This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…

In order to study children's strategies for solving geometric matrices similar to those in the Raven's Progressive Matrices, ninety 7-, 10-, and 13-year-old boys and girls were administered tests of auditory and visual memory, the Raven's, and geometric matrices. The matrices varied in number of elements (1 to 3) and number of transformations (0…

Unified Science and Mathematics for Elementary Schools (USMES) is a reality-oriented approach to teaching emphasizing activities in which students define and solve their own problems. Examples of problems and activities found in schools using USMES guides are presented as well as a brief history of the project. (JP)

Experiments by Russian educators on teaching algebra in elementary grades are summarized by the author. The algebra taught consisted of generalized solutions to concrete problems that are usually presented with fixed numerical values. (JP)

The purpose of this study was to relate children's cognitive processing capabilities and their grade level to their performance and to the strategies they used when working addition and subtraction problems. From two sets of data which assessed memory capacity and cognitive processing capacities, six groups of children with different cognitive…

The document notes that in health and medical research the need to compare rates or proportions for some event can often occur. It is the module's goal to illustrate the conditions necessary for recognizing potentially misleading situations, and to show how to cope statistically with such situations. The four sections show: 1) when to adjust…

Cognitive development during each of the major stages identified by Piaget is characterized by abilities to solve progressively more complex tasks (e.g., changes in the object concept during the sensori-motor stage, and in conservation of amount, weight, and volume during the concrete operational stage). Several theorists have suggested that these…

A study designed to investigate the association between Piagetian cognitive and long-term mnemonic (recall and recognition) levels and problem solving in mathematics was conducted with 152 eighth-grade students. Cognitive level was determined by two evaluations (seven months apart) of a subject's performance on a clinically administered balance…

Eleven students out of 94 selected a hexagonal container as larger than a triangular container having the same surface area, although the capacity of the former was 50% greater than the latter. When presented with hexagons and triangles of the same perimeter but different areas, 40 students selected the hexagon as the larger area. When the…

This guide is organized around six concepts: sets, numbers and numeration; operations, their properties and number theory; relations and functions; geometry; measurement; and probability and statistics. Objectives and sample activities are presented for each concept. Separate sections deal with the processes of problem solving and computation. A…

This study explores the potential effectiveness of a new procedure for identifying and studying certain of the cognitive processes used during problem solving. The procedure is used in an attempt to categorize the types of conceptual thinking problem solvers employ, to study trial-and-error behavior, and to investigate problem solvers' abilities…

This study attempted to gather empirical evidence to guide educators in their teaching of linear measurement to primary school children. It attempted to answer the question "What modes of instruction are most effective for teaching linear measurement concepts to conservers and nonconservers of length?" (as defined by Jean Piaget), using a…

THIS GUIDE FOR TEACHING HIGH SCHOOL PHYSICS INCLUDES--(1) CONCEPTS, (2) UNDERSTANDINGS, (3) ACTIVITIES, (4) REFERENCES, (5) AUDIOVISUAL AIDS, (6) EQUIPMENT, AND (7) REQUIRED SUPPLIES. THE COURSE CONTENT IS DIVIDED INTO EIGHT MAJOR TOPICS--(1) FUNDAMENTALS, (2) MECHANICS, (3) HEAT, (4) SOUND, (5) LIGHT, (6) ELECTRICITY, (7) SPACE, TIME, AND MOTION,…

This monograph focuses on educational research on the processes and natures of problem-solving activities in mathematics. The first chapter presents an overview to both the field and the document itself. All of the studies reported reflect interrelated investigations carried out at the University of Madison-Wisconsin, as partial fulfillments of…

Presented is a collection of materials developed and used with teachers in western Kentucky in workshops on the teaching of basic skills. The material is particularly concerned with methods teachers can use to provide motivation for students to learn and enjoy mathematics. Included are activities for problem solving, graphing, addition,…