Although equal sharing problems appear to support the development of fractions as multiplicative structures, very little work has examined how children's informal solutions reflect this possibility. The primary goal of this study was to analyze children's coordination of two quantities (number of people sharing and number of things being shared)…

This paper provides an overview of the realm of critical thinking. The document explores the development of a critical thinking attitude and specific skills relative to logic, rationality, and reasoning that must be fostered to facilitate and enhance future learning. The issue of ambiguity also is addressed as a central construct of the critical…

Team research is important in studying cognition as enactive. This paper contains four different pieces of research directed toward the evidences and artifacts of two students in Canada engaging in a sustained mathematical activity. These four portraits of mathematical cognition in action consider the conversation in which the activity occurs; the…

The purpose of this exploratory study was to examine the problem-solving behaviors and perceptions of (n=27) seventh-grade students as they worked on solving a mathematical problem within a small-group setting. An assessment system was developed that allowed for this analysis. To assess problem-solving behaviors within a small group a Group…

This book provides an overview of the creative problem-solving process and exercises to put the process the work. The illustrated, reproducible pages guide students through each step of the problem-solving process by using evaluation grids to track their ideas, solutions, and plans. The activities can be used in a variety of ways including for the…

This book provides a collection of brief biographical sketches with accompanying problems for students to learn the Creative-Problem-Solving (CPS) process. Selected profiles include man as the following: painter, writer, musician, composer, sculptor, actor, dancer, architect, photographer, and designer. In order for students to effectively use…

A 47-item structured Q-sort methodology was used to identify and analyze the frameworks held by experienced emergency response personnel. The questionnaire was designed to determine the following: the characteristics/behaviors considered important by people within specific fields of emergency response; differences between individuals within a…

This study is part of a longitudinal study of 22 elementary school children observed over a 3-year time span in the classroom and in individual task-based interviews. Through the examination of videotaped structured clinical interviews of Marcia, the first in 1992 when she was 9 years old (4th-grade), this study seeks to draw inferences about her…

The primary purpose of this study was to evaluate the application of a process approach for the teaching of algebra with a heterogeneous class of eighth-grade students. The assessment was conducted by identifying the processes used by above-average, average, and below-average algebra students in solving standard and nonstandard problems ranging…

It has been hypothesized that differences in mathematical word problems are the result of differences in spatial skill. Why complex spatial abilities are needed for an individual to represent the relatively simple spatial relations in word problems is not clear. It is possible that a third variable, cognitive strategy preferences, may partially…

This study investigated junior high school students' use of problem-solving heuristics and metacognitive processes and the relationships that might exist between the students' use of these processes and their cognitive style. Using a computer microworld called "Nimbot" based on the ancient game of Nim, 10 seventh- and eighth-grade…

This report describes the instruction, assessment, and staff development of the Multicultural Reading and Thinking (McRAT) program and summarizes the results of a one-year study conducted in 1989-90. (McRAT is a nationally recognized staff development program designed to help teachers infuse higher order thinking skills and multicultural concepts…

The performance of 57 Mexican American bilingual college students on Spanish and English versions of problem solving tasks was investigated. The tasks included word recognition, sentence verification, reading span, syllogisms, and reasoning. The results indicated that the subjects used similar cognitive skills in performing both the Spanish and…

To study and compare the problem-solving processes of experts and non-experts, students and faculty were asked what they would do if they were head of the Ministry of Agriculture in the U.S.S.R. to increase the poor level of crop productivity found in recent years. Individual responses and analyses of these responses make up the bulk of this…

This set of papers was originally developed for a conference on Issues and Directions in Mathematics Problem Solving Research held at Indiana University in May 1981. The purpose is to contribute to the clear formulation of the key issues in mathematical problem-solving research by presenting the ideas of actively involved researchers. An…