Discusses the formation of a conceptual framework for studying mathematics by stressing six principles. Instruction structured on these principles is illustrated and a curriculum for the first two collegiate years is outlined. (JP)

A duplicate of this article is in The Mathematics Teacher, November, 1972. For the abstract see se 506 987. (DT)

Uses the geoboard as an aid in developing an intuitive "feel for the relationship between sums of numbers in a two by two matrix. Numbers in the matrix are represented as "area numbers on the geoboard. (RP)

Presents a concept of the mantissa which is developed through the use of three theorems. The procedure described allows the student to develop a basis for understanding, as well as a method for finding the mantissa and characteristic of a logarithm. (LC)

Focuses on the mathematical activity generated by attempts to prove Euclid's Parrallel Postulate. (RP)

The author attempts to reconcile conflicting research regarding the effects of modern math courses on student achievement. (CP)

Reviews the learning theories of Robert Gagne and David Ausubel, and applies these theories to the three most common approaches to teaching division of fractions: common denominator, complex fraction, and inverse operation methods. Such analysis indicates the inverse approach should be most effective for meaningful teaching, as is verified by…