Cuisenaire, Dienes and traditional methods of teaching mathematics were compared by pre- and posttesting pupils in British junior schools during a three year period (1961-63) on mechanical and problem arithmetic, concept knowledge and attitudes. Details of the varied experimental design are given in addition to data and interpretation. (JP)

Finding patterns in the relationship between the number of sides in a polygon and the total number of diagonals is used as vehicle to discuss discovery learning. (DT)

A method of showing the meaning of decimal fraction without using fraction words or notation. One technique described in detail uses large squares, strips, and small squares; using the metric system and decimal coinage is also suggested. (DT)

Describes a method utilizing the library system to introduce children to mechanical and mental arithmetic. (RP)

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)

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

Three methods of proof are analyzed as a means of aiding teachers in presenting arguments for certain number concepts. These are: (1) proof by contradiction, (2) Venn diagrams, and (3) method of exhaustion. (MP)

A "flipping" clown figure can be used on a number line to help students conceptualize operations using negative numbers. (SJL)

Shows how all primitive Pythagorean triples can be generated from harmonic sequences. Use inductive and deductive reasoning to explore how Pythagorean triples are connected with another area of mathematics. (KHR)

Presents activities to find Pythagorean triples using the TI-83, a graphing calculator. (KHR)