The purpose of this study was to relate children's cognitive processing capabilities and their grade level to their performance and to the strategies they used when working addition and subtraction problems. From two sets of data which assessed memory capacity and cognitive processing capacities, six groups of children with different cognitive…

The focus is on the problem-solving behaviors of primary age children on one-step verbal or story problems involving addition and subtraction. When children are given a simple word problem for which they have not learned the necessary algorithms, they are often able to derive a solution on their own. This report focuses on the child-invented…

Cognitive development during each of the major stages identified by Piaget is characterized by abilities to solve progressively more complex tasks (e.g., changes in the object concept during the sensori-motor stage, and in conservation of amount, weight, and volume during the concrete operational stage). Several theorists have suggested that these…

A study designed to investigate the association between Piagetian cognitive and long-term mnemonic (recall and recognition) levels and problem solving in mathematics was conducted with 152 eighth-grade students. Cognitive level was determined by two evaluations (seven months apart) of a subject's performance on a clinically administered balance…

Information about individuals' representations of problems was obtained from studies on reasoning and problem categorization. College students (N=62) participated in a study of the transition from concrete to formal reasoning using the pendulum and chemical yellow tasks. Over a 10-12 week period, 47 students participated in 10 training sessions on…

The relationship of aptitude, strategy, and cognitive task performance is explored through the use of mathematical models of performance time. Models of strategy and strategy-shifting on a spatial visualization task were tested individually for 30 male high school and college subjects. For each of three successive task steps (encoding,…

Problem solving approaches often find a path from the givens to the unknown or from the unknown to the givens. This study explores those approaches using written protocols of Navy subjects while solving for the numerical value of an unknown from several knowns and a system of equations. For a subset of the items, solutions require subjects to…

This study explores the potential effectiveness of a new procedure for identifying and studying certain of the cognitive processes used during problem solving. The procedure is used in an attempt to categorize the types of conceptual thinking problem solvers employ, to study trial-and-error behavior, and to investigate problem solvers' abilities…

Presented are four interpretive reports and a list of current publications of the Mathematics Work Group at the Wisconsin R&D Center. The first interpretive report gives a brief overview of their work. Reports two through four are concerned with individual interviews, carried out during a longitudinal study, in which primary children are asked to…

This study attempted to gather empirical evidence to guide educators in their teaching of linear measurement to primary school children. It attempted to answer the question "What modes of instruction are most effective for teaching linear measurement concepts to conservers and nonconservers of length?" (as defined by Jean Piaget), using a…

This paper reports a study of cerebral dominance in 42 preschool and kindergarten children. In order to tap left hemisphere functioning, a story of approximately 650 words and 77 specific plot details was composed. Children listened to the 7 minute story and were asked to repeat it. Responses were taped. Tangram pieces were used to assess right…

IF COMPUTER PROGRAMS ARE TO SERVE AS USEFUL MODELS OF COGNITIVE BEHAVIOR, THEIR CREATORS MUST FACE THE NEED TO ESTABLISH AN INTERNAL ORGANIZATION FOR THEIR MODEL WHICH IMPLEMENTS THE HIGHER LEVEL COGNITIVE BEHAVIORS ASSOCIATED WITH THE HUMAN CAPACITY FOR SELF-DIRECTION, AUTOCRITICISM, AND ADAPTATION. PRESENT COMPUTER MODELS OF COGNITIVE BEHAVIOR…

THIS STUDY AIMED AT--(1) CHARACTERIZING PROBLEM-SOLVING PROCESSES OF DIFFERENT INDIVIDUALS AND (2) DETERMINING THE EFFECTS OF TRAINING ON THE SUBJECTS' APPROACHES TO THEIR PROBLEM-SOLVING PERFORMANCE. THE DESIGN INCLUDED 50 NINTH-GRADE STUDENTS AND 50 COLLEGE FRESHMEN DIVIDED INTO EXPERIMENTAL AND CONTROL GROUPS IN WHICH SUBJECTS WERE MATCHED ON…

This monograph focuses on educational research on the processes and natures of problem-solving activities in mathematics. The first chapter presents an overview to both the field and the document itself. All of the studies reported reflect interrelated investigations carried out at the University of Madison-Wisconsin, as partial fulfillments of…

Recent studies have shown perceptual instability to be related to visual creativity as reflected in career choice. In general, those who display greater perceptual instability perceive themselves to be more creative and tend to choose careers related to visual creativity, regardless of their gender. To test the hypothesis that field independents…