Directions are given for a game providing practice with multiplication combinations and for a game involving counting and number combinations. (DT)

An experimental task to determine the effects of materials and transformations on number concept development was administered to 120 educable mentally handicapped children from 8 to 10 years of age and 60 nonretarded kindergarten children. (Author/DB)

Helping children to bridge the gap between physical materials and symbolic representations is the focus of this article. Examples are drawn from numerical topics, with several hierarchies illustrated. (MNS)

The Cockcroft Report on English Schools recommends that all schools design their syllabuses and examinations on the assumption that all students will have access to calculators. How to use calculators sensibly to improve what is taught and how curriculum content may change are discussed. (MNS)

The study looked at the initial learning of decimal concepts at grades three, four, and five. Helping children understand the concepts of decimals prior to computational use is promoted as a major goal for elementary education. The investigation is seen to have provided insights that could be applied to instruction. (Author/MP)

The subtraction ideas presented are designed for elementary and junior high school children, yet are felt to be flexible enough to offer some challenge for high school students, particularly in algebra. (MP)

A different method of teaching students the basic addition facts is presented. If a child is able to conserve quantity, then the organized program designed to aid in the memorization of facts is possible. (MP)

A teaching sequence providing a smooth transition from concrete materials to the subtraction algorithm is presented. (MP)

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

One teacher's struggle with conveying a concrete realization of the subtraction algorithm to students leads to a discussion of elementary mathematics instruction in general. (MP)

This article offers specific strategies to diagnose and remediate difficulties students may have in learning multiplication facts. Analyzes strategies students use to go from a known fact to an unknown fact. The point is made that, for many students, the order of interpretation of a number fact may affect accuracy. (DB)

Describes a low-tech, hands-on activity to improve student understanding of irrational numbers. Each student creates a number line from adding machine tapes and uses a square and a precisely folded triangle as the only measuring device. (KHR)

The described activities give children an opportunity to use geometric ideas to reinforce arithmetic concepts and to use arithmetic ideas to generate geometric figures (both circles and polygons). (MNS)

Use of a microcomputer spreadsheet program to help students understand long division is described. An example of a problem with powers of 10 used with seventh graders is presented, with note of another lesson on decimals for grade 6. (MNS)

Why students have difficulty with a proof (such as Cantor's) is discussed, with the focus on proof by contradiction. Methods may fail due to the difficulty of the concept and lack of understanding of how students are thinking. (MNS)