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,…

The English translations of the first six volumes of Studies on the Teaching and Learning of Mathematics in the Soviet Union are viewed in this document. The contents of each volume are briefly described: vol. 1, The Learning of Mathematical Concepts; vol. 2, The Structure of Mathematical Abilities; vol. 3, Problem Solving in Arithmetic and…

This study investigated whether instruction with or without simultaneous conversion to English measures is more effective in improving the ability of students to perform tasks in the metric system. Also investigated was the relationship of mathematical problem solving ability and sex to the ability of students to perform such tasks. Six seventh…

This paper notes three objections to the use of hand-held calculators in schools: they would (1) block reasoning, (2) make individuals machine-dependent, and (3) broaden the gap between developed and underdeveloped nations. Each is addressed, with specific examples used to refute them. The belief is strongly expressed that calculators can aid in…

The need to promote mathematical creativity and suggestions for developing it are discussed in this document. The largest portion of this document consists of a collection of problem sheets, arranged according to 26 content areas. Puzzles, activities, and a variety of problems are included, with an answer key. An annotated bibliography of selected…