Tuesday, March 3, 2009

Teaching of Mathematics & Methods and Techniques of Teaching Math

Teaching of Mathematics

Introduction:

Mathematics is the pure science which is often referred to as “mother of sciences’. The importance of mathematical knowledge can be realized from the fact that almost all educational philosophies have emphasized its teaching at all levels because it develops the abilities of logical and critical thinking among the students. Mathematics is a highly conceptual science and teaching mathematics is not an easy job. It requires highly trained teachers who know concept learning and concept teaching in detail. More -over an in-depth knowledge and understanding of latest methods and techniques in teaching of mathematics.

Better teaching of Maths leads to better understanding of Maths which in turn results in the development of science and technology. The following courses are intended to produce competent teachers of Math having command over contents of class I to X and O’& A’ levels as well as latest methodologies of teaching them.


Course –I: Content of Mathematics upto Secondary and O’ level

Course code: BED-526.

Objectives:

On the successful completion of this course the prospective teachers will be able to:

  • Understand the concepts, principles and laws of mathematics

  • Solve practical problems about various concepts, principles and laws of Maths included in the syllabi of elementary level

  • Teach the concepts, principles and laws of Mathematics effectively through the practical problems at elementary level

  • Apply the basic concepts, laws and principle of Maths in solving daily life problems related to Mathmatics

  • Develop analytical thinking, critical thinking and reasoning through mathematical problem solving

  • Understand the concepts, principles and laws of mathematics in ‘ O’ & ‘A’ levels

  • Solve practical problems about various concepts, principles and laws of Maths included in the syllabi in ‘O’ & ‘A’ levels

  • Teach the concepts, principles and laws of Maths, effectively through the practical problems at secondary level.

  • Apply the basic concepts, laws and principles of Maths in solving their daily life problems related to Maths.

  • Develop analytical thinking, critical thinking and reasoning through mathematical problem solving.


Course outline

Part-1: Content of Mathematics at Elementary Level

Unit-1: Numeration Systems

Unit-2: Concept of Addition and Subtraction

Unit –3: Concept of Multiplication

Unit-4: Division and Exponents

Unit-5: Measurement

Unit-6: Numbers Theory & Integers

Unit-7: Fractions

Unit-8: Set & Set Theory

Unit-9: Elementary Statistical Concepts and Information Handling:

Unit-10: Percentage, Ratio and Proportion

Units-11: Algebraic Expressions

Part –II

Section-1: (Matric)

Content of Mathematics at Secondary Level

Unit –I: Set and its Teaching

Unit-2: System of Real Numbers, Exponents and Radicals

Units-3: Logarithms

Unit-4: Algebraic Expression and Their Teaching

Unit-5: Factorization, HCF, LCM and Square Root

Unit-6: Matrices

Unit-7. Fundamental Concepts of Geometry

Unit-8: Demonstrative Geometry

Unit-9: Practical Geometry

Unit-10: Algebraic Sentences

Unit-11: Elimination

Unit-12: Variations

Unit-13: Information Handling

Unit-14: Fundamental Concepts of Geometry and Theorems of Geometry

Unit-15: Concepts of Circle

Unit-16: Practical Geometry

Unit -17: Trigonometry

Section –II. Content of Mathematics (O’ Level)

A review of the following topics from Mathematics Book 1 to 4 (O’ levels)

Unit -1: Congruence and similarity

Unit -2: Scales and maps

Unit -3: Symmetry and angle properties of polygons

Unit -: Solving quadratic equations by factorization

Unit -5: Simultaneous linear equations

Unit -6: Linear graph and their applications

Unit -7: Graphs of quadratic functions

Unit -8: Motion geometry

Unit -9: Pythagorean theorems

Unit -10: Measurement of areas

Unit -11: Linear equalities

Unit -12: Coordinate geometry

Unit -13: Area and volume of similar figures and solids

Unit -14: Geometrical properties of circles

Unit -15: Tangents and alternate segment theorem

Unit -16: Frequency distribution

Unit -17: Locus and construction

Unit -18: Vectors in two dimensions

Unit -19: Geometrical transformation

Unit -20: Probability

Unit -21: Exponential and logarithm function

Unit -22: Remainder and factor theorem

Unit -23: Linear law

Unit -24: Circular measures

Unit -25: Permutations and combinations

Unit -26: Binomial theorem

Unit -27: Differentiation and its techniques

Unit -28: Rates of change

Unit -29: Higher derivatives and applications

Unit -30: Integration

Unit -31: Relative velocity

Unit -32: System of real numbers: Exponent and radicals

Recommended Books

Anwar , M.; Qureshi, M.F. et al (2003). Mathematics -10 ( Part-II). Lahore: Punjab Text Board

Bennett –Jr., A. B. and Nelson. L.T. (2004). Mathematics for elementary teachers : A conceptual approach . (6th ). Boston: McGrew-Hill, Inc.

Bennett-Jr., A. B.and Nelson, L. T. (2004). Mathematics for Elementary teachers: A Conceptual approach. Boston: Mc Grew-Hill.

Lodhi, S.M. Sipea, G.S. et al (2003). Mathematics -9. Lahore: Punjab Text Board

Rabbani, M.I. (2003). New millennium: Introduction to Pakistan studies Lahore: Carvan Book House.

Saleemi, F. (2003). Mathematics. (from class 1 to 8 ). Lahore: P T B.

Sidhu, K.S. (1998). The teaching of mathematics (4th ed.). New Delhi: Sterling Publishers.

Thong , H.S. and Hong ,K.N.(2003). New additional mathematics (for O’ level ). Karachi: paramount publishing Enterprise.

Yee, L.P., Huo, F. L. et al (2003 a). New syllabus: Mathematics – 1. (5th ed.). Oxford: OUPS

Yee, L. P., Huo, F.L. et al (2003 b). New syllabus: Mathematics -2 ( 5th ed.) Oxford: OUP.

Yee, L.P. and Huo, F.L. et al (2003 c). New syllabus: Mathematics- 3 (5th ed.). Oxford: OUP.

Yee, L. P., Huo, F.L. et al (2003 d). New syllabus: Mathematics- 4 (5th ed.). Oxford: OUP.

Yee, L.P and Huo, F.L et al (2003 e). New syllabus: Mathematics -4.Work book. Oxford :OUP.





Course –II: Methods and Techniques of Teaching Mathematics

Course code: BED-527.

Objectives:

On the completion of this course the prospective teachers will be able to:

  • Understand the concepts, principles and laws of mathematics

  • Solve practical problems about various concepts, principles and laws of maths included in the syllabi up to secondary level

  • Teach the concepts, principles and laws of mathematics effectively through the practical problems at elementary level

  • Teach the concepts, principles and laws of math, effectively through the practical problems at secondary level

  • Apply the basics concepts, laws and principles of maths in solving daily life problems related to maths

  • Develop analytical thinking, critical thinking and reasoning through mathematical problem solving


Course outline


Part-1: Theoretical Perspective


Unit -1: Introduction

  • What is Mathematics?

  • The nature of mathematics : The science of logical reasoning

  • Mathematical language and symbolism

  • Pure and applied mathematics

  • Topology

  • The educational value of mathematics :

Practical, disciplinary, social, moral, aesthetic, intellectual, vocational, artistic, economical and scientific values of mathematics

  • The place of mathematics (scope ) in everyday life

Unit-2: History of Mathematics

  • The origin of mathematics / forms of mathematics in the beginning

  • Contributions of the followings in the historical development of mathematics :

  • The Babylonians

  • The Egyptians

  • The Greeks

  • The Romans

  • The Chinese

  • The Arabs / Muslims

  • The Japanese

  • The Hindus

  • Historical review of mathematical developments: From simple arithmetic’s to modern computer mathematics

  • Great Muslims & non-muslim mathematicians

Unit -3: Structure & Organization of Mathematics

  • Number system and comparison of arithmetics

  • Comparison of structures in the system of natural basic algebraic structures

  • Group theory, ring theory, field theory and vector space

  • Modern mathematics: Meaning, need, importance, essentials and applications

  • Euclidean and non-Euclidean geometries

  • Hilbert’s modified Euclidean geometries: Hyperbolic and elliptical geometrics

  • Relationship of mathematics with following subjects:

  • Physics, chemistry, biology, engineering, agriculture, economics, philosophy, logic, fine arts, geography, statistics etc.


Part –II: Pedagogical Perspective

Unit-4: Aims and Objectives of Teaching Mathematics

  • Aims and objectives of teaching mathematics

  • Objectives of teaching mathematics at elementary level

  • Objectives of teaching mathematics at secondary level

  • Formulation of objectives

Unit-5: Curriculum of Mathematics

  • Approaches to curriculum development in mathematics

  • Principles & criteria of curriculum development and design in mathematics

  • Mathematical projects & problems: Puzzle problems, catch problems, unreal and real problems, oral & written problems, theoretical / conceptual & practical problems

  • Analyzing & critically evaluating a mathematics syllabus

  • Why revision of the present curriculum of mathematics and by whom?

  • Defects in the current teaching of mathematics: Causes & remedies

  • Topical vs spiral arrangement of content

Unit -6: Methods and Approaches to Teaching of Mathematics

  • Lecture method / expository method

  • Dogmatic approach

  • Inductive and deductive approaches

  • Heuristic approach

  • Analytic & synthetic approaches

  • Laboratory / practical / constructivist approach

  • Project method

  • Problem solving method

  • Topical & concentric approaches

  • Advance organizer method

  • Conceptual approach : Concept teaching & concept building

  • Activity-based method

  • Selecting & applying an appropriate method or technique of teaching a mathematical topic.

Unit-7: Techniques of Teaching Mathematics

  • Oral and written work (problems and exercises) technique

  • Drill and homework techniques

  • Assignment technique

  • Self-study & supervised study techniques

  • Group work technique

Unit -8: Planning and Delivering Lessons

  • How to plan a mathematics lesson?

  • Lesson planning using a computer

  • Planning a lesson manually

  • Delivering a mathematics’ lesson

  • Some sample lesson plans

  • Selecting & applying an appropriate method or technique of teaching a

mathematics topic

  • Acquiring and placing equipment & material in mathematics laboratory

  • Establishing and organizing a mathematics library

  • Mathematics text books : Need, importance , uses and characteristics of a good text book of mathematics

  • Establishing a mathematics club

Unit -9: Measurement & Evaluation in Mathematics

  • Criteria of measuring tests

  • Prognosis & diagnosis

  • Different types of tests used in assessment of mathematical achievement

  • Construction of a quality test : Nature , steps , process , need & importance

  • Scheme for preparing an evaluation tool

  • What is special with measurement & evaluation in maths?


Part-III: Technological Perspective

Unit-10: Using Modern Educational Technology in Teaching of Maths

  • Integrating following educational technologies in teaching of mathematics:

Projectors, filmstrips, radio, T.V., interactive video, computer, internet etc.

  • Using following A.V. Aids in teaching of mathematics:

  • Blackboard, whiteboard, concrete material, number kit, Venn diagrams, place value pockets, fractional parts, charts, models, excursions, puzzlers, online activities, collections of locally prepared / developed low cost teaching material (home-made equipment) and some specials instruments etc.

Unit-11: Mathematics Laboratory, Library and Text-Books

  • Setting up a mathematics laboratory

  • Acquiring and placing equipment & material in mathematics laboratory

  • Establishing and organizing a mathematics library

  • Mathematics text books: Need, importance , uses and characteristics of a good text book of mathematics

  • Establishing a mathematics club


Part-IV: Teaching Perspective

Unit-12: Effective Teaching of Mathematics

  • Prerequisites of an effective teacher of mathematics: Qualification, training, professionalism and personality traits (aptitude, attitude & logical and critical thinking etc.)

  • Characteristics of the effective teachers of mathematics

  • Duties & activities of the teachers of Maths.

  • Arousing and maintaining interest in Maths

  • Principles of productive thinking & meaningful learning in mathematics

  • Physical & psychological conditions for studying Maths: Some suggestions


Unit-13: The Teaching of Arithmetics

  • Basic concepts: Meaning, aims, and importance of arithmetics

  • Methods of teaching arithmetics: Numeration and notation

  • Teaching of four simple rules of arithmetics

  • Teaching of the selected topics of arithmetics up to secondary level

Units –22: Problems of Teaching Math at Elementary and Secondary Level.

Units –23:Issues and Trends in Teaching of Math at Elementary and Secondary Level.


Recommended Books


Bennett-Jr, A.B and Nelson , L.T.(2004).Mathematics for elementary teachers: A conceptual approach. (Sixth ed.). Boston: McGraw-Hill

Sidhu, K.S. (1998). The teaching of mathematics (4th ed.) New Delhi: Sterling publishers.

Ellington, H. and Race, P. (1994). Producing teaching materials: A hand book for teachers and trainers. (2nd ed.). London: Kogan Page



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