Two models for teaching people to think, the Deweyan problem-solving model and the traditional discipline-oriented model, are described and evaluated. (GW)

This book is designed to help teachers understand children's intuitive problem solving and computational processes and to figure out how to use that knowledge to enhance students' understanding of arithmetic. This book provides numerous examples of classroom dialogues that indicate how algebraic ideas emerge in children's thinking and what…

GED "Scoreboost" materials target exactly the skills one needs to pass the General Educational Development (GED) tests. This book focuses on the GED Mathematics test. To prepare for the test, the test taker needs to learn skills in number and operation sense, data and statistics, geometry and measurement, and algebra. To pass the test,…

Occasions where children oppose each other have been viewed as promoting intellectual development through their association with "transactive" dialogue. Yet such occasions have also been regarded as causing problems for social relations through their association with aggression. Although it is inconceivable that the intellectual and…

Cover story, in the sense of context, is a potentially relevant factor in the assessment of reasoning and problem solving in science, given repeated demonstration of its effects on laboratory tasks. This study follows up on a preliminary interview study that showed cover story influenced the way students were assessed at the end of an…

This paper analyses changes in the quality of a mathematical task as a result of its reformulation from a proof mode into an inquiry-based mode. The task is borrowed from the reformulation assignment given to the in-service teachers. The analysis of the task is based on implementation of the task with pre-service teachers. Through the lens of the…

This paper explores the role of diagrams in a specific problem solving process. Two types of tests were administered to 194, 12 year old students, each of which consisted of six non-routine problems that could be solved with the use of a diagram. In Test A students were asked to respond to the problems in any way they wished whereas in Test B…

The analysis of interaction among students is becoming very important in mathematics education, especially among the scholars who view knowledge as socially constructed and negotiated. One of the features of human interaction is the roles that people perform while interacting. Using a symbolic interactionist perspective, we analyzed the evolution…

In the present study, we assert that pictures serve four functions in problem solving: decorative, representational, organizational and informational. We, therefore, investigate the effects of pictures based on their functions in mathematical problem solving (MPS), by high achievement students of Grade 6 in Cyprus, in a communication setting. A…

This resource book contains an eclectic and quirky collection of event anniversaries. Each entry suggests a mathematical problem, investigation, or activity suitable for students in grades 3-6 and provides teachers with a rich and diverse collection of ideas to help integrate math with other areas of the curriculum, relate math to the real world,…

The Physics Education Research Group at the University of Minnesota has developed an interview tool to investigate physics faculty views about the learning and teaching of problem solving. In the part of the interview dealing with grading, faculty members were asked to evaluate a set of five student solutions and explain their reasons for the…

This paper describes the design and initial data analysis of an ongoing study to determine the important elements, as perceived by faculty, of the learning and teaching of problem solving in the context of an introductory calculus-based physics course. To elicit instructors' beliefs that inform their instructional choices, an interview around…

A student's understanding of a problem before he or she solves it is a critical component of successful problem solving. This understanding is based on how a problem is represented; that is, whether a problem is understood in terms of principles or solution methods or whether the focus is on features that are irrelevant to its solution. In this…

This handbook presents a collection of over 35 experiential and adventure-based activities using only a single item of equipment--a 15-foot long section of 1-inch tubular climbing webbing, called a raccoon circle. Some of the activities are quiet, some are loud, and they range from low to high challenge levels. Different-sized groups can be…

After conducting several studies on young students' understanding of particular concepts before, during, and after instruction, this paper focuses on the two small scale and several informal teaching experiments based on the idea that the teacher should pose problems to students for which they do not yet have a routine solution method available,…