SEMESTER I
EDU.05.10. THEORETICAL BASES OF TEACHING MATHEMATICS
Maximum: 100 marks (external: 80, internal: 20)
Course objectives
1.
To develop an insight into the nature of mathematics
2.
To develop an understanding about the interrelationship of different
branches of mathematics, relationship of mathematics with other subjects and
with daily life.
3.
To familiarise the history of mathematics and mathematics education
4.
To know the recommendations of various committees and commissions (in
India) about the role of mathematics in school curriculum
5.
To understand the values of learning mathematics.
6.
To understand the aims and objectives of teaching mathematics.
7.
To analyse the objectives of teaching Mathematics at different levels of
education
8.
To understand the Taxonomies of Educational objectives (Bloom’s&
RBT)
9.
To understanding about the desirable teacher behaviour for effective
teaching of mathematics
10.
To understand different approaches , methods, and techniques of teaching
mathematics.
11.
To understand the implications of theories of Piaget, Bruner and Gagne
in mathematics education.
12.
To understand the steps of development of mathematics curriculum.
13.
To understand the principles of curriculum construction and
organization.
14.
To analyse the various approaches to curriculum organization.
To familiarise with important reforms in mathematics curriculum in India and abroad
COURSE CONTENT
UNIT I
NATURE OF
MATHEMATICS
- ·
Mathematics-
meaning and definition
- ·
Nature
of Mathematics- Mathematics as a Science, Mathematics as a game, Mathematics as
a language, Mathematics as a tool, Difference between Mathematical science and
basic science
- ·
Pure
and applied Mathematics, Role of axioms and postulates
- ·
Fundamental
branches of Mathematics (Arithmetic, Algebra, Geometry, Trigonometry)- Origin,
nature of content link between the branches
- ·
Correlation
of mathematics with other subjects and real life
- ·
Evolution
of Mathematics as a discipline: Development as a science, History of
Mathematics from ancient period to 20th century
- ·
Role
of Mathematics in school curriculum in India- Recommendations of various
Committees and commissions (NPE, NCF, KCF)
UNIT II
AIMS AND
OBJECTIVES TEACHING MATHEMATICS
- ·
Values
of learning Mathematics, aims and objectives of teaching Mathematics
- ·
Objectives
of teaching Mathematics at elementary, secondary and senior secondary levels
with respect to NCF and KCF
- ·
Taxonomy
of educational objectives- Blooms Taxonomy, Revised Bloom’s Taxonomy- a
conceptual overview
UNIT III
MICRO
TEACHING
- ·
Teaching-
Meaning, Definition, Principles and Functions
- ·
Phases
of Teaching
- ·
Maxims
of Teaching
- ·
Teaching
skills
- ·
Micro
teaching- Meaning, Definition, Phases, Micro Teaching Cycle, Link practice and
preparation of Microteaching Lesson plan
UNIT IV
APPROACHES,
METHODS AND TECHNIQUES OF TEACHING MATHEMATICS
- ·
Behaviourist
approach, problem-based learning, constructivist approach and heuristic
approach
- ·
Methods
of teaching mathematics- Inductive- Deductive method, Analytic- Synthetic
method, Project method, laboratory method, problem solving method
- ·
Techniques
of teaching mathematics- questioning, brainstorming, assignment
- ·
Teaching
for understanding proofs, Kinds of proofs- direct, indirect, by mathematical
induction, by contradiction, by causes, the contra positive and disproof by
counter example.
UNIT V
MATHEMATICS
CURRICULUM
- ·
Curriculum-
meaning, types
- ·
Curriculum
development: Construction, organization and evaluation
- ·
Principles
of Mathematics curriculum construction, principles and approaches of curriculum
- ·
Organization
- ·
Mathematics
curriculum reforms- SMP, SMSG, NCERT, NCF, KCF, Nuffield
TASK AND
ASSIGNMENT
- 1.
Critically
analyse the implications of SMP/ SMSG/ Nuffield in secondary school mathematics
curriculum in Kerala with the supporting evidences (interview/ questionnaire,
content analysis etc. Items for interview or questionnaire may be framed based
on each dimension of the concerned reform)
- 2.
Prepare
a picture album of famous mathematicians (including western and Indian) with
descriptions of their biography and contributions
Some Reference Books
- 1. Fundamentals of Mathematics Education- Dr.
Vijayakumari, Dr. Mumthas. N.S, Dr. V. Sumangala
- 2. Mathematics Education- Dr. K. Soman, Dr. K.Sivarajan
- 3. Teaching of Mathematics- S.K. Mangal
- 4. The teaching of Mathematics- Kulbir Singh Sidhu
- 5. Teaching of Mathematics- Dr. Anice James
- 6. Mathematics Education methods & Techniques-
Zubair. P.P
- 7. Teaching of Mathematics- Sudhir Kumar, D. N.
Ratnalikar
