**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 .** (6^{th} ).
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** (4^{th}
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.** (5^{th} ed.). Oxford: OUPS

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

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

Yee, L. P., Huo, F.L. et al (2003 d). **New syllabus: Mathematics-
4** (5^{th} 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** (4^{th}
ed.) New Delhi: Sterling publishers.

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

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