Using various aspects of mathematical structure as unifying concepts is stressed. Specific examples are given based on the concept of equivalent fractions and on the addition property of equality. (LS)

A teaching sequence for the division algorithm is detailed. (MP)

How graph paper has been used to illustrate the algorithm for division of fractions is presented. The combined use of graph paper and an overhead projector can make the presentation even more convincing. A review of whole number division is recommended prior to the lesson. (MP)

The author promotes an earlier introduction of decimals than is currently standard practice in most elementary mathematics programs. Suggested activities and related skills are reviewed. (MP)

Activities are given to assist students in seeing a rationale for the difficult algorithms we teach for fractions. Both interpretations of fractions and operations with fractions are discussed. (MNS)

Prior studies indicate that, given time to develop their own algorithms, primary students will process multidigit addition or subtraction problems from left to right. Gives evidence to support that idea, describes methods of getting students to invent their own algorithms, and discusses advantages of child-invented procedures. (21 references) (MDH)

Compares the development of two students' understanding of addition and subtraction. One student's understanding is based on memorized rules and the other's on understanding the concept of place value. Discusses the effects of different goals for instruction and the importance of understanding place value. (MDH)