This paper summarizes the thinking of 84 middle school mathematics students' about variability in three stochastics tasks that involve repeated trial. Differences in students' acknowledgment of variability were found, depending on whether the task was from a sampling environment, or a probability environment. Students tended to neglect variability…

The major purpose of this book is to introduce teachers (and by that the author means all types of teachers-classroom teachers, administrators, teacher aids, parents and coaches) to various individual and group thinking strategies related to specific questions and activities. This guide is a personal interpretation and critique of those strategies…

Two studies investigated upper elementary school students' informal understanding of sampling issues in the context of interpreting and evaluating survey results. The specific focus was on the children's evaluation of sampling methods and means of drawing conclusions from multiple surveys. In Study 1, 17 children were individually interviewed to…

Seldom are college students introduced to theories that describe how they and other students change intellectually during their college years. Two epistemological perspectives on cognitive development in college students and how they can be presented to students are examined in this paper. The first perspective is William Perry's forms of…

The purpose of this book is to teach the basic principles of problem solving in both mathematical and non-mathematical problems. The major components of the book consist of learning to translate verbal discussion into analytical data, learning problem solving methods for attacking collections of analytical questions or data, and building a…

By studying and practicing metacognition, teachers and parents are instilling positive attitudes toward learning by teaching how-to-learn skills that prepare children for assessing their own thinking about learning as they become more and more developmentally prepared. This book stresses the strategies for thinking in mathematical terms without…

Ways in which to identify the correct problems to solve thereby avoiding the misappropriation of time, talent, and resources are presented. The text is divided into 3 parts: "The Foundation for Smart Thinking,""How to Solve the Right Problems," and "Systems Thinking for the Systems Age." The chapters under these headings are: Chapter 1, "The…

This 1998 yearbook aims to stimulate and answer questions that all educators of mathematics need to consider to adapt school mathematics for the 21st century. The papers included in this book cover a wide variety of topics, including student-invented algorithms, the assessment of such algorithms, algorithms from history and other cultures, ways…

A comparative study of parent-child interaction and its relation to children's intellectual achievement is presented in examining the question of cultural continuities in cognitive development. Problem-solving behavior of fifth graders with their mothers from urban settings in Peru and the United States (N=64) was videotaped. In contrast to…

A study used conversational analysis to examine the reasoning students use in a Problem-Based Learning (PBL) environment as they formulate a theory (in medical contexts, a diagnosis) which accounts for evidence (medical history and symptoms). A videotaped group interaction was analyzed and transcribed. In the segment of interaction examined, the…

This study examined abilities and conditions necessary to educate teens for the 21st century, surveying teachers worldwide on: characteristics necessary to meet 21st century challenges; opportunities and challenges to realizing those characteristics; beliefs about teaching practice and curriculum design; visions of an educated teen; and beliefs…

The logical mysteries in this book are designed to develop critical thinking and deductive reasoning skills, motivate children to read carefully, and develop memory skills. The mystery solutions are explained at the end of the book. The first nine mysteries are intended for third grade students to work on with their teacher or parents. The second…

This study considered differences in induction of biological properties between children and preadolescents based on differences in stimuli processing in these two groups. Two experiments tested predictions that young children, but not preadolescents, base their inductive inference on aggregating information from different sources rather than…

Exponential, and logarithmic functions are pivotal mathematical concepts that play central roles in advanced mathematics. Unfortunately, these are also concepts that give students serious difficulty. This report describe a theory of how students acquire an understanding of these functions by prescribing a set of mental constructions that a student…

This research reports results of a survey of content area educators who completed an in-service content area reading course in May 2000. Educators completed two surveys, one each year following the course to determine the most effective content area strategies utilized during the two years following the course. In the surveys, teachers reported…