Designed for students who have mastered the skills and concepts in the regular geometry series of the Quinmester Program, this guidebook presents an additional course on the study of the nature of proof, using a Euclidean geometry model. The development of techniques of formal proof is simplified through the liberal use of partially-constructed…

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…

The first chapter presents representative criticism of the teaching of mathematics, some typical testimonials of its values, and suggestions for certain improvements. Next comes a survey of the educational situation with particular emphasis on the reorganization of secondary mathematics instruction. Chapter 3 presents arguments for the value of…

Transformation geometry topics are covered in one chapter of Unit 11 of this SMSG series. Work with translations, reflections, rotations, and composition of motions is included; vectors are briefly discussed. The chapter on computers and programming deals with recent history and uses of of the computer, organization of a digital computer, an…

The purpose of this study was to investigate attempts to modify teachers' verbal behavior characterized as direct by the Flanders' system of interaction analysis. An initial observation showed that out of 12 teachers, 3 were indirect and 9 were direct. Three groups were determined: Group I, 3 indirect teachers (control); Group II, 4 direct…

The Farallones Designs group is dedicated to "helping ourselves and other people create more human places for living, learning, working, playing,...to returning architecture to its roots in each person,...to creating access to the design process and tools." The Scrapbook is a "partial record of eighteen months together helping kids and teachers to…

This teaching guide outlines a semester course for those students who need review work in concepts from algebra and geometry. Successful completion of this material would serve as a prerequisite to the study of trigonometry. Sequence, textbook references, and time allotments are suggested. Units studied are: the real numbers; operations on the…

Behavioral objectives for geometry, algebra, computer mathematics, trigonometry, analytic geometry, calculus, and probability are specified for grades 10 through 12. General objectives are stated for major areas under each topic and are followed by a list of specific objectives for that area. This work was prepared under an ESEA Title III…

Evaluation sheets and developmental checklists, prepared by three special education departments, are provided to facilitate continuous measurement of student progress in elementary school mathematics. One hundred forty-three objectives are given, and each is followed by a continuum-oriented set of worksheet-type pages on mathematics skills. The…

Sixteen mathematicians from universities, schools and industries met for five days in 1966 to plan a "second round" curriculum which would place greater emphasis on the relevance of mathematics to problems of the real world. Their deliberations are reported in this document. The three main recommendations were that the curriculum should…

This report of a statewide Mathematics Advisory Committee outlines the kindergarten through grade eight mathematics curriculum in terms of nine "strands": Numbers and Operations, Geometry, Measurement, Applications of Mathematics, Statistics and Probability, Sets, Functions and Graphs, Logical Thinking, and Problem Solving. Broad goals…

Twenty second- and third-grade children were tested on their ability to make judgements of certain area and volume equivalences. The children were then presented a conservation-of-liquid task. Of the 17 children who gave correct conservation responses, only two had solved the area and volume problems. Thus, contrary to what is suggested by…

This nineteenth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 17. First, a time allotment for each of the chapters in Units 17 and 18 is given. Then, for each of the chapters in Unit 17, the goals for that chapter are discussed, the mathematics is explained, some teaching suggestions are given, answers…

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…

After a unit on Euclidean geometry which stresses both the development of intuition and the use of deductive methods, non-Euclidean concepts are introduced by having students read and consider science fiction stories. (SD)