1. MATHEMATICS CURRICULUM
INTRODUCTION
The word curriculum is derived from the Latin word ‘currere’ which means
‘run’. Thus curriculum means a course to be run for reaching a certain goal or
destination. Thus the traditional definition of curriculum is a course of study or training
leading to a product or education. Teaching learning process does not operate in a
vacuum. Certain planned experiences have to be provided in a school so that optimum
human development according to the needs of a particular country is possible. Thus 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
dynamic and changes according to the pupils and society.
1. Definition of Curriculum
Curriculum has been defined differently by many authors and over the years the
focus is being shifted from ‘course of study’ to ‘learning activities and experiences’.
According to Alberty A. and Alberty E. curriculum is the sum total of student activities
which the school sponsors for the purpose of achieving its objectives. H. Robert Beck
and W. Walter Cook define curriculum as “The sum of the educational experiences that
children have in school”. Cunningham says “Curriculum is a tool in the hands of the
artist (teacher) to mold his material (the pupil) in accordance with his ideals in his studio
(the school)”. A good curriculum in fact is the sum total of good learning experiences
that the pupils have in order to achieve the goals of education which determine the
direction of these experiences.
2. Curriculum and syllabus
Curriculum is not merely syllabus, because the latter is only verbal, book
oriented and theoretical, while the former is not. Syllabus is much more specific,
speaking of the details of the contents to be learnt, the hierarchical order of presenting
the content, etc. It forms the basis for writing textbooks, preparing teacher’s guide and
2. planning lessons. Syllabus places more stress on the specific learning materials to be
internalized. In addition to what is prescribed in the syllabus, the curriculum
encompasses various kinds of curricular and co-curricular activities as well as the
various aspects of the social, natural and educational environment with reference to
which the experiences are transacted. In short, it includes all learning experiences that
would lead the learner to the anticipated goal.
3. Major Objectives of the Mathematics Curriculum
The mathematics curriculum aims at the following objectives.
- Proficiency in fundamental mathematical skills.
- Comprehension of basis mathematical concepts.
- Appreciation of significant meanings.
- Development of desirable attitudes.
- Efficiency in making sound mathematical applications.
- Confidence in making intelligent and independent interpretation.
4. General principles of curriculum construction
Educationists have laid down certain general principles for developing
curriculum. Some of these basic principles are indicated below:
1. The principle of Child-Centeredness: The curriculum shall be based on the present
needs and capabilities of the children. The curriculum should help in developing
initiative, cooperation and social responsibility among the children. This implies that
the curriculum should meet the physical, intellectual, emotional and social needs of the
pupils.
2. The principle of community-centeredness: Besides treating each child as an
individual, we should also view him as a member of the community to which he
belongs. He is to be educated in a school established by the society and by interacting
with other members of the society. Society is dynamic and continuously changing.
Living in this ever changing modern world is not as simple as it used to be in the past.
Any curriculum has to prepare the learners to face this challenge posed by the
community, with efficiency.
3. 3. The principle of Activity –Centeredness: Action is the sign of life. Man is an active
being. Therefore, the curriculum should provide for a variety of activities both physical
and mental in which children are naturally interested. Emphasis should be given to
‘learning by doing’ through the activities of hand, head and heart.
4. The principle of integration: By integration we do not merely mean integration of
subjects. What is required is the integration of the child’s needs on the hand and the
needs of the democratic society on the other.
5. Forward looking principles: The aim of education is to prepare the child for an
effective adult life. Therefore, the curriculum should reflect an insight into the future
life of the child. It should enable the child to prepare for a worthy life. It should prepare
him for a vocation. It should equip him with the caliber to meet the challenges posed
by all domains of human life.
6. Conservative principles: the curriculum should preserve and transmit the traditions
and culture of human race. It should embrace such subjects, topics or activities by which
students should cultivate a sense of respect for their traditions and their culture.
Selection of such items should be made with great care, according to the mental
development of children.
7. Renewal Principles: While conserving and transmitting the cultural heritage,
education should cater to renewal of the culture to suit the requirements of changing
times. Hence curriculum should be so constructed as to facilitate renewal of the society
by infusing dynamism in all aspects.
8. Creative principle: God has created the universe and men have created other things in
it. By nature, man is creative. Therefore education should be so molded as to enable
one develop one’s creativity.
9. Motivation Principle: The curriculum should be tailored to suit the needs and interests
of the pupils. It must be goal directed. It should thus motivate the pupils to actively
participate in the learning process with an innate desire arising out of intrinsic
motivation.
10. Maturity Principle: The curriculum should be suited to the mental and physical
maturity of the pupil.
11. The principle of preparation for life: The school curriculum should include such
elements that would prepare children for their future life. That is, they should be able
4. to earn their livelihood sufficiently and adjust themselves with the society efficiently.
It should equip the child with the caliber to meet the challenges of life.
12. The principle of Elasticity and Flexibility: Since the needs of the individual and the
society go on changing, a rigid and static curriculum cannot meet the requirements of
the child or of the society. Moreover, experiences to be presented have to presented
have to be modified to suit the environment, societal conditions, learning atmosphere,
etc. Also pupil differ in intelligence, tastes and skills too.
13. The principle of comprehensiveness: The curriculum must be comprehensive enough
to confirm to the needs of various individuals or communities. It must be broad-based
to include a wide variety of subjects suited to the needs of various types of pupils and
the society with all its diversities.
14. The principle of Balance: Curriculum should maintain proper balance between direct
and indirect experiences, liberal and professional education, individual and social aims,
compulsory and optional subjects, etc.
15. The principle of Utility: Curriculum should be of practical use to the pupil, and hence
should maintain vocational and technical bias. Due emphasis should be given to work
experiences.
In short, a curriculum should be well balanced, properly graded, fairly broad-
based and appropriately designed for meeting the needs of the child on the one hand
and those of the society, on the other.
5. Approaches to curriculum Organization
There are different approaches to organize the mathematics curriculum. The
important among them are
a. Topical approach
In topical approach a topic once presented should be completely exhausted in
the same class. This method demands that the entire topic, the portions easy as well as
the difficult, should be covered in the same stage.
5. Disadvantages
- This is not a psychological approach as the student are forced to learn many things for
which they have no immediate need and relevance.
- Some parts of the topic will be more complex and difficult for the learner to understand
at the stage.
- It does not take into account the mental development of the students.
- It introduces a large amount of irrelevant matter, the use of which cannot be appreciated
by the learner at the stage.
- Topics once completed receive no attention at larger stages and there is every likelihood
of them being forgotten.
b. Spiral approach
The Cambridge Report (1963) on Mathematics Curriculum emphasized the
importance of interrelating and interweaving the different mathematical topics to be
taken up throughout the school period and envisaged the progressive broadening and
deepening of the child’s mathematical knowledge and insight by what is called the
“Spiral Approach”. Therefore, contrary to topical approach, spiral approach demands
the division of the topic into a number of smaller independent units to be dealt with, in
order of difficulty, suiting the mental capacities of children. For example, ‘Set Theory’
can be split up into various subunits and arranged in the increasing order of difficulty.
The spiral approach has the following advantages over topical approach.
- Subject matter is introduced in the increasing order of difficulty, in accordance with the
needs and capacities of the students.
- It satisfies the psychological needs of the students
- The students are able to appreciate the relevance and significance of what they learn.
- It provides sufficient motivation for the students to learn.
- It provides opportunities to relate the topic with other topics, other branches and other
subjects.
c. Logical and psychological Approach
The arrangement of subject matter based on the principles of psychology is
known as psychological approach.in other words this approach is in tune with the
principle of child-centeredness. In the logical approach stress is given to the logical
6. sequencing of the subject concerned. Content of every subject have been developed in
tune with such a logical sequence. Logical approach demands maintaining the logical
sequence while developing a curriculum. At the same time, a good curriculum, if
carefully developed can maintain the psychological approach without sacrificing the
logical sequence of the subject. The only thing is that the logical continuity is taken
care of at every stage of curriculum transaction done in tune with the psychological
approach.
d. Unitary Approach
The students learn mathematics with its different branches and topics in
watertight compartments. So in the last few decades, the teachers in mathematics have
searched for broad unifying principles which could be made the core of the
mathematical course. Suppose that complete understanding of the function Y=ax+b be
made one of the major division of first year algebra, all the other concepts can be
developed through this because the attainment of an understanding of this important
function will develop upon many experiences. Such an organization enables the pupils
to see clearly the relationship between the various facts, processes and principles taught
in the course. They know that each unit contributes to the course as a whole.
The question of time and size need not enter in the organization of a unit. But
for most high school pupils it may take more than a month to assimilate. Experiences
seem to show that a unit which can be studied in the four weeks is most suitable as to
size. When it is not possible to finish it within that time the teacher should find a way
of simplifying the unit either by transferring some of the materials to other units or by
diving it into two smaller units.
Characteristics of the Unitary Organization
- It organizes a body of facts, theorems or processes, closely related to one another and
so organized as to contribute to the understanding of an important aspects of the course.
- It must be possible to present the theorems and process as a group in a form so definite
that the learner may attain a conception of them before he undertakes the detailed study
of the content of the unit.
- It must be possible to set up outcomes of the study so definite that they are clear not
only to the teacher but also to the pupils.
7. It should be clear that there is no single type of organization which may be set up to
determines as “only acceptable” list of units for the course. Unitary organization makes
teaching and learning purposeful and intelligent. Because the instructional materials are
closely related to each other, they are easily retained. Economy of time and effort should
be the result.
e. 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. The study of every subject should highlight the unity of knowledge.
While teaching any subject, the teacher can cite instances and examples to show that
knowledge is a single integrated whole and the knowledge that one gains through
courses like mathematics, physical/biological sciences, social sciences, language, arts
and other constitute the whole. Such an integrated approach helps the students to get a
holistic view of the school programme and thereby the study of each subject becomes
more meaningful and significant.
6. Characteristics of Modern Mathematics Curriculum
Certain characteristics features of a modern mathematics curriculum may be
specified briefly as follows.
- Mathematics course materials should prepare the students for college, but could be used
with less talented students if they are given more time.
- New concepts and different points of view which are useful for the students should be
there in the mathematics curriculum.
- Changes 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 mathematics curriculum should provide experiences to explore the behavior of
numbers and invent new numbers to describe new situations.
- The mathematics curriculum should be in harmony with the cultural experiences the
children have at home and outside the school.
8. - The mathematics curriculum should be built on the mathematical experiences that the
students already have gained.
7. Major reforms in Mathematics Curriculum
1. SMSG (School Mathematics Study Group)
School Mathematics Study Group (SMSG) is a massive endeavor started in
USA, in 1958 with a view to improve the existing system of mathematics curriculum.
In addition to its improvement and compilation of study materials, SMSG prepared
textbooks separately for both teachers and students.
2. SMP (Scottish Mathematics Project)
Scottish Mathematics Project (SMP) was started in 1961 for making
improvements in mathematics curriculum. The mathematics curriculum was
reconstructed in Scotland with the intension of teaching mathematics heuristically in
schools. They prepared with this intention 5 textbooks for the pupils studying for GCE
(General Certificate of Education) examination at O level. Later in 1967 they prepared
a series of textbooks from A to H levels for the students studying for CSE examination.
These textbooks were prepared by considering the problems and needs of teachers and
students. It includes a number of experiments and problem solving activities. They also
prepared handbooks for the teachers for effective teaching.
3. NCERT (National Council for Educational Research and Training)
In our nation we restricted our mathematics curriculum in the following way.
At first a council was formed namely NCERT. They brought SMSG books from
America and took copies of them and published them at low cost in our country. The
teachers studied these books and taught mathematics in the way suggested in the books.
NCERT arranged classes for teachers to make them aware of the new changes in the
teaching of mathematics. Later the council prepared the overall curriculum. This is
known as CBSE curriculum and was introduced in the Central schools. The state
government was at liberty in using this curriculum. At present most of the states have
restructured mathematics curriculum in the line of the NCERT.
9. CONCLUSION
Arthur Cunningham says, Curriculum is a tool in the hands of an artist (teacher)
to mould his materials (pupils) according to his ideals (objectives) in his studio
(School). In brief, curriculum is the means for achieving the goals of education. It
includes all those experiences, activities and environment influences, which the student
receives during his educational career, for the realization of a variety of anticipated
goals.
