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
No comments:
Post a Comment