This publication, designed to help teacher educators profit from the experience and wisdom of colleagues, brings together articles from "The Arithmetic Teacher" on preservice elementary school mathematics teacher education. This collection of articles has two specific purposes. One is to serve as a reminder of the broader issues and concerns that…

Teachers can partially remedy misconceptions and anxiety about mathematics by incorporating a historical perspective into mathematics teaching. Numerous examples of how this can be done are presented, along with ideas illustrating the growth and evolution of mathematical ideas. (MNS)

Two alternatives are given to the decomposition and equal addition subtraction algorithms. (MK)

Four ideas for the teaching of mathematics topics are suggested. The suggestions are: "To Prove or Not to Prove--That Is the Question"; "Fun at Christmastime"; "A Simple Technique for Factoring Trinomials"; and "An Alternate Method for Factoring" Quadratic Trinomials." (MK)

The author feels teaching division of fractions is worthwhile because it will help students understand other algorithms. (MK)

This article reviews four ways to approach percent problems, discusses percents of increase or decrease, and makes some suggestions for improvement in the teaching of percent problems. (Author/MK)

Three short essays provide teaching suggestions for lessons on base two, order of operations, and ratios used to motivate a number of mathematical ideas. (MK)

Four problems are presented and solutions using a calculator are illustrated. (MK)

A four-step sequence of desirable student cognitive behaviors is described and discussed. Teaching implications are noted. (MK)

Practical tips on the teaching of various secondary mathematics topics are given. Topics include geometric concepts related to circles, mathematical properties and procedures illustrated with a scrabble game, and the limit concept and infinity. (MK)

How the concept of function sheds new light on one of the central tasks of algebra, that of solving equations, is discussed. Many specific examples are presented, and a theoretical basis is included. (MNS)

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)

The purpose of this article is to stimulate a discussion about the teaching of algebra. It seeks to raise questions which are more fundamental than those so far generated by the manipulative skills debate. (Author/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)

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