Techniques of Teaching Mathamatics

Contents
Unit - I
THE NATURE AND SIGNIFICANCE OF MATHEMATICS
1. Meaning and Nature of Mathematics
1.1 Mathematics: Meaning and Definitions
1.2 Nature of Mathematics
1.3 Need and Significance of Learning Mathematics... 9
2. Importance of Knowledge of History of Mathematics to a Mathematics Teacher
Unit - II
CONTRIBUTIONS OF GREAT MATHEMATICIANS
3. Contribution of Euclid to Mathematics
4. Contribution of Pythagoras to Mathematics
5. Contribution of George Cantor to Mathematics
6. Contribution of Rene Descartes to Mathematics
7. Contribution of Aryabhatta to Mathematics
8. Contribution of Bhaskaracharya to Mathematics
9. Contribution of Srinivasa Ramanujan to Mathematics
Unit - III
AIMS AND VALUES OF TEACHING MATHEMATICS
10. Aims of Teaching Mathematics
10.1 Utilitarian or Practical Aims
10.2 Disciplinary Aims
10.3. Cultural Aims
10.4 Social Aims
11. Values of Teaching Mathematics at Secondary Level
11.1 Utilitarian or Practical Values
11.2 Cultural Values
11.3 Disciplinary Values
11.4 Social Values
11.5 Recreational Value
11.6 Aesthetic Value
12. Correlation of Mathematics to Sciences and Social Sciences
12.1 Correlation of Mathematics with Life Activis
12.2 Correlation of Different Branches of Mathe
12.3 Correlation of Topics in the Same Branch of Mathematics
12.4 Correlation of Mathematics with Physics
12.5 Correlation of Mathematics with Chemistry
12.6 Correlation of Mathematics with Biology
12.7 Correlation of Mathematics with Engineering
12.8 Correlation of Mathematics with Social Scien
12.9 Correlation of Mathematics with Language an Literature
12.10 Correlation of Mathematics with Art and Architecture
Unit - IV
OBJECTIVES OF TEACHING MATHEMATICS
13. Meaning and Importance of Objectives
13.1 Meaning of Objectives
13.1.1 Comparison between Aims and Objectives
13.2 Instructional Objective Definition and Meaning...
13.2.1 Importance of Stating Instructional Objectives
13.3 Objectives-based Teaching and Testing
14. Bloom's Taxonomy of Educational Objectives
14.1 Cognitive Domain
14.2 Affective Domain
14.3 Psychomotor Domain
15. Specific Behavioural Objectives (Instructional Objectives)
15.1 General Instructional Objectives
15.2 Specific Behavioural Objectives
15.3 Five Elements in Writing Specific Behavioural Objectives
15.4 Guidelines for Stating Objectives
15.5 General Objectives and Specifications Relating to Cognitive, Affective and Psychomotor Domains for Teaching Mathematics
15.6 Skills to be Developed in Mathematics
16. Critique on Bloom's Taxonomy
Unit - V
APPROACHES AND METHODS OF TEACHING MATHEMATICS
17. Methods of Teaching Mathematics
18. Techniques of Teaching Mathematics
18.1 Oral Work
18.1.1 Suggestions for Improving Oral Work
18.1.2 Advantages of Oral Work
18.2 Written Work
Methods...
18.2.1 Functions of Written Work
18.3 Drill Work
18.3.1 The Functions of Drill
18.3.2 Principles of Drill
18.3.3 Demerits of Drill
18.3.4 Review
18.4 Assignments
18.4.1 Steps in Giving Assignment
18.4.2 Importance of Class Assignments
18.4.3 Home Assignment
Effective 18.4.4 Some Guidelines for Making Homework more
18.5 Means of Securing Speed and Accuracy in Mathematics
Unit - VI
132 EVOLVING STRATEGIES FOR THE GIFTED STUDENTS AND SLOW LEARNERS
19. Gifted Students in Mathematics Identification Enrichment Programmes
19.1 The Identification of the Gifted in Mathematics
19.1.1 Characteristics of the Mathematically Gifted
19.2 Enrichment Programme for the Gifted
20. Slow Learners in Mathematics Identification
Remedial Programmes
20.1 Identification of Slow Learners
20.2 Causes and Remedies
20.3 Some Useful Classroom Techniques for Slow Learners
20.4 Arousing and Maintaining Interest in Mathematics
Unit - VII
PLANNING FOR EFFECTIVE INSTRUCTION IN MATHEMATICS
21. Meaning and Purpose of Year Plan
21.1 Year Plan: Need and Significance
21.2 Advantages of Year Plan
22. Meaning and Purpose of Unit Plan
22.1 Meaning and Definition of a Unit
22.2 Steps in Unit Planning
22.3 Uses of a Unit Plan
23. Meaning and Purpose of Lesson Plan
23.1 Definitions of Lesson Plan
23.2 Functions of a Good Lesson Plan in Mathematics
23.3 Important Features of a Good Lesson Plan
23.4 Steps in Preparing a Lesson Plan
23.4.1 Preparation
23.4.2 Presentation
23.4.3 Association or Comparison
23.4.4 Generalisation
23.4.5 Application
23.4.6 Recapitulation
23.4.7 Steps in Writing Lesson Plan in Mathematics
23.5 Lesson Plan
Unit-VIII
MATHEMATICS CURRICULUM
24. Principles of Carriculum Construction
24.1 Mathematics Curriculum Meaning and Significance
24.2 Characteristics of Modern Mathematics Curriculum
24.3 Principles of Curriculum Construction
24.4 Principles of Curriculum Organisation
25. Approaches to Curriculum Construction
25.1 Logical Approach
25.3 Topical Approach
25.2 Psychological Approach
25.4 Concentric and Spiral Approach
25.5 Place of Mathematics in the School Curriculum...
26. Qualities of a Good Mathematics Textbook
26.1 The Mathematics Textbook
26.1.1 Need for a Good Textbook in Mathematics
26.2 Qualities of a Mathematics Textbook
26.2.1 Physical Features
26.2.2 Author
26.2.3 Content
26.2.4 Organisation and Presentation
26.2.5 Language
26.2.6 Exercise and Illustrations
Unit - IX
NON-FORMAL MATHEMATICS EDUCATION
27. Mathematics Clubs
27.1 Functions of the Mathematics Club
27.2 Organisation of Mathematics Club
27.3 Suggested Activities for a Mathematics Club
28. Mathematics Fairs
28.1 Purposes of Mathematics Fairs
28.2 Advantages of Mathematics Fairs
28.3 Mathematics Fairs at Different Levels 28.4 Organization of the Mathematics Fairs
29. Aesthetic Structure of Mathematics
29.1 Meaning of Aesthetics
29.2 Mathematics and Aesthetics
29.3 Pattern and Order
29.4 Sequence
Unit X
EVALUATION
30. Concept and Process of Evaluation
30.1 Measurement in Education: Meaning and Significance
30.2 Evaluation: Concept and Process
30.3 Purpose of Evaluation
31. Types of Evaluation
31.1 Formative Evaluation
31.2 Summative Evaluation
31.3 Diagnostic Evaluation
31.4 Prognostic Evaluation
32. Tools and Techniques of Evaluation
32.1 Oral Tests
32.2 Written Tests
32.2.1 Essay Type Tests
32.2.2 Short Answer Type Tests
32.3 Performance Tem
32.4 Anees Rend
32.5 Oervation
328 Questionnaire (Survey)
32.7 Inverwy
32.8 Interview
329 Checklist
32.10 Rating Scale
32.11 Sociometric Methods
32.12 Case Study
32.13 Cumulative Record
33. Preparation of Scholastic Achievement Tests (SAT)
33.1 Functions of Achievement Testa
33.2 Preparation of a Scholastic Achievement Test
33.3 Characteristics of Good Achievement Test
33.4 Diagnostic Tests
33.4.1 Levels of Educational Diagnosis
33.4.2 Construction of Diagnostic Tests
34. Analysis and Interpretation of Scores.
34.1 Steps Involved in Statistical Analysis and Interpretation
34.2 Types of Descriptive Analysis
34.2.1 Measures of Central Tendency
34.2.2 Measurement of Dispersion of Variability
34.3 Graphs
34.4 Correlation Analysis