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…

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…

Written to fulfill the requirements for a University of Minnesota College of Education off-campus Indian education course for public school teachers, this Native American curriculum unit for middle and high school reflects the mathematical achievements of the Maya, Aztec, and Inca Indians. The number systems, notation, and calendar techniques of…

Fourteen papers that were presented at an NCTM-sponsored conference on Piagetian research are included in this document. Topics covered include explanations of Piaget's developmental theory and descriptions of studies concerned with the development and growth of the mathematical concepts of proof, logical operations, functions, proportionality,…

The project, consisting of five experiments, attempted to develop remedial procedures and materials for retarded children with learning deficits in the area of arithmetic. Standardized training procedures were devised to facilitate development of operations (conservation, ordination, cardination, and classification) which J. Piaget describes as…

A series of experiments, all concerned with the topic of mathematical concept learning by the young child, were conducted. The concept mainly focused upon was that of inequalities. Five experiments were run. These are: (1) acquisition of mathematical concepts under experimental situation and in traditional pedagogical situation, (2) cued vs.…

This collection includes 50 mathematical games and puzzles for classroom use at all grade levels. Also included is a wide variety of activities with cubes, flash cards, graphs, dots, number patterns, geometric shapes, cross-number puzzles, and magic squares. (MM)

This study investigates the relationship of socio-economic status to the acquisition of two basic ideas underlying the concept of number conservation, "conservation of identity" and "conservation of equivalence." Tests for conservation of identity and of equivalence, detailed in the paper, were given to kindergarten, first, and second grade…

This paper examines some of the manipulative aids used in elementary mathematics instruction from the point of view of the cognitive structures needed to understand them. The number line, measurement activities, models for place value, and models for fractions are discussed. (SD)

The purpose of this study was to investigate the relationship between a student's confidence in his computational procedures for each of the four basic arithmetic operations and the student's achievement on computation problems. All of the students in grades 5 through 8 in one school system (a total of 6186 students) were given a questionnaire to…

Boys' and girls' achievement in arithmetic computation was compared with their feelings of self-confidence in performing computations. A total of 2654 girls and 2786 boys from grades 5 through 8 in one school system participated. Each student was given a test to assess the degree of self-confidence in methods of performing the four basic…

A previous study had confirmed that a substantial number of low achievers in grades 5 through 8 had high algorithmic confidence in each of the four arithmetic operations with whole numbers. The purpose of the present study was to follow up the results through interviewing low achievement-high confidence students in order to ascertain if they…

The teacher of mathematics or science must be aware of the concepts, facts, and generalizations of his field, of psychological principles of learning, and of teaching methods. Methods appropriate to the teaching of concepts differ from methods for teaching generalizations. (SD)

Ancient numeration systems form the basis for these worksheets. (SD)