Investigates the effects of two context variables on the performance of seventh-grade students on a qualitative and numerical proportional reasoning test. Explores the nature of the relationships between rational number skills, qualitative reasoning about ratios, and numerical proportional reasoning. (Author/YP)

Utilizes the problem of determining the number of different ice cream cones and cups that can be made from a choice of 31 flavors to investigate the concepts of combinations and permutations. Provides a set of six related problems with their answers. (MDH)

First of three experiments compared third graders who had studied worked, two-step arithmetic word problems to those learning through conventional problem solving. The former grouped showed superior test performance. In experiments two and three, children presented with integrated worked examples outperformed those presented with split-source…

This paper describes a proportional reasoning problem set within a real-life context and a complete analysis of one small group discussion of this problem over the course of a 90-minute block. The seventh-grade students' discourse is described to provide insights into typical mathematical interpretations of this problem, as well as some…

Project carried out under Contract No. PH 43 65-1011 between the Public Health Service, National Institutes of Child Health and Human Development and the Fels Research Institute.

The aim of this monograph is to describe a program of research investigating the problem-solving responses of young children and to present in summary form the results of the analyses completed so far. Attention is given to characteristics of clinical studies which are thought to make the clinical method particularly useful with young children.…

These student worksheets include activities in counting, place value, estimation, the four operations with whole numbers, number patterns, volume, inequalities, decimal equivalents of fractions, and percents, all to be worked with a calculator. (MP)

Five different ways are outlined in which calculators can be used to develop a student's ability: (1) to solve problems which use real-world data; (2) for solving a greater number of standard word problems; (3) for using different approaches to solve problems; (4) for extending problem situations; and (5) for using the calculator in an…

MENTAL ABILITY CAN BE MEASURED BY THE PROBLEM-SOLVING PROCESS RATHER THAN BY THE NUMBER OF CORRECT SOLUTIONS. THE OBJECTIVES OF THIS STUDY ARE--(1) TO DEVELOP AND STUDY PROPERTIES OF MEASUREMENT TECHNIQUES WHICH REVEAL THE PROBLEM-SOLVING PROCESS, (2) TO DEVELOP WAYS OF DESCRIBING INDIVIDUALS THROUGH THEIR PROBLEM-SOLVING PROCESSES, AND (3) TO…

This teaching guide presents six lessons on using tables to solve problems. For each lesson, the guide gives the purpose, the rationales, materials, and detailed teaching procedures. The six lessons involve making a table, completing a table, using tables to solve problems (lessons 3 and 4), reading tables, and solving problems. Each lesson opens…

NINETY FIRST GRADE CHILDREN WERE RANDOMLY SELECTED FROM 3 SCHOOLS (WHICH EACH USED A DIFFERENT ARITHMETIC PROGRAM) TO PARTICIPATE IN A STUDY TO INVESTIGATE THE EFFECTS OF 2 VARIABLES ON THE CHILDREN'S ABILITY TO SOLVE ADDITION PROBLEMS. THE VARIABLES WERE (1) THE PRESENCE OR ABSENCE OF AN EXISTENTIAL QUANTIFIER PRECEDING THE START OF THE PROBLEM,…

Five segments of the Self-Paced Physics Course materials are presented in this problems and solutions book for use as the first part of student course work. The subject-matter topics are related to significant digits, vectors, dimensions, dot and cross products, speeds, velocities, problem solving procedures, projectiles, Newton's laws, and…

Five segments of the Self-Paced Physics Course materials are presented in this problems and solutions book for use as the second part of student course work. The subject-matter topics are related to circular motion, work, power, kinetic energy, potential energy, conservative forces, conservation of energy, spring problems, center of mass, and…

Four segments of the Self-Paced Physics Course materials are presented in this problems and solutions book for use as the third part of student course work. The subject-matter topics are related to impulses, inelastic and elastic collisions, two-dimensional collision problems, universal constant of gravitation, gravitational acceleration and…

The second review segment of the Self-Paced Physics Course is presented in this volume and arranged to match study segments 19 through 40. The segment is divided into five subsegments, each of which is composed of a set of problems and solutions. A study guide is provided for each subsegment. The problem set is designed in a back-referencing…