This paper contributes to consideration of the role of conceptual frameworks in the doctoral research process. Through reflection on the two authors' own conceptual frameworks for their doctoral studies, a pedagogical model has been developed. The model posits the development of a conceptual framework as a core element of the doctoral…

Examines the feasibility of including instruction in common schemes of inference in the elementary grades. (CP)

This paper presents a cognitive theoretical framework for the learning of mathematics which has generic implications for other disciplines. The framework has been developed using a combination of established theories about learning and the authors' research into the understanding of some specific types of learning. It is based on the integration…

Sixty Japanese children ranging in age from 3 years 4 months to 7 years 5 months were individually interviewed with three Piagetian tasks. Children's levels of representation were assessed by asking for a graphic representation of 4 dishes, 6 pencils, 8 small blocks etc. A conservation-of-number task was then given to assess children's level of…

Children's understanding of Euclidian space was investigated using three Piaget-type tasks to examine the ability of children to quantitatively locate a point in one, two, and three dimensions. Among the findings were that a disagreement exists between Piaget's data and the results of this study. (BT)

Examples are given illustrating a facet of early learning involving insights into abstract thinking. Several learning theories examined fail to account for this phenomenon. (MP)

Interviews 60 Japanese children between the ages of 3 and 7 years to investigate the relationship between levels of abstraction and representation. Indicates that abstraction and representation are closely related. Implies that educators need to focus more on the mental relationships children make because the meaning children can give to…

To study the developmental interrelationships among various aspects of logico-mathematical knowledge, 80 one- to 4-year-olds were individually asked to build "something tall" with 20 blocks. Percentages of new and significant behaviors increased with age and were analyzed in terms of the development of logico-mathematical relationships. It was…

Article describes an experiment to deterimine how to promote cognitive growth in terms of classroom mathematics learning. (MM)

Reported is a study involving six group administered tasks concerning proportional, probablistic, and correlational reasoning with 505 students aged 11.5 to 20.0 years. Investigated were the effectiveness of the tasks for assessing formal reasoning; categories of classification for students' responses and implications for teaching are suggested by…

Discusses geometrical reasoning in the framework of the theory of Figural Concepts to highlight the interaction between the figural and conceptual components of geometrical concepts. Examples of students' difficulties and errors in geometrical reasoning are interpreted according to the internal tension that appears in figural concepts resulting…

The papers contained in this document were originally presented at the May 1978 conference on Modeling Mathematical Cognitive Development sponsored by the Models of Learning Mathematics Working Group of the Georgia Center for the Study of Learning and Teaching Mathematics. Most have been revised to reflect comments and suggestions made at the…

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…

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)