Checklist items are suggested to help teachers diagnose strengths and weaknesses of students who have difficulty learning mathematics. Tasks involve the use of manipulative aids to determine such concepts as grouping, counting, quantity, and estimating. (CL)

Models for developing addition, subtraction, and multiplication with integers are given. (MNS)

Discoveries of Charles Babbage in the 1800s are described. Origins of the difference engine, his calculating machine, the principles of computation applied to tables, and the design and construction of his engine are included. (MNS)

Presents an elementary physics problem, the solution of which illuminates physical meaning and its relation to real, imaginary, and complex mathematical quantities. (JRH)

Understanding rational numbers is often an elusive goal in mathematics. Presented is an approach for teaching rational numbers that has been used with many preservice and elementary school teachers. With some adaptation, the approach could be used with secondary school students. (RH)

A method for making divergent series converge is described. Proofs of the procedure are presented. (MNS)

A general method and a variant for divisibility are presented, with specific examples. (MNS)

The use of fingermath, a form of arithmetic computation with the fingers, is compared to use of the abacus in helping visually impaired and blind students develop mathematic concepts. Fingermath is explained to be more concrete, simple, and accessible. (CL)

An interesting, alternative proof for an arithmetic series is developed in detail. (MNS)

Two algorithms are developed for finding the square roots of numbers. One is based on the rule that x square is the sum of the first x odd numbers; the other is algebraic. (MP)

A teacher describes an activity designed to help children understand the number concepts of the basic addition facts with sums of 11 or greater. (CL)

A study of a class of numbers called 'Good numbers' can provide students with many opportunities for investigation, conjecture, and proof. Definitions and proofs are presented along with suggested questions. (MNS)

Demonstrated is how the concept of equivalence classes modulo n can provide a basis for solving a wide range of problems. Five problems are presented and described to illustrate the power and usefulness of modular arithmetic in problem solving. (MNS)

A math strategy using an "add-card" which illustrates simple addition facts was originally developed for learning disabled students but was also successfully used with mildly retarded students. (CL)

Two traditional presentations introducing the calculus of exponential functions are first presented. Then the suggested direct presentation using calculators is described. (MNS)