Examples of four interviews are presented to serve as sample evidence in support of more comprehensive diagnostic procedures in assessing reliably and validly the weaknessess and strengths of learners. The search for computational errors is seen to go beyond standard paper and pencil tests. (Author/MP)

Work with recurring decimals provides pupils with an opportunity for exploration and examination of a wide variety of mathematical ideas and strategies. Examples of work done by one group of pupils who were presented with an opportunity to explore such decimals is featured. (MP)

Ways in which bead strings can be used for reinforcement and concept development are noted. After discussion on how to make bead strings, the material looks at: (1) prenumber concepts; (2) more than, less than; (3) conservation of number and numerals and numerousness; (4) addition and subtraction; and (5) place value. (MP)

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)