This study focused on (1) the relation or transition between the measurement and partitive settings for division, and (2) the study of these two interpretations in general case where the remainder is not necessarily zero. Ninety-four second-grade pupils from four classrooms (two in each of two schools) were presented, through individual…

This report, in the form of a teacher's guide, presents materials for a ninth grade introductory course on Introduction to Quantitative Science (IQS). It is intended to replace a traditional ninth grade general science with a process oriented course that will (1) unify the sciences, and (2) provide a quantitative preparation for the new science…

This study investigated five ability tests related to the water-jug problem. Previous analyses identified two processes used during solution: means-ends analysis and memory of visited states. Subjects were 240 undergraduate psychology students. A real-time computer system presented the problem and recorded responses. Ability tests were paper and…

A computer-based curricular package was developed to teach elementary school students to solve arithmetic word problems and to teach problem solving skills applicable to situations not involving word problems. An information processing model for solving word problems was used to sequence the problems. Pilot test results with five students…

Abstracts of 28 research reports are provided. The reports were prepared by investigators for presentation at the 54th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education are covered. Three reports concern the effects of differing presentations of mathematics, four are related…

A study involving 20 emotionally disturbed boys (9- to 11-years-old) was conducted to determine the effects of tactile and verbal reinforcement on attention to task and accuracy. Ss were given arithmetic problems to work during 16 20-minute sessions under four conditions: tactile reinforcement (intermittent touch pressure applied to Ss shoulders…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program see ED 086 545. In this guide, the teacher is provided with objectives for…

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program see ED 086 545. In this guide, the teacher is provided with objectives for…

This book is a sequel to MATHEMATICAL CHALLENGES, which was published in 1965. In this sequel are 100 problems, together with their printed solutions. The problems range from those that are quite simple to those that will challenge even the most ardent problem solver, and they include examples from algebra, geometry, number theory, probability,…

This report contains four papers describing research based on the view of mathematical knowledge as a hierarchy of "rules." The first paper: "The Role of Rules in Behavior" was abstracted in ED 040 036 (October 1970). The second paper: "A Theory of Mathematical Knowledge" defends the thesis that rules are the basic building blocks of mathematical…

THE STUDIES REPORTED WERE ATTEMPTS TO LEARN THE INNER ARRANGEMENT OF DOING MATHEMATICS. MATHEMATICS WAS VIEWED AS A MATTER OF SOLVING PROBLEMS BY A SEQUENCE OF STEPS PERFORMED AS AN ALGORITHM. THE PROCESSES STUDIED WERE--(1) COUNTING OR ENUMERATING SETS, (2) SIMPLIFYING COMPLEX LOGICAL STATEMENTS, (3) ADDING LARGE NUMBERS, AND (4) MULTIPLYING.…

The general purposes of a model are discussed, then seven papers are presented which demonstrate several different facets of the problems associated with constructing and using models of mathematics learning. In the first paper, the task addressed concerns how to incorporate developmental psychology into perceptions of what is happening in the…

Using mathematics as an example, the nature of the confusion between "knowledge" and "coming to know" is elucidated. The range of curriculum choices available to structuralists once the distinction is clarified is larger, and teaching a body of knowledge and teaching by discovery are compatible. (Author/MLF)

Using a great variety of word problems drawn from many contexts can make multiplication and division rules more relevant to the student's needs. (SD)

A series of maps is presented for coloring with the fewest possible colors. (SD)