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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

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described by specified prior units in the sequence have already been mastered by the

learning.

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

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curriculum lies in the distribution of subject matter of the curriculum in different

classes.

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.

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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.

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,

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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.

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