This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

The purpose of this investigation was to determine the relationship between the acquisition of conservation skills and achievement in mathematics. The conservation skills measured were numbered, mass, area and volume. Mathematics achievement was measured by the Computation, Concepts, Problem-Solving and Total Mathematics scores on the Metropolitan…

Compares the Genevan and Cattell-Horn theories of intelligence and describes both similarities and differences. Describes a study investigating the relation of the Piagetian operative level to the child's ability to use crystallized solution procedures (aids) in making elementary numerical comparisons. (HOD)

A study with 29 preschoolers showed that a statistically significant number of them successfully reassigned tags in counting (ordinality) but failed to predict that differently ordered counts would produce the same outcome (cardinality). Results indicated that children may not entirely understand implications of their counting actions. (Contains…

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…

Attainment relative to six cognitive operations and four number and computational skills was assessed for 90 elementary students using clinical procedures. Variance associated with conservation of number, seriation, and logical classification competency accounted for a significant proportion of the variance in achievement scores. (Author/MK)

This document focuses on one child's skip counting methods. The pupil, a second grade student at Steuben School, in Kankakee, Illinois, was interviewed as she made several attempts at counting twenty-five poker chips on a circular piece of paper. The interview was part of a larger study of "Children's Conceptions of Number and Numeral,"…

Presents a computational framework for modeling cognitive development that provides a language paradigm with which to compare and contrast different facets of children's knowledge. Describes the generative connectionist algorithm "cascade-correlation," the successful use of the algorithm to model cognitive development in various…

This document focuses on research on the relation between children's use and understanding of counting as a symbol system for number and the development of number conservation concepts. An underlying assumption is that a better match between mathematics curricula and the educational needs of children will be facilitated by learning more about the…

Results of research on the acquisition of counting skills in children is presented. The material, originally published in the Soviet Journal "Questions of Psychology," was deemed an important document that should be translated and made accessible to English readers. The question of how basic, extended processes are…

In the first chapter Brownell critically examines the psychological bases of the three most common theories of arithmetic instruction: drill, incidental learning, and meaning. In chapter 2 the results of a nation-wide survey of actual teaching practices are reported. Chapter 3 presents a contrast between "informational arithmetic" and…

Focuses on a single case study of a mentally handicapped child to examine directly the relation between the development of number-after rules and a counting-on from the larger addend (COL) strategy. Examines the development of children's proficiency with n+ and 1+n combinations and the evolution of their counting-on strategies over time. (AA)

This experiment tested the hypothesis that combining operational strategies with free verbalization facilitates development of competencies, percepts of self-efficacy, and interest in arithmetic activities. Children lacking division skills received treatments in which they either verbalized division strategies, verbalized freely, did both, or did…

The results of an investigation of the development of children's knowledge of addition and subtraction concepts before they start school are detailed. The purpose of the study was to test the predictions of the three-stage model about the distinctions between the last two stages. Twenty-four children participated in the investigation. None of…

An intensive, naturalistic study tracked one six year old's learning for six months and more. The study was inspired by the hope that with concepts of Artificial Intelligence and sufficiently detailed observation, the path of knowledge development could be described through observing significant learning experiences. Included is a reasonably…