A major goal of mathematics teaching is the involvement of students in the personal process of discovering mathematical ideas and formulating problems. The process of an inductive leap followed by a deductive argument is used in mathematics courses at Phillips Exeter Academy (New Hampshire). Mathematical problems are presented in which the givens…

Thinking-aloud protocols of human problem solvers working on geometry problems are presented and discussed. Protocols were obtained from six individuals working on nine different problems in which constructions were used. Nineteen protocols are presented with annotation and discussion, and other protocols are summarized. The primary purpose of the…

The research described here seeks to characterize the "managerial" aspects of expert and novice problem-solving behavior, and to describe the impact of managerial or "executive" actions on success or failure in problem solving. A framework for analyzing protocols of problem-solving sessions based on "episodes" of…

Teachers in elementary schools, supervisors of instruction, and other educational practitioners are the primary audience for this publication. The paper presents philosophical, psychological, and practical reasons for including a problem-solving approach in elementary school instruction. It draws on the writings of John Dewey, Jean Piaget, James…

This curriculum guide outlines the mathematics objectives of each of the grades K-8 under the headings of operations, sentences and problem solving, numbers and numeration, measurement, geometry, statistics, and applications. Examples of each of the objectives are given. High school minimal skills are listed. The sequence of mathematics courses…

This guide represents the final experimental version of an extended pilot project which was conducted in the United States between 1973 and 1976. The manner of presentation and the pedagogical ideas and tools are based on the works of Georges and Frederique Papy. They are recognized as having introduced colored arrow drawings…

This longitudinal study is one of a series which is devoted to the task of evaluating new, secondary school mathematics curricula. This series of studies has involved ninth and eleventh grade teachers teaching a new mathematics curriculum (School Mathematics Study Group, University of Illinois Committee on School Mathematics, or Ball State…

Designed for the instruction of emotionally handicapped children and youth, this guide presents mathematical concepts and activities which may be utilized in outdoor education. Three authors provide three individualized resource guides on mathematics; Guide 1 deals with the concepts of measurement, time, estimation, geometry, counting, and…

Theory and research regarding four levels of concept attainment and three uses of concepts as specified by the conceptual learning and development (CLD) model are described. The strategy and objectives of a longitudinal assessment of children's conceptual learning and development are presented. Perspective is provided regarding the role of the…

Theory and research regarding four levels of concept attainment and three uses of concepts as specified by the model of conceptual learning and development (CLD) are described. Subtests, utilizing three-dimensional stimuli, were developed to assess each level of attainment and each use of the concept equilateral triangle. The tests were…

The guide (one-quarter trigonometry course; two-quarter analytic geometry course) provides both subject matter and career preparation assistance for advanced mathematics teachers. It is arranged in vertical columns relating curriculum concepts in trigonometry and analytic geometry to curriculum performance objectives, career concepts and teaching…

GRADES OR AGES: K-6. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The introductory material describes the philosophy behind the guide, its purpose, and the way it should be used, and also contains a set of graphs which provide a quick overview of the scope and sequence. The main body of the guide is arranged by grade level in…

The purpose of this study was to investigate the effects of perceptual focus and planar orientation of rods on conservation responses when parallel translations are utilized. The translations along the major axes of symmetry utilized two modes: (1) translation of one of two rods, and (2) simultaneous translation of two of three rods in opposite…

Sample materials from a primary training packet are included. The packets were developed as a part of a teacher development program aimed at improving elementary mathematics by giving teachers practical ideas. The sample student materials are drawn from the areas of geometry and oral mathematics. (PK)

Information is presented on organizing a geometry fair using student projects. Preparation, construction and display of projects are addressed. Project ideas and suggestions for mathematics supervisors are included. (PK)