Research in mathematical problem solving has produced significant results in trying to understand what people do to solve problems. An important part of the solution process is the presence of both cognitive and metacognitive strategies. This paper documents the extent to which 13 ninth grade students are able to recognize the basic structure of a…

Fifth grade children's (n=16) understandings of simple fractions such as 1/2, 1/3, and 1/4 were investigated. The study identified three alternative conceptions of fractions: (1) 1/"N" is one of "N equal" parts, (2) 1/N is one of "N equal" parts, and (3) parts must fit together to form the whole. In addition, many…

Students need in-school mathematical experiences to build on and formalize the mathematical knowledge they gain in out-of-school situations. This paper presents illustrations from research that was conducted to better understand how mathematics practice and problem solving in everyday work situations compared to secondary students' solutions of…

Models occupy the content core of physics, and modeling is a major process for constructing and employing physics knowledge. A model is characterized by its domain, composition, structure, behavior, and organization. Problem solving is a schematic modeling process consisting of model selection, construction, validation, analysis, and deployment. A…

This booklet explains the background, rationale, and issues addressed in the NCTM Curriculum and Evaluation Standards. A detailed vignette of a classroom lesson is presented as an example of what is envisioned for the future. A comparison of the differences between the reform urged by the Standards and the efforts of the "New Math"…

It was hypothesized that receiving a problem of the day would result in higher mathematics scores on the Ohio Ninth Grade Proficiency Test. An experimental group consisting of 19 students received a problem of the day treatment every day during the 5 month period. The 19 students in the control group received no special treatment. Test scores of…

This study was an investigation of the influence of word-problem context--the nonmathematical, verbal aspect of a problem--on fourth- and sixth-grade students' preferences for and problem solving performance on word problems. Problems were parallel in mathematical structure but differed by major context category--fantasy and real-world.…

As illustrated by a concept map in chapter 1, this book discusses three concepts: (1) the nature of knowledge, its capture, creation, and use; (2) the nature of human learning; and (3) a theory of education tying together the first two concepts. Chapter 2 discusses the need for a theory of education to resolve numerous questions, issues, and…

This publication is designed to educate high school students about the problems and challenges of transportation. The parent project was conceived as a mathematics curriculum project, but developed into an interdisciplinary project to ensure that students would become well informed regarding the transportation decisions they make. In the…

Vygotsky argued that children's development is most likely to occur when, in the course of collaboration, assistance is provided within their zone of proximal development--the distance between what a child can achieve independently and what he or she can do with the assistance of a more competent member of their culture. This paper reports the…

An experiment compared solving of operational and diagnostic problems after different instruction about a fictitious device. Solution of both kinds of problems was facilitated by instruction (1) that focused on functional relations among components of the device or (2) that focused on states of the individual components. For operational problems,…

This book explores conflict resolution strategies and presents a systematic approach to mediation for peer helpers. The first part examines conflict resolution. Internal and external sources of conflict are considered. Irritations, inappropriate expectations, and unknown sources of external conflict are examined. A section on looking inside…

This paper describes the design and development of an instructional planner for an intelligent tutoring system for cardiovascular physiology that assists medical students to learn the causal relationships between the parameters of the circulatory system, to understand how a negative feedback system works, and to solve problems involving…

A replication study tested functional theory utilizing untrained full-fledged groups. One hundred forty undergraduate students who were enrolled in a small group communication course at a large midwestern university participated in small group discussions analyzing a plagiarism case used in an original study by R. Y. Hirokawa. Results indicated…

Modern society is full of examples of people's inability to employ techniques of critical thinking in everyday situations. Learning to think critically is important because within this complex society, individuals are constantly placed into situations where difficult choices must be made. An ability to analyze critically available alternatives…