This study focused on analyzing children's difficulties with two-step mathematical word problems. Seventy-one fifth-grade children in Puerto Rico were individually observed solving five problems. Two of these were two-step problems; the remaining three were one-step problems with the same mathematical structures as the components of the two-step…

This study sought to determine if success and continuance in an accelerated high school mathematics program could be predicted, and which identifying tools would best accomplish this purpose. The sample consisted of 72 tenth- and eleventh-grade students in one high school who were either identified for acceleration or had accelerated on their own.…

A prime concern of problem-solving instruction is to maximize positive transfer of learning from a previously solved problem to a new problem. One aspect of the relationship between transfer of learning and problem-solving instruction is the order of problem presentation. In this study, order of problem presentation is controlled, while certain…

The relationship between expert teachers' classroom behavior and their subject matter knowledge is an area of research that has not been examined extensively. To begin that study, one topic, fraction knowledge, was explored in depth as it occurred in natural teaching settings. Fractions are one of the more difficult topics in elementary…

Outlined is an interdisciplinary unit on statistics. Discussed are the goals, organization, the preinstruction survey, the math lessons, results, and evaluation. The survey and examples of the students' work are provided. (CW)

One important finding from recent research on multiplication word problems is that children's performances are strongly affected by the nature of the multiplier (whether it is an integer, decimal larger than 1 or a decimal smaller than 1). On the other hand, the size of the multiplicand has little or no effect on problem difficulty. The aim of the…

A comparison of three approaches to problem solving in fourth grade mathematics is presented. Three classes participated in the study. Class One studied problem solving in a structured classroom setting, Class Two studied problem solving incidentally, and Class Three studied problem solving when it appeared in the text. The structured study of…

This study examines in detail a sample of widely used teacher guides in order to describe a picture of instruction as it is represented in these guides and to compare it with classroom practices. Mathematics and social studies were selected as the subject areas because of observed differences in classroom practices. Six questions guided the…

This paper describes a research and development project in teaching designed to examine whether and how it might be possible to bring the meaning of knowing mathematics in school closer to what it means to know mathematics within the descipline by deliberately altering the roles and responsibilities of teacher and students in classroom discourse.…

Results of a study designed to gather evidence about the effect of student's overt verbalization on performance and retention after instruction on a set of geometric concepts are reported. The independent variable, overt verbalization, was manipulated following the procedure used by Pereira (l973) which involved an experimenter questioning…

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fractions. It was determined that all students possessed a rich store of prior knowledge about parts of wholes in real…

This exploratory study describes fourth-grade students' opinions and knowledge about fractions. A coherent and elaborate fraction knowledge base results when students establish connections between their conceptual knowledge and procedural knowledge of fractions. One possible juncture between concepts and procedures might involve establishing…

Classroom decision-making was conceptualized within the framework of person-environment fit. A longitudinal sample of 2239 sixth graders in 117 mathematics classrooms were surveyed. The findings include: (1) students typically report fewer decision-making opportunities than they think they should have in their mathematics classrooms; (2) students…

Eight sixth-grade students received individualized instruction on the addition and subtraction of fractions in a one-to-one setting for 6 weeks. Instruction was specifically designed to build upon the student's prior knowledge of fraction ideas and to emphasize estimation. It was determined that all students possessed a rich store of prior…

The ways in which students in grades five and six solve problems is the focus of this paper, which provides background for the staff of the Skills Essential to Learning Television Project, (a multi-level series of video and print resources for classroom use). It considers the problem-solving process categories of understanding, transformation, and…