B.Ed Notes

1. NEW B.Ed COLLEGE
NELLIMOODU
THIRUVANANTHAPURAM – 695524
ASSIGNMENT ON
EDU-09-THEORITICAL BASE OF MATHEMATICS
(SEMESTER-II)
B.Ed. COURSE 2013 – 2014
SUMI S. V.
MATHEMATICS
180/13376012

2. Introduction
Curriculum is the crux of the whole educational process. Without curriculum
we cannot conceive any educational endeavor. The mathematics curriculum is the
medium required for the purpose. As such every Mathematics teacher has to get a
clear and through knowledge about the meaning, function, foundation and types of a
good mathematics curriculum together with the principles for its development and
transaction. In this sense curriculum is the path through which the student has to go
forward in order to reach the goal envisaged by education. Usually the term
curriculum in understood as a group of subjects prescribed for study in a particular
course. But curriculum is not confined to this narrow concept. Curriculum should in
no way be considered as synonymous with courses of study. The courses of study do
list much of the content to be learnt and indicate some of the major activities but these
form only part of the curriculum. Curriculum should be considered as a board – based
term encompassing every aspect concerning course of study. Curriculum for a course
of study may be conceived as the totality of experiences a pupil is exposed to within
the boundaries of the school and outside while undergoing that course with a view to
achieve the anticipated educational goals.
MATHEMTICS CURRICULUM
A fundamental aim of the Mathematics curriculum is to educate students to be
active, thinking citizens, interpreting the world mathematically and using mathematics
to help form their predications and decisions about personal and financial priorities.
APPROACHES TO MATHEMATICS CURRICULUM SUGGESTED BY NCF
NATIONAL CURRICULUM FRAME WORK
Inspite of the recommendations of the NPE, 1986 to identify competencies and
values to be nurtured at different stages, school education came to be driven more and
more by high – stake examinations based on information loaded textbooks. Despite
the review of the curriculum Frame work in 2000, the vexed issues of curriculum load
and the tyranny of examinations remained unresolved. The current review exercise
takes into cognizance both positive and negative developments in the field, and
attempts to address the future requirements of school education at the turn of the
century. In this endeavor, several interrelated dimensions have been kept in mind,

3. namely, the aims of education the social milien of children, the nature of knowledge in
its broader sense, the nature of human development and the process of human
learning.
The term National Curriculum Frame Work is often wrongly construed to mean
that an instrument of uniformity is being proposed. The intention as articulated in the
NPE, 1986 and the programme of Action (POA) 1992 was quite the contrary.
Mathematics
Developing children’s abilities for mathematisation is the main goal of
mathematics education. The narrow aim of school mathematics is to develop ‘useful’
capabilities, particularly those relating to numeracy – numbers, number operations,
measurements, decimals and percentages. The higher aim is to develop the child’s
resources to think and reason mathematically, to pursue assumptions to their logical
conclusion and to handle abstraction. It includes a way of doing things, and the ability
and the attitude to formulate and solve problems.
This calls for a curriculum that is ambitious, coherent and teaches important
principles of mathematics. It should be ambitious in the sense that it seeks to achieve
the higher aim mentioned above rather than only the narrower aim. It should be
coherent in the sense that the variety of methods and skills available piecemeal (in
arithmetic, algebra, geometry) cohere into an ability to address problems that come
from other domains such as science and social studies in high school.
VISION FOR SCHOOL MATHEMATICS
 Children learn to enjoy mathematics rather than fear it.
 Children learn important mathematics : Mathematics is more than formulas and
mechanical procedures.
 Children see mathematics as something to talk about, to communicate through
to discuss among themselves, to work together on.
 Children pose and solve meaningful problems.
 Children use abstractions to perceive relationships to see structure to reason out
things to argue the truth or falsity of statements.

4.  Children understand the basic structure of mathematics, Arithmetic, algebra,
geometry and trigonometry, the basic content areas of school mathematics all
offer a methodology for abstraction, structuration and generalization.
 Teachers engage every child in class with the conviction that everyone can
learn Mathematics.
Visualization and representation are skills that mathematics can help to develop.
Modeling situation using quantities shapes and form are the best use of mathematics.
Mathematical concepts can be represented in multiple ways and this representation
can serve a variety of purpose in different contexts. All of this adds to the power of
mathematics.
The importance of systematic reasoning in mathematics cannot be
overemphasized, and is intimately tied to notions of aesthetics and elegance so dear to
mathematicians. Proof is important, but in addition to deductive proof, children should
also learn when pictures and construction provide proof.
Mathematical communication is precise and employs unambiguous of language
and rigour in formulation which is important characteristics of mathematical
treatment. The use of jargon in mathematics is deliberate, conscious and stylised.
Mathematicians discuss what appropriate notation is since good notation is held in
high esteem and believed to aid thought.
THE CURRICULUM
At the pre - primary stage, all learning occurs through play rather than through
didactic communication. Rather than the rote learning of the number sequence,
children need to learn and understand, in the context of small sets, the connection
between word games and counting and between counting and quantity.
Having children develop a positive attitude towards and liking for, Mathematics at the
primary stage is an important, if not more than the cognitive skills and concepts that
they acquire Mathematical games, puzzles and stories help in developing a positive
attitude and in making connection between mathematics and everyday thinking. The
suggestions of the National curriculum frame work regarding the learning of
Mathematics are:

5.  Learners should enjoy learning mathematics.
 They should gain a deeper insight into the subject than a more study of
numbers or theories can give. Mathematics does not comprise merly of
equations and mechanical steps.
 Learners should be able to communicate in numerical terms.
 Study of the subject should help the learners raise sensible issues the solutions
for which should be arrived at.
 Learners ought to equip themselves to understand mathematical relations
perceive structures think logically and differentiate between what is right and
what is not, while examining statements and facts.
 Learners should understand the basics of mathematics.
 Every learner should be confident that he/she can manage mathematics well.
The basic content of mathematics provided at school in the form of Arithmetic,
Algebra and Trigonometry provide the ability to understand abstraction,
stucturalization and generalization.
Approaches to Mathematics curriculum Suggested by KCF
The basic characteristic of mathematics is to analyze and interpret the world on
the basis of numbers. Most of the times when facts are explained with figures they are
understood better. When we present the numerical relations inherent in natural
phenomena through algebraic equation, it becomes possible to arrive at minute forms
of knowledge and accurate predictions. From the angle mathematics is a numeric
centered language.
Students find if difficult to imbibe the basic tenets of mathematics. The
condesed forms of mathematical theories are not palatable to a large section of the
student body. As these theories begin to explain primary numbers and abstract ideas
the fissure windens. The established methods of mathematical calculations have been
moulded over centuries. Learning mathematics becomes a herculean task when the
student is not familiar with the early methods and without training in the proper
method for the formation of ideas.

6. Importance of Learning Mathematics
Usually noble ideas such as mathematics is essential in daily life or
mathematics helps in the evolution of logical reasoning are presented during the
discussions on the necessity of learning mathematics. More clarity is required in this
regard.
Necessity of Learning Mathematics
Different mathematical ideas are used for different purposes. During the
formation of any idea, the necessity for such a formation makes as use whole numbers
and fractions as the case may be. By organizing discussions and activities that inspire
the learner we can relate the activities and the problem to the learners’s life.
The suggestions of the Kerala Curriculum frame work regarding the learning of
Mathematics are :
 Mathematics that is required in daily life.
 Mathematics that is useful for higher studies.
 Ideas that go deeper into the complex details of mathematics.
Conclusion
The Mathematics curriculum at the higher Secondary stage is to provide
students with an appreciation of the wide variety of the application of Mathematics,
and to equip them with the basic tools that enable such application. A careful choice
between the often conflicting demands of depth versus breadth needs to be made at
this stage. The rapid explosion of Mathematics as a discipline, and of its range of
application, favours an increase in the scope of the coverage.
Reference
1. Soman K., & Sivarajan K. (2008, Mathematics education Methodology of
teaching and pedagogic analysis, Calicut university)
2. www.ncert.in
3. www.scert.kerala.gov.in