The author describes a way of teaching a one-year geometry course which includes plane geometry, solid geometry, coordinate methods of proof, and vector methods of proof. His method is based upon encouraging students to use the properties of geometric figures that they already accept without formal proof. He employs paper folding extensively to…

Assessed was the performance of subjects who had been exposed to transformational geometry treatment. The performance test consisted of geometry achievement and spacial ability measures. Second and third grade subjects were randomly assigned to experimental and control groups. The experimentals received a twelve lesson treatment and the controls a…

This document is a progress report on the implementation of the recommendations of the Commission on Mathematics regarding the teaching of mathematics in secondary schools. Data were obtained from a survey of about 38,000 students who represented more than 7,500 secondary schools in the United States and who took College Board Achievement tests…

The Mathematics Content Authority List for K-6 represents an attempt to list in one volume the mathematics concepts and skills currently taught in the elementary schools. The list consists of approximately 300 items of mathematical definitions, explanations, and examples. This list is used by the Pennsylvania Retrieval of Information for…

This document is a reprint of the geometry section from the 1954 syllabus Mathematics 10-11-12, An Integrated Sequence for the Senior High School Grades. The text outlines a tenth year geometry course integrated with arithmetic, algebra, and trigonometry, which progresses from an informal to a formal level. The topics suggested include definition,…

This basic guide to a complete secondary mathematics curriculum is designed to ensure that each student will be presented uniform mathematical concepts and principles, geared to his individual needs, abilities, and interests. The guide is not planned for use with a particular textbook; instead, it is to serve as a core around which each teacher…

The first chapter of the seventh unit in this SMSG series discusses perpendiculars and parallels; topics covered include the relationship between parallelism and perpendicularity, rectangles, transversals, parallelograms, general triangles, and measurement of the circumference of the earth. The second chapter, on similarity, discusses scale…

A theory of psychophysics is discussed that enlarges the classical theory in three general ways: (1) the multidimensional nature of perception is made explicit; (2) the transformations of the theory are interpreted geometrically; and (3) attributes are distinguished from sensations and only partially ordered. It is shown that, with the enlarged…

Development of a second-grade mathematics instructional unit is discussed in terms of activities, evaluation procedures, and results of evaluation. The report is organized by topic. Behavioral objectives are followed by descriptions of activities and materials used. Topics include: review of symbols, pictorial representation of numbers, writing…

This teacher's guide for a semester course in trigonometry is prepared for use with the text "Plane Trigonometry with Tables" by E. R. Heineman. Included is a daily schedule of topics for discussion and homework assignments. The scope of each lesson and teaching suggestions are provided. The content for the course includes trigonometric functions,…

The plans for a field test of teaching tenth grade plane geometry through transformations is described. Text and homework materials have been written, and teachers have been trained. Eight intact classes are now being taught utilizing the materials. Data to be collected will include: (1) teacher descriptions of the course via questionnaire; (2)…

This is the second volume of a series produced by the State Education Department of the University of the State of New York. Mathematics objectives and sample items included were originally developed by four local school districts and are not intended to be official or comprehensive, but an aid to teachers in constructing curricula and making…

This is the third volume of a series produced by the New York State Education Department. Originally developed by four local school districts, the mathematics objectives and sample items included were not intended to be official or comprehensive but rather to be used as an aid to teachers in constructing curricula and in making classroom goals…

This is volume five of a series produced by the New York State Education Department. Originally developed by four local school districts, the mathematics objectives and sample items are not intended to be official or comprehensive, but to be an aid to teachers in constructing curricula and in making classroom goals clear and precise. The document…

This fifteenth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 13. A time allotment for each of the chapters in Units 13 and 14 is suggested. Then, for each of the chapters in Unit 13, a guide for the selection of problems is provided, the goals for that chapter are discussed, the mathematics is explained,…