Discusses overall mental computation achievement and limits discussion to strategies middle school students used when computing with whole numbers, decimals, and fractions. Suggests that the development of conceptual knowledge of numbers is an important prerequisite for the understanding of mental computation procedures. (Contains 31 references.)…

The mechanisms, images, and language needed for the development of rational-number ideas are briefly discussed. Such ideas are sophisticated and different from natural-numbers ideas. (MNS)

Questions about teaching rational numbers are discussed, dealing with when to teach the meaning of fractions and of decimals, when and how to teach computation with fractions and with decimals, and other issues. (MNS)

The purpose of this study was to assess the ability of students in grades 6 and 7 to order rational numbers in both decimal and fraction form, including the identification of their thinking strategies. Implications for instruction are included. (MNS)

The approaches taken by two elementary school teachers in using computers as tools to stimulate and guide mathematical thinking are described. One had students design a BASIC program for counting; the other used demonstration programs to develop ideas about fractions and decimals. (MNS)

Research on fractions and decimals is reviewed. Understanding is vital, and thus children need experiences with concrete materials for the various interpretations of rational numbers. (MNS)

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)

Discusses area models that can be used in grades three through nine, showing how the model generalizes from discrete situations involving the arithmetic of whole numbers to continuous situations involving decimals, fractions, percents, probability, algebra, and more advanced mathematics. (14 references) (MDH)

It is suggested that elementary school students find rational numbers troublesome because some teachers have an inadequate understanding of rational number concepts and poor facility with rational numbers skills. How to help them overcome difficulties, develop concepts, and know what topics to emphasize are discussed. (MNS)

The conceptual difference between understanding and algorithmic performance is examined first. Then some dilemmas that flow from these distinctions are discussed. (MNS)

An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

Division of fractions and division of decimals, both troublesome, are discussed in relation to helping students learn well and retain what they have learned. A strong conceptual base, mastery of related concepts and skills, and meaningful development are stressed. (MNS)

Decimal numbers have become an increasingly important topic of the elementary and junior high school mathematics curriculum. However, national and state education assessments indicate that students have incomplete and distorted conceptions of decimal numbers. This paper reports initial data from a two-year project designed to elicit and describe…

This brief report focuses on the cognitive level of decimal problems in 16 textbooks. Activities at the application level are included, but seldom are higher-order intellectual behaviors found in the books. (MNS)

The process of transition from a novice's state to that of an expert, in the domain of decimals, is described in terms of explicit, intermediate, and transitional rules which are consistent yet erroneous. Data from students in grades 6-9 are included. (MNS)