally to negative rationals. Methods and rules for operations in positive and negative rational bases greater than one or less than negative one are summarized in tables. Sample problems are explained and illustrated. (KM)

To discover a generalization from a pattern of data, students need to know how to analyze the data. This is a description of how high school students can find a formula to predict the number of spherical fruits in a piling by using differences. (JP)