Thirty-five students from all ability levels in the first and second year of secondary school were interviewed to determine their understanding of appropriate application of number operations. Results of the interviews are classified into five different levels of understanding. (DT)

Seven papers presented at a research conference on number and measurement are presented in this volume. The first paper provides an overview of research concerning number and measurement, and suggests directions for future research. The second paper discusses the relationships between measurement and number concepts, and psychological and…

Children's responses to an alternative model over three lessons were described and their learning assessed in a posttest. Their responses and performances were compared to that of a similar group of children learning through a conventional number line model. The two models were compared from practical and theoretical viewpoints. (Author/CW)

Examples of topics and problems which demand Piaget's formal operational thought at an early stage in the secondary school are provided. (DT)

This study examines the effects of using different classes of ratios on adolescent performance on proportionality problems. Problems of the form a/b = c/x varied on four dimensions: size of a/b, equality or inequality of b and c, complex or simple fractions, and form of the test. Tests consisted of six proportionality problems involving sizes of…

The limitations in mathematics learning ability inherent in the logical thinking of elementary and junior high students, and the broad spectrum of activities directly affected by these limitations, are discussed. (DT)

This paper reports further on the study described in SE 019 717. Correlational data relating success on proportionality tasks to understanding of related concepts and processes are presented. The five correlative tests involve (1) reducing fractions, (2) multiplying fractions, (3) facility with fractions, (4) inverse relations, and (5) more…

The purposes of this study were: (1) to develop a skills hierarchy for rational number multiplication using modified intraconcept analysis procedures developed by Uprichard and Phillips in two preview studies, and (2) to evaluate and modify the hierarchy using the Walbesser technique (AAAS) and pattern analysis. Subskills were delineated from two…

On the basis of studies reported elsewhere (SE 019 717 and 719) the author discusses the implications of research on cognitive development for teachers whose subjects involve an understanding of proportionality. Several common methods of teaching chemistry students to use proportionality in chemical problems are described. Research on the…

The purpose of this paper is to identify how the theory and techniques of research in cognitive development can be applied to the study of learning and instruction in mathematics. Five basic research paradigms are characterized; major directions of research on number, measurement, geometry, and adolescent reasoning are identified. Most of the…

The Number Test of the ACER Mathematics Profile Series, contains 30 items, for each of three suggested grade levels: 7-8, 8-9, and 9-10. Raw scores on all tests in the ACER Mathematics Profile Series (Number, Operations, Space and Measurement) are converted to a common scale called MAPS, a major feature of the Series. Based on the Rasch Model,…

A three-dimensional classification system of mathematical problems is given. A background philosophy is constructed through an analysis of different approaches to problem-solving research, leading to the statement of 5 theses and the objectives for the study. An exploratory study of mathematical problem-solving processes is conducted within this…

Does conceptually oriented instruction jeopardize students' computational competence? If it does, then why are so many reform efforts continuing to emphasize the importance of teaching for conceptual understanding? If it does not, then why are the majority of teachers at all grade levels continuing to teach for computational competence without…

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…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…