Details of an instructor's attempt to solve a problem in combinatorics taken from a textbook used by some of his students are presented. It is felt the material raises a number of significant points about problem solving and mathematics. Teachers are encouraged to put themselves in such situations. (MP)

Masters of three worksheets are provided which require students to name selected polygons, compute areas of triangles, rectangles, squares, and trapezoids, and compute cost per square unit. (MK)

Three alternative methods of finding averages of two numbers are presented. (MP)

An introductory multiplication lesson, used successfully with second graders, is detailed. The method takes advantage of prior knowledge acquired in a geometry unit of study. The lesson is seen to have potential for other grades teaching multiplication for remedial work, and explaining the commutative law. (MP)

Ideas are presented regarding: (1) unique learning activities for students who have difficulty with operations with signed numbers; (2) a mathematical inspection of a unique card trick that can be expressed as an equation; and (3) sketching of graphs of composite trigonometric functions. (MP)

The use of money to teach mathematical topics such as fractions, percents, decimals, and nondecimal numeration is encouraged. (MP)

The teaching of numeral representations other than decimals is seen as a necessary and important step in the education of pupils in computing. Basic arithmetic procedures for binary, octal, and hexidecimal bases are discussed. (MP)

Problems focusing on number theory that can make good use of the calculator in discovering and proving simple theorems are proposed. The focus is on the properties of subtracting the smaller of a three digit number and its mirror number from the larger in a process that leads to zero. (MP)

Activities and manipulative materials that teach pupils regrouping, also known as borrowing or carrying, are reviewed. Several examples of typical student errors and the reasons for these mistakes are outlined. (MP)

Learning activities using a two-pan balance to teach the concept of equality are described. Construction of a poster board balance is illustrated. (MP)

Some patterns in prime numbers and their implications for general theorems are presented. Much of the material is taken from "The Strong Law of Small Numbers," an unpublished paper by Richard Kenneth Guy. (MP)

Investigates which aspects of the mother behavior in interaction would be related, and in what way, to the child's acquisition of number conservation as a criterion measure of later cognitive development. (MP)

Described are graphing activities which can be instrumental in introducing the mathematics concepts of counting, sorting, grouping, and comparing on the primary level. On the intermediate level, these activites can be used to introduce collecting and sorting unorganized data, and creating graphs to represent the data. (Author/TG)

Described are activities and games incorporating a technique of "one step" which is used with children with learning difficulties. The purpose of "one step" is twofold, to minimize difficulties with typical trouble spots and to keep the step size of the instruction small. (Author/TG)

Rule learning in mathematics among elementary school children is described. Samples of dialogue between experimenters and children are presented, and the concept of rule learning is described in relation to two subgroups, gifted children and "regular" ones. (MP)