# The Teaching of Mathematics 4th Revised and Enlarged Edition, 12th Reprint

by Kulbir Singh SidhuPaperback

## Book Information

Publisher: | Sterling Publishers Private Limited |

Published In: | 2008 |

ISBN-10: | 8120717473 |

ISBN-13: | 9788120717473 |

Binding Type: | Paperback |

Weight: | 1.04 lbs |

Pages: | xiv + 413 Pages, Figures, Tables, Reference |

The Title "The Teaching of Mathematics 4th Revised and Enlarged Edition, 12th Reprint" is written by Kulbir Singh Sidhu. This book was published in the year 2008. The ISBN number 8120717473|9788120717473 is assigned to the Paperback version of this title. The book displayed here is a 4th Revised and Enlarged Edition, 12th Reprint edition. This book has total of pp. xiv + 413 (Pages). The publisher of this title is Sterling Publishers Private Limited. We have about 4509 other great books from this publisher. The Teaching of Mathematics 4th Revised and Enlarged Edition, 12th Reprint is currently Available with us.

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## Contents

Preface to the Fourth Edition

Preface to the Third Edition

Preface to the First Edition

Chap. 1 : THE EDUCATIONAL VALUES OF Mathematics :

Educational Values; Values and Aims; Practical Value; Disciplinary Value; Cultural Value; Social Value; Moral Value; Aesthetic Value; Intellectual Value; International Value; Vocational Value; Some More Values; Development of Concentration; Art of Economical Living; Power of Expression; Self-Reliance; Attitude of Discovery; Understanding of 3opular Literature; Quality of Hard Work; The Place of Mathematics in Everyday Life; The Place of Mathematics in the School Curriculum.

Chap. 2 : AIMS AND OBJECTIVES OF TEACHING MATHEMATICS :

Aims and Objectives; Aims of Teaching Mathematics; Objectives at the Entire School Stage; Objectives of Teaching Mathematics at Different Stages; Objectives at the Secondary Stage; Objectives at the Elementary Stage; Formulation of Objectives.

Chap. 3 : THE RELATION OF MATHEMATICS WITH OTHER SUBJECTS :

Mathematics and Physical and Biological Sciences; Mathematics and Physics; Mathematics and Chemistry; Mathematics and Biology; Mathematics and Engineering; Mathematics and Agriculture. Mathematics and Social Sciences; Mathematics and Economics; Mathematics and Psychology; Mathematics and Logic; Mathematics and Philosophy; Mathematics and Fine Arts; Mathematics and Geography

Chap. 4 : CURRICULUM IN MATHEMATICS :

The Dynamic Approach to Curriculum; The Teacher's Concern in Curriculum Construction; Objectives of Curriculum; Curriculum as a Means to an End; Flexibility in the Curriculum; Why Revision of the Present Curriculum in Mathematics? Who should Organise and Revise?; Principles Governing Curriculum Construction; Criterion of Preparatory Value; Criterion of Disciplinary Value; Criterion of Cultural Value; Use is the Chief Criterion; Child-Centred Curriculum; A Comprehensive Curriculum; Principles and Methods of Arranging the Curriculum; Psychological and Logical Arrangement; Scope for Practical Work; The Criterion of Difficulty; Voice of the Teacher; Topical Versus Spiral Arrangement; The Principle of Cyclic Order; Incidental Versus Organised Teaching; Individual Versus Class Teaching; The Dalton Plan; The Project Plan; From the Empirical to the Rational; The Principle of Correlation; Correlation with Life; Correlation with other Subjects; Correlation of Different Bunches of Mathematics; Correlation of Topics in the Same Branch; Problems : Puzzle Problems; Catch Problems; Unreal Problems; Real Problems; Oral and Written Forms; Suggestive Learning Experiences; Methods and Techniques for Evaluation; Recommendations of Kothari Commission in Respect of Mathematics Curriculum; The Commission Observes; Analysis or Critical Evaluation of a Syllabus

Chap. 5 : METHODS OF TEACHING :

Lecture; Dogmatic; Inductive-Deductive; Heuristic; Analytic; Synthetic; Laboratory; Project; Topical; Concentric; Problem; an Assessment

Chap. 6 : TECHNIQUES OF TEACHING :

Oral Work; Written Work; Drill Work; Home Work; Assignment; Self-Study; Group Work; Review; Supervised Study

Chap. 7 : AIDS TO TEACHING AND MATHEMATICS LABORATORY :

Personal Equipment of the Student; Equipment of the Mathematics Laboratory; Placement of the Material; Blackboard; Concrete Materials; Teach a Number Kit; Place-Value Pockets; Fractional Parts; Charts; Models; Excursions; Collections; Filmstrips; Radio; Television; Some Special Instruments; Computer; Home-Made Equipment

Chap. 8 : MATHEMATICS LIBRARY AND THE TEXT-BOOK :

Importance of Library; General School Library; Mathematics Department Library; The Use of Library; The Text-book; Its Importance; Uses of the Text-book; Essentials of A Good Text-book

Chap. 9 : AROUSING AND MAINTAINING INTEREST IN MATHEMATICS-PRINCIPLES OF MEANINGFUL LEARNING-MATHEMATICS CLUB :

Arousing and Maintaining Interest; Intellectual Activity; Application to other Fields of Study; Application of Mathematics to Professional Fields; Practical Values; Cultural Values; Recreational Values; Practical Work; The Principle of Change; Physical Conditions for Study; Psychological Conditions for Study A List of Study Suggestions; Principles of Meaningful Learning in Mathematics; Mathematics Club

Chap. 10 : MATHEMATICS TEACHER :

Prerequisite Qualifications; Professional Training; Selective Academic Training; Supervised Practice of Teaching; In-service Training; Professional Activities; School Activities; Mathematical Organizations; Departmental Duties; Administrative Duties; Community Activities

Chap. 11 : MEASUREMENT AND EVALUATION :

Purposes of Evaluation; Criteria of Measuring Tests; (Validity, Reliability, Administrability, Student Consciousness, Objectivity, Motivation for the Student, Utility, Comprehensiveness); Prognosis and Diagnosis; Survey Test; Achievement Test; New Type Tests; Intelligent Essay Type Questions; Construction of a Test; Steps in Test Construction; Scheme for Preparing an Evaluation Tool

Chap. 12 : GIFTED STUDENTS AND BACKWARD STUDENTS :

Gifted Students; Locating the Gifted; Enrichment Programme for the Gifted; Backward Students; General Backwardness; Particular Backwardness; Causes and Remedies

Chap. 13 : DEFECTS IN THE PRESENT-DAY TEACHING OF MATHEMATICS IN SCHOOLS AND THEIR POSSIBLE REMEDIES :

Teachers' Qualifications; Burden; Salary; Attitude; Lack of Purpose; Lack of Equipment; Method of Teaching; Rigour in Study; Large Classes; Practical Aspect; Mathematical Language; Syllabus; Text-books; Students; Child-Centre Approach; Libraries and Laboratories; Short-Cut Methods; Examinations

Chap. 14 : History OF MATHEMATICS :

Value of History; The Babylonians; The Egyptians; The Greeks; The Romans; The Chinese; The Japanese; The Hindus; The Arabs; Historical Reviews of Developments; Notation System; System of Weights and Measures; Logarithms; Computer Mathematics; Structure of Modern Computers

Chap. 15 : SOME GREAT MATHEMATICIANS :

Aryabhata; Brahmagupta; Bhaskara; S. Ramanujan; Euclid, Pythagoras; Gauss

Chap. 16 : THE NATURE OF MATHEMATICS :

Science of Logical Reasoning; Mathematical Language and Symbolism; Pure and Applied Mathematics; Topology

Chap. 17 : STRUCTURE OF MATHEMATICS :

Number System; Comparison of Structures in the System of Natural Basic Algebraic Structures; Group; Ring; Field; Vector Space

Chap. 18 : MODERN MATHEMATICS :

What is New Mathematics?; Understanding of Modern Mathematics; Importance and Aims of Teaching; Essentials of Deductive Reasoning; Set Language and Set Notation; Venn Diagrams

Chap. 19 : EUCLIDEAN AND NON-EUCLIDEAN GEOMETRIES :

Euclidean Geometry; Shortcomings of Euclidean Geometry; Non-Euclidean Geometries; Hilbert's Modified Euclidean Geometry; Hyperbolic Geometry; Elliptical Geometry

Chap. 20 : THE TEACHING OF ARITHMETIC :

What is Arithmetic ?; Aims of Teaching; Methods of Teaching; Numeration and Notation; The Teaching of Four Simple Rules; LCM and GCM; Fractions; Decimal Fractions; Metric Measures; Decimal System in India; Square Root; The Unitary Method; Ratio Proportion; Percentage; Profit and Loss; Simple Interest; Compound Interest; Discount; Area; Volume

Chap. 21 : THE TEACHING OF Algebra :

What is Algebra?; Why Teach?; The Signed Numbers; The Use of Brackets Graphs; Factorising; and Formulae; Indices; Quadratic Equations

Chap. 22 : THE TEACHING OF Geometry :

Geometry; Demonstrative Geometry; Practical Geometry; Why Teach?; Functions in the Middle School; Functions in the High School; Functions in the Senior High School; Different Stages of Teaching; When to introduce Reasoning?; Axioms and Postulates; Fundamental Concepts; Definitions; Propositions; Kinds of Proofs; The Key Propositions; Symbolic Notation; Induction and Deduction; Synthesis and Analysis; Angle-Sum of a Triangle; Congruent Triangles; Similarity; Locus; Riders; Constructions

Chap. 23 : THE TEACHING OF Trigonometry :

Why Teach?; Meaning of a Trigonometric Function; Inverse Functions; Functions of Special Angles; Functions of the General Angle; Use of Trigonometric Functions; Functions of Two Angles; Variation of the Functions; The Solution of Triangles; Radian Measure; Trigonometric Equations and Identities

Chap. 24 : THE TEACHING OF SOLID GEOMETRY :

What is Solid Geometry?; introduction; Some Axioms; Scope; Methods to Teach; Parallel Planes; Projection; Correlation

Chap. 25 : LESSON PLANS :

i. Proposition : A Side of a Triangle is Produced so as to Form an Exterior Angle. Prove that the Sum of the Opposite Angles is Equal to this Exterior Angle

ii. Identity a² - b² = (a + b)(a - b)

iii. True Discount

iv. Square Root of Surd of the Form a + √b

v. To Prove Sin (A + B) = Sin A Cos B + Cos A Sin B