Tested was the hypothesis that learning will be significantly enhanced and classroom activities will tend to be more frequently student-initiated when the learning situation contains three elements--a means of operationally clarifying learning objectives for students, a feedback system to provide the student and teacher with information regarding…

This instructional bulletin was prepared to assist teachers in planning and presenting the sequence of mathematics topics to slow learners. The course is designed to fulfill the high school graduation requirement of one semester of mathematics in the ninth grade. This course combines simple presentations of topics from modern mathematics with new…

This book is a reissue of the second edition which appeared in 1940. It has the distinction of being the first vintage mathematical work published in the NCTM series "Classics in Mathematics Education." The text includes a biography of Pythagoras and an account of historical data pertaining to his proposition. The remainder of the book shows 370…

This booklet is a collection of the papers presented at a joint session of the Mathematical Association of America and the National Council of Teachers of Mathematics during the fiftieth annual meeting of the MAA. These papers were presented under the headings of "Geometry and School Mathematics,""High School Geometry," and…

This study tested and compared the effects of an audio-tutorial method and a traditional lecture method of instruction for an Intermediate College Algebra course and investigated how improvements should be made for the commercially-prepared and teacher-made audio-tutorial materials. A sample of 186 students was randomly selected from the…

The teacher's guide for Unit 10 of this SMSG series covers the chapter on problem solving and the chapter on solution sets of mathematical sentences. The overall purpose for each of the chapters is described, the prerequisite knowledge needed by students is specified, the mathematical development of each chapter is detailed, behavioral objectives…

The first chapter in the twelfth unit of this SMSG series deals with the following topics involving quadratic functions: parabolas, translations of the parabola, completing the square, solving quadratic equations, "falling body" functions, and the use of quadratics in solving other equations. The chapter on statistics discusses…

This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…

The author presents material suitable for use by teachers of gifted students in the junior or senior year of high school. The mathematics presented includes mathematical induction, the binomial expansion, number theory and Pascal's triangle. The author weaves much of the history of mathematics into the materials. Included are student tests and…

Research reported deals with identifying stages in attaining a concept of function by students, eleven through fourteen years of age, of above average ability, taking the experimental mathematics program of the Secondary School Mathematics Curriculum Improvement Study. In order to obtain a hierarchy of the learning stages, both a written test and…

This pamphlet offers information and advice to secondary school mathematics teachers in England. The background is set in the first three chapters, entitled "The History of Mathematics Teaching in England,""The Present Position in the Secondary School," and "The First Stages" (a brief review of elementary school…

The inadequacies in present measurement models are indicated and a description is given of how tree theory, a theory-generative model, overcomes these inadequacies. Among the weaknesses cited in many measurement models are their untested assumptions of linear order and unidimensionality and their inability to generate non-associational…

This document consists of test questions used in three state high schools teaching the new Matriculation pure mathematics course (approximately grade 12). This material was circulated to all schools teaching this course as a teacher resource. The questions are arranged in 14 papers of varying structure and length. Most questions are of the essay…

The first of three volumes of a mathematics training course for Navy personnel, this document covers a wide range of basic mathematics. The text begins with number systems, signed numbers, fractions, decimals, and percentages and continues into algebra with exponents, polynomials, and linear equations. Early chapters were designed to give insight…

This is the sixth 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…