This paper reports further on the study described in SE 019 717. Correlational data relating success on proportionality tasks to understanding of related concepts and processes are presented. The five correlative tests involve (1) reducing fractions, (2) multiplying fractions, (3) facility with fractions, (4) inverse relations, and (5) more…

This paper analyzes Brainerd's work in assessing the developmental sequence or ordination and cardination concepts of number, and describes a study which investigated the hypothesis that task-specific difficulty could explain Brainers's data. Three new tasks were designed for the assessment of ordination and cardination and administered to a…

A study was undertaken of the effects of formal education and conservation of numerousness on addition and subtraction problem types. Thirty-six kindergarten and 36 first-grade subjects randomly selected from one area of a school district were administered measures of conservation, problem-solving success, and modeling ability. Following factor…

In this paper the author reviews and synthesizes the research literature concerning the developmental relationships between conservation of number and linguistic capability in handling of quantitative and relational terms. Several models for the development of these competencies are discussed. On the basis of this review the author concludes that…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

The sixteen chapters of this book provide the core material for the Elements of Mathematics Program, a secondary sequence developed for highly motivated students with strong verbal abilities. The sequence is based on a functional-relational approach to mathematics teaching, and emphasizes teaching by analysis of real-life situations. This text is…

A fourth grade class (49 students) with a mean grade equivalent score of 2.8 on the Stanford Diagnostic Arithmetic Test was placed in a Sequential Computational Skills Math Program. The program consisted of 12 units (from basic addition and subtraction facts to fractions computation), and individual Ss' entry levels were determined by computation…

The Minnesota School Mathematics and Science Teaching (MINNEMAST) Project is characterized by its emphasis on the coordination of mathematics and science in the elementary school curriculum. Units are planned to provide children with activities in which they learn various concepts from both subject areas. Each subject is used to support and…

The Minnesota School Mathematics and Science Teaching (MINNEMAST) Project is characterized by its emphasis on the coordination of mathematics and science in the elementary school curriculum. Units are planned to provide children with activities in which they learn various concepts from both subject areas. Each subject is used to support and…

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 guide outlines the curriculum for a ninth-year mathematics course for students not prepared to cope with the usual first-year algebra course. It is intended to provide personal relevance for these students by including supplementary units on probability and statistics, slide rule use, flow charting and use of calculators, consumer…

This material, organized in a workbook format, was developed to be used with the non-college bound, lower one-third of the ninth-grade student population. Topics covered are flowcharts, set theory, number systems (natural numbers, whole numbers, integers, and rationals), number operations, percentage, measurement, finance, geometric constructions,…

This monograph attempts to provide the teacher with examples, techniques, and tips for developing order in number. Topics covered include pre-number order and classification; beginning number activities; number lines; the 100-square counting chart; ordering the integers; fractional numbers; and games, counting rhymes, and other activities. A…

The ten chapters in this booklet cover topics not ordinarily discussed in the classroom: Fibonacci sequences, projective geometry, groups, infinity and transfinite numbers, Pascal's Triangle, topology, experiments with natural numbers, non-Euclidean geometries, Boolean algebras, and the imaginary and the infinite in geometry. Each chapter is…