Supporting young students in developing meanings for the set-theoretic function definition is emphasized in 6th-12th grade curricula around the world. In prior work, we have highlighted how covariational reasoning supports college students in constructing relationships that afford considering mathematical properties important for a set-theoretic…

This book includes two main sections: a discussion of problem solving and a section on computation with whole numbers. A primary theme of the text is that problem solving sets the stage for meaning and conceptual development with respect to numbers. The section on problem solving includes numerous problem-solving activities that have a dual…

This article is based on a doctoral dissertation submitted to the Department of Psychology, University of Michigan. (MH)

The study with 30 five-year-olds and 30 seven-year-olds demonstrated that children as young as five have an emerging ability to solve both verbal and perceptual proportional analogy problems and to detect the meaning of proportional metaphoric sentences. (Author/DB)

This book, containing conference papers and a summary of activities, focuses on the contributions which current research in cognitive psychology can make to the solution of problems in instructional design. The first three parts of the book include sets of research contributions followed by discussions: part one deals with different strategies for…

This paper begins by examining two approaches to defining and measuring adolescents' understanding of the public good: (1) theories concerning stages of moral and cognitive development and political socialization; and (2) attitudinal survey methods. Methodological deficiencies of the approaches are identified. The paper presents a new method of…

Mismatch between gesture and speech was used to study cognitive processes that characterize the transition between incorrect, but rule-governed, problem understanding to correct rule-governed understanding among 90 fourth graders in Chicago (Illinois). Data support the idea that the transitional state is characterized by concurrent activation of…

This study sought to determine the basis for young children's understanding of fundamental addition and subtraction processes, and to expose any limitations on such arithmetic reasoning. Thirty-six two-year-olds and 36 three-year-olds participated in six experiments which examined children's relational quantity judgments about pairs of arrays in…

This book shows how to increase one's power to analyze and comprehend problems. First, it outlines and illustrates the methods that good problem solvers use in attacking complex ideas. Then it gives some practice in applying these methods to a variety of questions in comprehension and reasoning. Chapters include: (1) "Test Your Mind--See How…

This study investigated the effects of K. J. Klauer's (1989) inductive reasoning training program of teaching children. Effects of training and the range of transfer of the training were assessed. The subjects were 34 third-grade Dutch children of average ability, matched on age, sex, and IQ. Children from the training condition (N=17) received…

Researchers from four projects with a problem-solving approach to teaching and learning multidigit number concepts and operations describe a common framework of conceptual structures children construct for multidigit numbers, and categories of methods children devise for multidigit addition and subtraction. Conceptions include unitary, decade and…

Discusses the potential that school mathematics has for being a source of exploration and discovery for students and teachers. Provides a process-oriented definition of understanding mathematics. Presents activities in which students construct computer and actual models of polyhedra and make conjectures regarding a medical research application of…

Because adult basic education (ABE) students often have difficulty with problem solving and comprehension, a study was initiated to determine (1) at what levels of cognitive development ABE students are operating and (2) how teaching materials and methods relate to these cognitive levels. Thirty-two ABE students were given a written test of…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…