The document discusses the mathematics curriculum and its organization. It defines curriculum as the sum of all student activities and experiences provided by the school. The key components of developing a mathematics curriculum include setting goals, planning learning experiences and content, and assessing outcomes. When organizing the curriculum, principles like logical and psychological order, correlation across topics and grades, and adapting to individual differences should be followed. Approaches to organizing the curriculum include the topical, spiral, logical-psychological, unitary, and integrated approaches.

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ONLINE ASSIGNMENT
TOPIC: CURRICULAM
Submitted To Submitted By
Mrs. VIDHYASOUMYA S NAIR
13384002
MATHEMATICS

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INTRODUCTION
According to Gauss “mathematics is the queen of science and arithmetic is
queen of all mathematics. Mathematics is the science of number and space. Also it is
the science of measurement, quantity and magnitude. There are clearly indicated that
mathematics is an accepted science which deals with the quantitative aspects of our
life and knowledge. It helps us in drawing necessary conclusions and interpreting
various ideas with useful meaning. In the beginning our knowledge of mathematics is
based in our observations of physical and social environment. Mathematics is also
called science of reasoning.
The mathematics curriculum forms the basis for the entire mathematics
education. The word curriculum is derived from the Latin word ‘curresre’ which
means ‘to run’.Thus curriculum means a course to be run for reaching a certain goal
or a destination. Thus the traditional definition of curriculum is acourse of study or
training leading to a product or education .The term curriculum in recent years has
come to mean all the planned activities and experiences available to the students
under the direction of the school. Curriculum is dynamicand changes according to the
needs of the pupils and society.
DEFFENITION OF CURRICULUM
Curriculum has been defined differently by many authors and or the years the
focus being shifted from ‘course of study’ to ‘learning activities’ and
‘experience’.According to Alberty “curriculum is the sum total of student activities
which the school sponsors for the purpose of achieving its objectives.
MORE DEFFENITION OF CURRICULUM
Descriptive: -Those aspects of schooling which have been deliberately planned
comprise the curriculum.
Perspective: - Curriculum is a set of content units which are arranged in a way that
the learning each unit may be accomplished as a single act provided the capabilities

3. described by specified prior units in the sequence have already been mastered by the
learning.
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Static: -Curriculum is judiciously organized subject matter.
Dynamic:- It is an organized set of processes, procedures, programs and the likes
which are applied to learners in order to achieve certain kinds of objectives.
Schematic: -Curriculum is purely and simply a teaching strategy .A teaching strategy
is ,in turn conceived of as being a series of goal oriented teachers with respect to a
class of teachers and in the content of a syllabus or a body of subject matter.
NEED AND OBJECTIVES OF MATHEMATICS CURRICULUM
The mathematics curriculum forms the basis for the entire mathematics education.
It is the pivot on which the whole process of teaching, learning revolves. It provides
the necessary insight to the mathematics teacher in the selection of the learning
activities, teaching methods, learning resources and experiences which are best suited
to the age of the learner, the emotional, physical and intellectual maturity of the
learner and his previous experiences and learning.
 Comprehension of basic mathematical concepts.
 Appreciation of significant meanings.
 Development of described attitudes.
 Efficiency in making sound mathematical application.
 Confidence in making intelligent and independent interpretation.
CURRICULUM DEVELOPMENT
The definition of curriculum has been changing according to the social
changes and society’s expectation for the school, the processes of curriculum
development has remained unaltered. It is a cyclic process involving the following
stages.

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 Analysis: What are the educational goals of the institution?
 Design: What are the educational experiments to be provided to
achieve these goals?
 Implementation: How can these educational experiences to be
provided to achieve these goals?
 Evaluation: How effective are the educational experiences in attaining
the goal?
Throughthese stages of curriculum development the curriculum planners set
goals, plan experiences, select content and assess outcomes of a school program.
Curriculum development is fundamentally a plan of structuring the environment to
coordinate in an orderly manner the elements of time, space, materials, equipment and
personnel. The basic cycle analysis,design,implementation and evaluation,guides the
curriculum improvement processes,regardless of focus or operation.
Thus in developing a curriculum, three choices must be made of syllabus
content, of curriculum experiences or pedagogical ‘style’ and of evaluative
techniques. Effective curriculum planning provides evidences that the teacher in
deciding the ‘what’ lesson has also considered the ‘how’ and given thought to asking
‘what will constitute evidence of attainment? These three decisions then look together
into experience which provides a leaner with the structures necessary to make
effective class room experiences.
The curriculum involves two major stages:
 Curriculum construction.
 Curriculum organization.
PRINCIPLES OF CURRICULUM CONSTRUCTION
There are certain basic principles of curriculum planning which should form the
basis for construction of a good mathematics curriculum. They are as follows
 Principles of child centeredness.
 Curriculum should provide a fullness of experiences for children.

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 Curriculum should be dynamics and no static.
 Curriculum should be related to everyday life.
 It must take into account the economic aspects of life of the people to whom
an educational institution belongs.
 Curriculum should be real and rationalistic.
 Curriculum should be emphasis on learning to live rather than living to learn.
 Curriculum should help in processing and transmitting our cultural traditions.
 Curriculum should be flexible and elastic.
 Curriculum should emphasis attitude rather than acquisition of knowledge.
 The curriculum should be well integrated.
 The curriculum should provide both for uniformly and variety.
 The curriculum should be useful to the students.
 Guidelines For Selecting The Topics In The Mathematics Curriculum
Cultural Perspective
Some ideas in mathematics that enable the student to appreciate and understand
the culture and environment which is a part of, could find a place in mathematics
curriculum.
 Participation In The Technological, Commercial Industrial Civilization.
Those topics which develop the mathematics skill and which are important for an
individual to actively participate in his technological, commercial and industrial
civilization should find a place in the mathematical curriculum.
 Utility value
Utility value is most important criteria in selecting topics for mathematics
curriculum.
ORGANIZATION OF THE CURRICULUM
Curriculum has to be organized on the basis of certain principle.It is these
principles that help the scientific planning of the curriculum. Organization of

6. curriculum lies in the distribution of subject matter of the curriculum in different
classes.
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Good advantages are:
 Every topic should be divided into parts.
 Those parts should be graded according to difficulty.
 Each part should be introduced at the proper stage.
a. Principle of correlation
While organizing the content in mathematics curriculum the principles of
correlation should followed. The following four types of correlation should be
considered.
 Correlation with life.
 Correlation with subjects.
 Correlation between difference branches of mathematics.
 Correlation between different topics in the same branch of
the mathematics.
b. Principles of logical and physiological order.
An integrated approach combining both logical and psychological order
should be followed in the curriculum. The arrangement of the content should
display sequential development of topics which is most appropriate for the student
of that age level.
c. Principle of activity.
The curriculum organization should take into consideration the type of
activities that could be provided for the effective learning of the content.
The activities include:
 Personnel and home activities.
 Vocational activities.
 Recreational activities.

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 National activities.
 Community, civic and social activity.
Principle of verti0cal correlation.
The content organized for a class should be based on the syllabus covered in
the lower classes and in turn, it should form the basis for the organization of the
content in the higher classes. This called the vertical correlation. The topic arranged in
any class also should follow the vertical correlation leading from simple topics to
complex ones.
The criterion of difficulty
The organization of the content should be in increasing order of difficulty .The
difficulty level of a topic is to be judged from the pupil’s point of views based on the
mental development and capabilities of the pupil’s.
Principle of motivation.
The organization of the content should enthuse the children to learn .The
content presented should be challenging, interesting and exciting.
Adaptation of individual differences.
The arrangement of the content for each class and level should later to needs
of the different categories of children. There should be topics which are challenging
for mathematically gifted students and topics suitable for average and slow learners in
mathematics.
APPROACHES TO CURRICULUM ORGANISATION
There are different approaches to organize the mathematics curriculum. The
important among them are
 Topical approach.
 Spiral approach.

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 Logical approach psychological
 Unitary approach.
 Integrated approach.
1. Topical approach
Topical approach means that a topic should be finished entirely at one stage. It
takes the topic as a unit. Topical approach requires that easy and difficult portions
of a topic should be dealt with at one stage which is not psychological. This
approach has a no. of drawback also.
2. Spiral approach
Spiral approach implies that a topic should be split up into different portions
and these portions should be spread over different grades. Easier portions should
be dealt with in the lower grades and the difficult portions should be gradually
introduced in the next grade. This approach is simple or easy topic may be
finished at one stage, while spiral arrangement is good, long grinding at all grades
is undesirable.
3. Logical and psychological approach
Logical approach leads to the vigorous treatment of the subject matter
which is based on logical reasoning whereas psychological arrangement is the
form the point of view of the student. It seems that both the approaches an
different but these can be easily merged.
4. Unitary approach
The students learn mathematics with its different branches and topics
in watertight compartments. An organization enables the pupils to see clearly
the relationship between the various facts course as a whole.
The steps in unitary organization of the curriculum:
 Setting up objectives.
 Preview of the units

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 The study outline of the unit.
5. Integrated approach
The main aim of education is acquisition of knowledge and the transfer
of knowledge to study other subjects and to solve successfully the problems
that arise in everyday life. Each subject in the curriculum aims at realizing
these aims through different means.
CHRECTERISTICS OF MODERN MATHEMATICS
CURRICULUM
 Mathematics course materials should prepare the students for college, but it
could be used with less talented students if they are given more time.
 Change in the curriculum should help the students in meeting their present
needs.
 The curriculum should provide an understanding of mathematics for future
change and development.
 The curriculum should provide application of mathematical structures and
matric and nonmetric relations in geometry.
 The curricular materials should involve experience with and appreciation of
‘abstract concepts’ the role of definitions, the development of precise
vocabulary and thought and experimentation and proof.
CURRENT TRENDS IN MATHEMATICICS CURRICULUM
In the secondary school program the most essential innovation that needs to be
made is the introduction of basic concepts of abstract algebra and their application to
geometry, through an appeal group s and vector system. The concrete foundation for
teaching abstract algebra is laid in arithmetic operations, set theory and physical
geometry.
The geometry content in the mathematics curriculum should be such the algebra
studied in the earlier class becomes a more useful tool. The curriculum for higher
secondary school mathematics can be traditional mathematics which is developed
from a more up to date point of view.

10. Another important view point is an integrated approach where mathematics is viewed
as a single subject and not to divide it into water tight compartments labeled
‘arithmetic’ ‘algebra’, ‘geometry’, ‘trigonometry, and so on. The sharp distinction
between these subjects must be blunted.
A conference on “new thinking in school mathematics” convened by the organization
for European Economic Cooperation has made the following observation regarding
the high school mathematical curriculum. New mathematics has been included in the
secondary school mathematics curriculum because modern mathematics may be
easier to learn and give a better understanding to mathematical structure.
The above mentioned topics have been included in the mathematics curriculum for
higher secondary classes in almost all the Indian states. However, the study of pure
geometry with courses on triangles and congruency with system of circles, with
constructions, and with theorems still continues to be a part of the high school
mathematics.
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RECOMMENDATIONS OF KOTHERI COMMISIONS (1964-66)
The Indian education commission (1964-66) has envisaged acourse of
compulsory mathematics in primary and junior secondary courses. Diversification of
course has been recommended at higher secondary level with the result that
mathematics at higher secondary stages is optional and meant only for those who
wanted to study higher mathematics or to take up vocations and professions requiring
specialized knowledge of mathematics.
At primary stage, mathematics is at present divided into arithmetic, algebra and
geometry. At secondary and higher secondary levels also, the mathematics syllabus
which at present are divided in the traditional manner into arithmetic, geometry and
algebra, trigonometry, statistics, calculus and coordinate geometry, need to be
revitalized and up to date.
SOME MODERN APPROACHES TO MATHEMATICS
CURRICULUM

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Cultural induction
This way of viewing in curriculum is based on the work of Alan Bishop
(1986) who experienced and studied in detail he challenges of teaching and learning
mathematics in a culture very different from his own. Bishop had suggested six
cultural activities which drew heavily on, or are essential to, mathematics and which
are crucial to each individual in order to be adequately inducted into the culture.
Counting
The various types of counting:
 Using parts of the body as names.
 Using counters and abstract names.
 Using names alone.
Mathematics tools
This way of viewing the curriculum considers the entitlement of each and
every child to achieve familiarity and facility in the use of the mathematical tools
available in the society.
Essence
This way of viewing the curriculum considers that if pupils are to make sense
of their mathematical lesson, then they need to be able to connect these experiences
with what they already know. Mathematics lessons can truly start from where the
pupils are by attending root mathematical experiences or essences, evoking and
building on them to engage with the desired mathematical content.
Place of problems in mathematics curriculum
Problem- which Stephen Leacock described as “short stories of adventure and
industry with the end omitted” are the very flesh and blood of mathematics and should
appear at every stage of teaching and subject. But the problems must be real and
significant and the more they arise from the needs and interest and activities of
children, so much the better. All artificial problems should be avoided,

12. similarlysuperficial problems, invoking all sorts of complex and unrealistic operations
serve no useful purpose.
The presence of a puzzle element in the problems in often a great stimulus. Children
for whom mathematics has been nothing but “sums” will respond with undertrained
vigor and delight to number puzzles, magic squares etc. “Think of a number “ games
appeal even to those who dread algebra.
On the other hand it must be borne in mind that mathematics cannot consist entirely
of games and puzzles or purposeless, undirected investigations. System and
organization, method and planning are essential.
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CHARACTERISTICS OF A GOOD PROBLEM IN
MATHEMATICS
The following are the characteristics that help in selecting good problems
mathematics.
 The problem should be real and relevant to the mathematics syllabus.
 It should lead to a solution.
 It has practical and social values.
 It should be related to life and should arise out of life situations.
 It facilitates the realization of the objectives of teaching mathematics.
 It occurs in the everyday activities of the pupils, especially in the school
studies other than mathematics.
 It facilitates the integration of old and new processes.
 It arouses the curiosity of the students.
 I t challenges and trains the mental faculties of the students.
 It helps in the transfer of knowledge.
 It results in learning new higher order rules.
 It forms the basis for further learning.

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CONCLUSIONS
The main aim of education is acquisition of knowledge and the transfer of
knowledge to study other subjects and to solve successfully the problems that arise in
everyday life.The mathematics curriculum forms the basis for the entire mathematics
education.The definition of curriculum has been changing according to the social
changes and society’s expectation for the school, the processes of curriculum
development has remained unaltered.Curriculum has to be organized on the basis of
certain principle.It is these principles that help the scientific planning of the
curriculum. Organization of curriculum lies in the distribution of subject matter of the
curriculum in different classes.Thus in developing a curriculum, three choices must be
made of syllabus content, of curriculum experiences or pedagogical ‘style’ and of
evaluative techniques. Effective curriculum planning provides evidences that the
teacher in deciding the ‘what’ lesson has also considered the ‘how’ and given thought
to asking ‘what will constitute evidence of attainment? These three decisions then
look together into experience which provides a leaner with the structures necessary to
make effective class room experiences.
REFERENCES
1. Teaching of mathematics – S.K.MANGAL
2. Teaching of mathematics – Dr. ANICE JAMES