This investigation was made in a secondary school where the learning of algebra was studied during three years (Grades 7-9). There were 119 pupils divided into two experimental groups each of which had a different course in algebra. The content of these courses was measured by the number of written exercises. Many ability tests and attitude ratings were presented to the pupils. Then, essential differences between pupils were extracted by using several multivariate methods. As a result, the...

Topics: ERIC Archive, Achievement, Algebra, Learning, Prediction, Secondary School Mathematics, Student...

Described is a study concerned with the mode of presentation of printed mathematical word problems. Tenth grade students were given twenty word problems to solve, presented in one of three ways: (1) prose only, (2) prose with an accurate picture included, or (3) prose with a distorted picture. Experimental results showed that the group with an accurate picture performed significantly higher (.005) than the group with no picture, which in turn performed significantly higher (.005) than the group...

Topics: ERIC Archive, Achievement, Instruction, Learning, Problem Solving, Secondary School Mathematics,...

This newsletter summarizes findings from the research on secondary school mathematics published during 1971 that might be used by teachers. Covered is research on behavioral objectives, individualized procedures, comparisons of "modern" and "traditional" programs, activity learning procedures for teaching geometry, learning of logic, computer-aided instruction, homework, test development, student attitudes, problem solving, and patterns of teacher behavior. A list of 39...

Topics: ERIC Archive, Curriculum, Instruction, Mathematics Education, Newsletters, Research, Research...

This is the student's textbook for Algorithms, Computation, and Mathematics (Algol Supplement). This computer language supplement is split off from the main text to enable a school to choose the computer language desired, and also to make it easier to modify the course as languages change. The chapters in the text are designed to add language capability. Each can be read in conjunction with the main text section by section. (RH)

Topics: ERIC Archive, Algorithms, Computers, Instructional Materials, Programing Languages, Secondary...

Parabolic shapes are easy to find. Many homes outside the cable area have parabolic antennas to receive television transmissions from a satellite far out in space. Parabolic extrusions are used as reflectors behind fluorescent tubes and solar heated water pipes. Parabolic reflectors are used to build solar ovens, searchlights and radio telescopes. This article presents two work sheets: the first is designed for use with "Cabri Geometry" to study the parabola as a conic section and the...

Topics: ERIC Archive, Geometry, Geometric Concepts, Teaching Methods, Mathematics Instruction, Secondary...

Presented is a general guide and syllabus for each of 14 secondary school mathematics courses offered by the Kent School District. Statements of the philosophy, organization, implementation, course sequences, requirements, guidance, and evaluation involved with the program are included. The courses for which a complete syllabus is offered include: Accelerated Math 7, Modern Math 7, Basic Math 7, Modern Math 8, Basic Math 8, Basic Math 9, Basic Math 1-2, Pre-Algebra 1-2, Algebra 1-2, Geometry...

Topics: ERIC Archive, Curriculum, Curriculum Guides, Instruction, Mathematics, Secondary School...

This report carries the story of the establishment and expansion of the Schools Council-Nuffield Foundation project in primary mathematics (ages 5-13) up to the end of 1966, and looks ahead to the implications emerging for teachers, administrators, employers and parents. (Author/MM)

Topics: ERIC Archive, Curriculum Development, Curriculum Evaluation, Elementary School Mathematics, Program...

This is the teacher's guide and commentary for the SMSG textbook Algorithms, Computation and Mathematics (Algol Supplement). This teacher's commentary provides background information for the teacher, suggestions for activities found in the student's Algol Supplement, and answers to exercises and activities. The course is designed for high school students in grades 11 and 12. Access to a computer is highly recommended. (RH)

Topics: ERIC Archive, Algorithms, Computers, Mathematics Education, Programing Languages, Secondary...

This document suggests ways of setting up a "Math Resource Center" and ideas for particular resources. Briefly discussed are the following: purpose of a resource center; supervision; physical facilities; and materials-library, math lab and games, computer, autio-visual materials, and office machines. Lists in the appendices include: journals, paperback booklets, selected bibliographies, selected sources of math lab equipment, games, and enrichment materials, commercial producers of...

Topics: ERIC Archive, Bibliographies, Enrichment, Instructional Materials, Resource Centers, Resource...

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 type. The topics covered include integral and differential calculus, algebraic and trigonometrical functions, the binomial expansion, linear algebra,...

Topics: ERIC Archive, Algebra, Calculus, Essay Tests, Grade 12, Mathematics Education, Secondary School...

This supplement was written for students who are especially good in mathematics and who have a lively interest in the subject. It is suggested that the supplement be read with pencil and paper in hand. All questions should be considered and answered, if possible, when they occur. A casual reading of the supplement is, in most cases, unprofitable. For the most part, the units are independent of each other. Some of the sections in this publication relate to the chapters of the eleventh-grade...

Topics: ERIC Archive, Algebra, Instructional Materials, Number Concepts, Secondary Education, Secondary...

This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This text, Part I, contains the first five chapters of the course and two appendices. Chapters included are: (1) Polynomial Functions; (2) The Derivative of a Polynomial Function; (3) Circular Functions; (4) Derivatives of Circular Functions; and (5) Exponential and Related Functions. The appendices are: (1) Functions...

Topics: ERIC Archive, Algebra, Calculus, Instructional Materials, Mathematics, Number Concepts, Secondary...

This booklet contains copies of the two major presentations at the SMSG Conference on Future Responsibilities for School Mathematics: "A History of Attempts to Improve School Mathematics in the United States" (Phillip S. Jones), and "The Future of Mathematics Education in the United States" (Marshall H. Stone). A summary of the discussions following these two addresses is included, along with a listing of the final recommendations for general operational procedures, research...

Topics: ERIC Archive, Conference Reports, Curriculum, Curriculum Development, Elementary School...

GRADES OR AGES: Secondary. SUBJECT MATTER: Geometry. ORGANIZATION AND PHYSICAL APPEARANCE: The subject content of the guide is arranged in four columns--major areas, significant outcomes, observations and suggestions, references and films. The guide is mimeographed and spiral bound with a soft cover. OBJECTIVES AND ACTIVITIES: General objectives are listed in the introductory material, with more specific objectives in the significant outcomes columns. Activities are not listed in detail....

Topics: ERIC Archive, Curriculum Guides, Geometry, Mathematics, Secondary Education, Secondary School...

THIS TEACHING GUIDE IS THE THIRD OF FIVE EXPERIMENTAL EDITIONS CONCERNING MATERIALS AND METHODS FOR TEACHING A REVISED MATHEMATICS PROGRAM IN GRADE 8. BACKGROUND MATERIAL FOR TEACHERS AS WELL AS QUESTIONS AND ACTIVITIES FOR CLASSROOM PRESENTATIONS ARE PROVIDED IN THE CONTENT AREAS OF POLYNOMIAL EXPRESSIONS (UNIT 8) AND POLYNOMIAL EQUATIONS (UNIT 9). UNIT 8 CONTAINS SECTIONS ON ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION OF POLYNOMIAL EXPRESSIONS, AND FACTORING POLYNOMIAL EXPRESSIONS....

Topics: ERIC Archive, Algebra, Curriculum, Curriculum Guides, Grade 9, Mathematics, Secondary School...

This commentary is designed for use with "Unified Modern Mathematics, Course I," Parts 1 and 2. Included in the commentary are statements of the specific purposes and goals of each section of every chapter, suggestions for teaching the concepts presented in each section, time estimates for each section, suggested instructional aids for presenting various concepts, and references for further study. Also, suggested chapter examinations are provided which constitute comprehensive tests...

Topics: ERIC Archive, Course Descriptions, Curriculum Guides, Instruction, Instructional Materials,...

This is unit fourteen of a fifteen-unit SMSG secondary school text for high school students. The text is devoted almost entirely to mathematical concepts which all citizens should know in order to function satisfactorily in our society. Chapter topics include statistics and systems of sentences in two variables. (MP)

Topics: ERIC Archive, Algebra, Curriculum, Geometric Concepts, Instruction, Mathematics Education,...

Presented are more than 300 problems of varying difficulty along with answers and solutions. These problems were initially given to participants in mathematics contests among high school students. With each problem a time factor is included as well as a percentage of participants who successfully solved that problem. (CT)

Topics: ERIC Archive, Mathematical Enrichment, Mathematics, Problem Sets, Resource Materials, Secondary...

Unit 14 in the SMSG secondary school mathematics series is a student text covering the following topics in geometry: areas of polygonal regions, similarity, circles and spheres, characterization of sets, constructions, areas of circles and sectors, volumes of solids, and plane coordinate geometry. Appendices cover Eratosthenes' measurement of the earth, rigid motions, proof of the two-circle theorem, trigonometry, and regular polyhedra. (DT)

Topics: ERIC Archive, Curriculum, Elementary Secondary Education, Geometry, Instruction, Instructional...

This is part three of a three-part SMSG calculus text for high school students. The aim of the text is to develop some of the concepts and techniques which will enable the student to obtain important information about graphs of elementary functions. Chapter topics include area and the integral, differentiation theory and technique, mathematical induction, and further techniques of integration. (MP)

Topics: ERIC Archive, Calculus, Curriculum, Graphs, Induction, Instruction, Mathematics Education,...

This text contains material designed for about 18 weeks of study at grades 11 or 12. Use of a computer with the course is highly recommended. Developing an understanding of the relationship between mathematics, computers, and problem solving is the main objective of this book. The following chapters are included in the book: (1) Algorithms, Language, and Machines; (2) Input, Output, and Assignment; (3) Branching and Subscripted Variables; (4) Looping; (5) Functions and Procedures; (6)...

Topics: ERIC Archive, Algorithms, Computers, Instructional Materials, Programing Languages, Secondary...

This study was conducted to address two questions: (1) are deficiencies in fraction skills due to current instructional programs, and, if yes, (2) should instruction on fractions be postponed until secondary school or should instruction at the elementary levels be revised? A battery of fraction tests consisting of 78 items was developed; tests were classified according to cognitive level as computation, comprehension, or applications. Tests were given to average eighth-grade students. More than...

Topics: ERIC Archive, Achievement, Curriculum, Educational Research, Fractions, Instruction, Mathematics...

THIS GUIDE OUTLINES THE MINIMUM MATERIAL FOR WHICH STUDENTS OF NINTH YEAR MATHEMATICS - COURSE 1 - ALGEBRA WERE HELD RESPONSIBLE ON THE REGENTS EXAMINATIONS BEGINNING IN JUNE, 1966. THE REPORT ALSO PRESENTS THE SCOPE AND CONTENT OF THE ALGEBRA COURSE AND POSSIBLE SUGGESTIONS FOR TEACHING THE MATERIAL TO STUDENTS. (RP)

Topics: ERIC Archive, Algebra, Arithmetic, Curriculum Guides, Geometry, Grade 9, Mathematics, Secondary...

GRADES OR AGES: 7-12. SUBJECT MATTER: Mathematics laboratory. ORGANIZATION AND PHYSICAL APPEARANCE: The guide has 10 sections: (1) introduction, explaining the nature of the student and the duties of the teacher; (2) personnel and their duties; (3) physical characteristics of the lab; (4) testing program; (5) evaluation procedure; (6) record keeping; (7) types of instruction; (8) initial organization; (9) description of the program; (10) recommendations for equipping a secondary mathematics...

Topics: ERIC Archive, Curriculum Guides, Learning Laboratories, Mathematics Curriculum, Remedial...

One hundred forty-eight secondary school principals were chosen at random and asked to select one teacher at random from the mathematics faculty of their schools. Both were administered the Mathematics Inventory for Teachers, an instrument designed to measure attitudes toward mathematics as a subject and toward its teaching. The principals were asked to respond as they believed an ideal mathematics teacher would, while the teachers were asked to express their own beliefs and opinions. The...

Topics: ERIC Archive, Educational Research, Mathematics, Principals, Secondary Education, Secondary School...

This is part one of a two-part SMSG Programed Algebra Text for high school students. The general plan of the course is to build upon the student's experience with arithmetic. The student is initially led to extract from his or her experience the fundamental properties of addition and multiplication. The text then introduces negative real numbers and extends the fundamental operations to develop the real number system. Chapter topics include: sets and the number line; numerals and variables;...

Topics: ERIC Archive, Algebra, Curriculum, Instructional Materials, Mathematics Education, Programed...

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, axioms, congruence, constructions, lines, angles, parallelograms, loci, circles, angle measure, similarity, numerical trigonometry, area, coordinate...

Topics: ERIC Archive, Algebra, Arithmetic, Curriculum, Curriculum Guides, Geometry, Grade 10, Mathematics...

THIS TEACHING GUIDE FOR TRIGONOMETRY IS THE FINAL UNIT OF A SERIES OF 12 UNITS FOR AN EXPERIMENTAL COURSE IN MATHEMATICS FOR GRADE 9. BACKGROUND MATERIAL FOR TEACHERS AS WELL AS QUESTIONS AND ACTIVITIES FOR CLASSROOM PRESENTATIONS ARE PROVIDED. A GLOSSARY OF MATHEMATICAL TERMS FOR THE 12 UNITS CONCLUDES THE REPORT. (RP)

Topics: ERIC Archive, Curriculum, Curriculum Guides, Grade 9, Mathematics, Secondary School Mathematics,...

This is unit fifteen of a fifteen-unit SMSG secondary school text for high school students. The text is devoted almost entirely to mathematical concepts which all citizens should know in order to function satisfactorily in our society. Chapter topics include analyzing geometric figures and measurement. (MP)

Topics: ERIC Archive, Algebra, Analytic Geometry, Curriculum, Instruction, Mathematics Education,...

This is one in a series of manuals for teachers using SMSG high school supplementary materials. The pamphlet includes commentaries on the sections of the student's booklet, answers to the exercises, and sample test questions. Topics covered include sets, definition and graph of a function, constant, linear and absolute-value functions, composition, inversion, one-to-one functions, ordered pairs, circular motion, graphs of sine and cosine, angles, vectors, addition formulas, tables of circular...

Topics: ERIC Archive, Curriculum, Curriculum Guides, Enrichment, Graphs, Instruction, Mathematics...

Presented is the work of the calculus group of SMSG. The Advisory Board expressed a desire for a suitable high school calculus text. The calculus group surveyed available texts and, finding none which met advisory board requirements, outlined a suitable course. This outline was annotated for use by future writers. Some group members felt a more extended discussion of topics, suitable for use by students, was needed. A subgroup drafted this student version and in doing so changed the outline....

Topics: ERIC Archive, Calculus, Mathematics Curriculum, Mathematics Instruction, Secondary Education,...

Algebra word problems were analyzed in terms of the information integration tasks that are required to solve the problems. These tasks were classified into three levels: value assignment, value derivation, and equation construction. Novices (35 first year algebra students) and experts (13 analytic geometry students) were compared on the proportion of tasks completed at each level in their attempts to solve six word problems. As predicted, the novices showed greatest weakness on the tasks from...

Topics: ERIC Archive, Algebra, Educational Research, Error Patterns, Mathematics Instruction, Problem...

This commentary is designed for use with "Unified Modern Mathematics, Course II," Parts 1 and 2. As in the commentary for "Course I," statements of the specific purposes and goals of each section of every chapter are presented. Also included are suggestions for teaching the concepts presented in each section, time estimates for each section, suggested instructional aids to presenting various concepts, and references for further study. Chapter examinations are provided which...

Topics: ERIC Archive, Course Descriptions, Curriculum Guides, Instruction, Instructional Materials,...

This is a manual for teachers using SMSG high school programed text materials in algebra. The commentary is organized into four parts. The first part contains a discussion of ways to use this programed text. The second and main part consists of a chapter by chapter commentary on the text. The third part is a listing of topics keyed to a list of supplementary references from the volumes of the "New Mathematical Library" (NML), which is a series of expository monographs produced by the...

Topics: ERIC Archive, Algebra, Curriculum, Instruction, Mathematics Education, Programed Instruction,...

This sixteenth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 14. For each of the chapters in Unit 14, a guide to the selection of problems is provided, the goals for that chapter are discussed, the mathematics is explained, some teaching suggestions are given, the answers to exercises are listed, and sample test questions for that chapter are included. A final section, labelled "Talks to Teachers," discusses facts and theories; equality,...

Topics: ERIC Archive, Curriculum, Elementary Secondary Education, Geometry, Instruction, Mathematics...

Unit 13 in the SMSG secondary school mathematics series is a student text covering the following topics in geometry: common sense and organized knowledge; sets, real numbers, and lines; lines, planes, and separation; angles and triangles; congruences; proof; geometric inequalities; perpendicular lines and planes in space; parallel lines in a plane; and parallels in space. Appendices cover symbols, postulates of addition and multiplication, rational and irrational numbers, square roots, how to...

Topics: ERIC Archive, Curriculum, Elementary Secondary Education, Geometry, Instruction, Instructional...

This is part one of a two-part SMSG geometry text for high school students. One of the goals of the text is the development of analytic geometry hand-in-hand with synthetic geometry. The authors emphasize that both are deductive systems and that it is useful to have more than one mode of attack in solving problems. The text begins the development of geometry synthetically and teaches the method of synthetic proof, then leads quickly to the use of coordinate systems in the remainder of the work....

Topics: ERIC Archive, Analytic Geometry, Curriculum, Geometry, Instructional Materials, Mathematics...

This book is designed to illustrate how one general method of calculus is used in many different sciences and how different methods of calculus have furthered the development of essentially one field of science. The material is written so that it could serve as a math-science supplement for many courses. Chapters included are: (1) Introduction; (2) Growth, Decay, and Competition; and (3) Geometrical Optics and Waves. The Introduction contains suggestions for teaching, additional readings, and...

Topics: ERIC Archive, Calculus, College Mathematics, Instructional Materials, Mathematical Applications,...

This is part two of a two-part manual for teachers using SMSG high school text materials. The commentary is organized into four parts. The first part contains an introduction and a short section on estimates of class time needed to cover each chapter. The second or main part consists of a chapter-by-chapter commentary on the text. The third part is a collection of essays on topics that cannot conveniently be dealt with in the main part of the commentary in connection with a particular passage....

Topics: ERIC Archive, Analytic Geometry, Curriculum, Geometry, Instruction, Mathematics Education,...

This is part three of a three-part SMSG calculus text for high school students. One of the goals of the text is to present calculus as a mathematical discipline as well as presenting its practical uses. The authors emphasize the importance of being able to interpret the concepts and theory in terms of models to which they apply. The text demonstrates the origins of the ideas of the calculus in practical problems; attempts to express these ideas precisely and develop them logically; and finally,...

Topics: ERIC Archive, Calculus, Curriculum, Instructional Materials, Mathematical Applications, Mathematics...

This is part one of a three-part SMSG calculus text for high school students. The aim of the text is to develop some of the concepts and techniques which will enable the student to obtain important information about graphs of elementary functions. Chapter topics include: (1) polynomial functions; (2) the derivative of a polynomial function; and (3) circular functions. (MP)

Topics: ERIC Archive, Calculus, Curriculum, Graphs, Instruction, Mathematics Education, Secondary...

This is part two of a three-part SMSG algebra text for high school students. The principle objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure exhibited by the real number system, and the use of this structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real numbers, subtraction and division of real numbers, factors, exponents, radicals, and polynomials and rational...

Topics: ERIC Archive, Algebra, Curriculum, Instruction, Mathematics Education, Number Concepts, Secondary...

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 development of topics in algebra, and the search for generality and abstract structures. (Author/JG)

Topics: ERIC Archive, Algebra, Enrichment, Instructional Materials, Mathematical Concepts, Mathematics,...

Unit 21 in the SMSG secondary school mathematics series is a student text covering the following topics in elementary functions: functions, polynomial functions, tangents to graphs of polynomial functions, exponential and logarithmic functions, and circular functions. Appendices discuss set notation, mathematical induction, significance of polynomials, area under a polynomial graph, slopes of area functions, the law of growth, approximation and computation of e raised to the x power, an...

Topics: ERIC Archive, Curriculum, Elementary Secondary Education, Instruction, Instructional Materials,...

This guide includes a list of general objectives and a scope chart of units to be covered in grades K-12. Objectives for specific topics are listed and are coded to the scope chart; text sources and materials are suggested; and lists of learning activities and audiovisual aids are provided. Separate sections of the guide cover topics in elementary school mathematics and junior high school mathematics; an individual lesson program for Algebra II is detailed; and topics to be covered in grade 12...

Topics: ERIC Archive, Curriculum, Curriculum Guides, Elementary School Mathematics, Instruction,...

The slow learner is defined as a student whose IQ falls between 75 and 90 or who ranks below the thirtieth percentile of the student population in mathematical achievement. His characteristics and special needs are discussed in some detail. A presentation of selected methods and techniques for instructing slow learners to add and subtract non-decimal fractions follows. Behavioral objectives, specific topics, and an estimated schedule are given. Resources required for this instruction are...

Topics: ERIC Archive, Addition, Fractions, Instruction, Secondary Education, Secondary School Mathematics,...

Three Project Solo modules are presented. They are designed to teach the concepts of elementary matrix operation, matrix multiplication, and finite-state automata. Together with the module on communication matrices from Newsletter #17 they form a well motivated but structured path to expertise in this area. (JY)

Topics: ERIC Archive, Computer Assisted Instruction, Computer Programs, Computer Science Education,...

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, some teaching suggestions are given, and the answers to exercises are listed. For each of the chapters except the first, sample test questions are...

Topics: ERIC Archive, Curriculum, Elementary Secondary Education, Geometry, Instruction, Mathematics...

This is the teacher's guide and commentary for the SMSG textbook Algorithms, Computation, and Mathematics (Fortran Supplement). The teacher's commentary provides background information for the teacher, suggestions for activities found in the Fortran Supplement, and answers for exercises and activities. The course is designed for high school students in grades 11 and 12. Access to a computer is highly recommended. (RH)

Topics: ERIC Archive, Algorithms, Computers, Mathematics Education, Programing Languages, Secondary...

This is one of a series of publications written to supplement the secondary school School Mathematics Study Group program. This booklet will be most useful for enrichment at the eleventh and twelfth grade levels. It treats algebraic structures as abstract mathematical systems and introduces such important ideas as group, non-abelian group, field, and subfield. Proofs are rigorous, but not tedious. Answers to the problems are found in the back of the book. As background, the reader needs to be...

Topics: ERIC Archive, Algebra, Instructional Materials, Mathematics, Number Concepts, Secondary Education,...