Ben, a good mathematics student, participated in a seven-week study. Describes three tasks that reflect impact of textbooks, real-life connections, and mathematical symbols. Shows that Ben's notion of one-half was task-dependent, concrete, and based on physical actions. (NI)

A study interviewed 6 grade-6 students after participation in 21 lessons on basic concepts of fractions and decimals to determine how different children construct rational number concepts. Discussed the formation of the key concept of equivalent fractions based on student responses to interview questions. (MDH)

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 ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

Fourth-grade students' understanding of the order and equivalence of rational numbers was investigated in 132 interviews during an 18-week teaching experiment. Six children were instructed individually and as a group at two sites, with instruction relying heavily on manipulative aids. Strategies used to compare fractions were identified. (MNS)

Analyzed were 19 preservice teachers' understanding of division in 3 contexts. The teachers' knowledge was generally fragmented, and each case of division was held as a separate bit of knowledge. (Author/YP)

Recommends conducting interviews with students in order to grasp their understanding of fractions and provides interview questions. Presents results of a study using those interview questions and concludes student responses fell into three main categories: (1) described a mental image of an object; (2) drew a model of the fraction using a circle…

A study explored the effectiveness of an instructional approach designed to help students establish connections between their understanding of the decimal system and the stardard symbols and procedural rules used to solve decimal problems. Ten children each in grades 4 through 6 participated. They were individually interviewed prior to and six…

This paper presents results from a study of 19 teacher education students' knowledge of mathematics and discusses an analytic framework for examing and appraising teachers' and prospective teachers' subject matter knowledge. Participants in the study were 10 elementary education majors and 9 mathematics majors or minors who were preparing to teach…