This paper is a translation of a report on two Swedish investigations concerning children's lack of understanding of the quantitative value of numbers (specifically, decimals and fractions). (MN)

This study of seventh graders investigated the use of the calculator in learning conversion algorithms among fractions, decimals, and percents. The calculator was successful with some topics but not with others. (MP)

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)

Findings from a study with first-grade children on addition and subtraction help make a case for a conceptual rather than a mechanized approach to the operations. How base ten blocks were used in the program is illustrated. (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)

The results of this study indicate no significant differences on two achievement tests and one aptitude test between calculator and non groups. Nevertheless, the investigator notes several advantages of using the calculator. (MK)

This report summarizes a project to develop computational estimation materials for students in grades 6, 7, and 8. In chapter 1, the need for estimation skills is discussed and the goals of the project are stated: to develop a carefully sequenced set of lessons, activities, and maintenance work on estimation with whole numbers, fractions,…

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

What research says about the learning and teaching of decimal fractions is summarized, with some instructional strategies and activities to improve learning suggested. (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…

Research findings on decimals and money are briefly summarized, followed by suggestions for classroom use. (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 report illustrates procedures of item construction for addition and subtraction examples involving decimal fractions. Using a procedural network of skills required to solve such examples, an item characteristic matrix of skills analysis was developed to describe the characteristics of the content domain by projected student difficulties. Then…

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 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)