CURRICULUM AND
RESOURCE MATERIALS FOR TEACHING MATHEMATICS
Curriculum construction and organization in
mathematics
Meaning of Curriculum: According to Cunningham “The curriculum is the
tool in the hands of the artist (the teacher) to mould his material (the pupil)
according to his ideals (objectives) in his studio (the school)”.
CURRICULUM
1) Curriculum is “ A general overall
plan of the content or specific
materials of instructions that the school should offer the students by way of
qualifying him for graduation or certification or for entrance into a
professional or vocational field”.(Good,1959).
2) “All experiences a learner has under
the guidance of the school” (Foshay, 1959).
3) “Curriculum consists of all the
situations that the school may select and consciously organize for the purpose
of developing the personality of its pupils and for making behavioural changes
in them” (Payne).
PRINCIPLES OF CURRICULUM CONSTRUCTION
1) Principle of Disciplinary value: The
topics and contents of mathematics which help in the task of disciplining the
mind.
2) Useful for Higher Education: The
child aims to go higher and higher on the Education ladder. Therefore education
at one stage must aim to prepare the child for the education at the higher
stages. Therefore, curriculum of mathematics at any stage must cater to the
needs of the higher classes.
3) Principle of utility: According to
this principle all that which is useful should be minded in the curriculum.
Mathematics
curriculum should include all those topics which are,
i) Helpful in day to day life.
ii) Helpful in learning other subjects.
iii) Helpful in realization of aesthetic
and artistic value of the subject mathematics.
iv) Helpful in understanding the
scientific and technological progress and rendering help for the further
research work in the field of mathematics and science.
4) Child centeredness: In curriculum
construction we must give proper weightage to the needs and requirements of the
students for whom we are going to prepare a curriculum. Therefore in any scheme of curriculum construction,
the needs-ability, interest and other developmental characteristics of the
children of particular age, interest and society should be kept in view.
5) Integrity of theory with practice:
Mathematics curriculum requires the topics, contents, experiences and
activities in such a way that we may have enough opportunities of integrating
theory with practice.
6) Principle of flexibility: Curriculum
by all means should have a flexible nature, so that it can be modified and
reshaped according to the circumstances and demands of the resources in
hand.
7) Principle of community centeredness:
Curriculum be constructed and shaped for the welfare of the local community.
Principle of
consulting experts: Curriculum construction needs the help and guidance of
those persons whose interests are to be served by a particular curriculum
Principles of curriculum organization:
The following
methods in general are adopted while framing the curriculum of a subject.
1) 1) Topical and Spiral method: Topical approach suggested by its
name advocates to cover a topic as a whole in a particular grade. Here a few
topics of the subject mathematics may there by marked for being included as in
the curriculum of one grade or the other then it is expected to cover all the
content or learning experiences related to that very topic only in that very
class and not to repeat it in any way in the junior or senior grades. Thus a
topic marked for a particular grade should have its beginning and end it that
every grade without having its need to be taught in the earlier and later
grades. We have different sets of topic for their inclusion in the curriculum
of different grades of secondary stages of school education.
It has been described under the head
criterion of difficulty that easier topics should be dealt with earlier than
the difficult ones. Certain portions of a topic are always easier than the
other portions of the same topic. Thus Square Measure is easier than cubical
measure. Again V=LXBXH is easier than the area of a circle or a triangle.
Similarly in profit and loss, certain problems are easier than other. Inverse
problems are generally more difficult than the direct ones.
Spiral system is based on the principle
that a subject cannot be given an exhaustive treatment at the first stage. To
begin with, a simple presentation of the subject-matter is given, gaps are
filled in the following year and more gaps a year or two later, in accordance
with the amount of knowledge which pupils are capable of assimilating. Spiral
method demands the division of the topic or the subject into number oif smaller
independent units to be dealt with in order of difficulty suiting the mental capacities
of the pupils, while the topical method demands that a topic once taken should
be finished in its entirety. Spiral method is more natural and less tiring to
the pupil. The child loses nothing in accuracy and gains considerably in the
power of intelligent application of rules to problems.
Spiral approach may run contrary to the
topical approach there we do not include topic as a whole and finish it
entirely in a particular grade as practiced in topical approach but try to
spread it over to different grades by covering easier portion in the lower grades and the difficult ones
in the higher and higher grades. In this way while expecting concentric
(Spiral) approach in any single topic may find its place in the curriculum of
different grades on that school education in accordance of the difficulty level
of the subject matter/learning experience suiting to the mental level of the
students.
The chief defect in the topical plan is
that it introduces in the curriculum a large mass of irrelevant material for
which the pupil finds no time and no immediate need or the use of which cannot
be appreciated by the pupil at that stage. They are introduced with a view to
making the teaching of the topic complete and thorough.
Ex.
–Multiplication and division with 6 or 7 digits in the first or second
standard.
2) 2. .Logical and Psychological Arrangement: Logical arrangement leads to the
rigorous treatment of the subject-matter which is based on logical reasoning
whereas psychological arrangement is from the point of view of the students. It
seems that both the approaches are different but these can be easily merged.
The organization can both be psychological and logical. All thinking is
psychological. Psychology throws light on the power of understanding of
students at a particular stage. We can be logical in various ways. Psychology
should decide which logical approach will suit for a particular topic. Logic
will help in maintaining proper sequence of topics, so we should organize the
topics in such a way that we may follow psychology and logic at the same time.
The happy combination of two is always desirable.
Psychology
should decide what kind of logic is appropriate for the pupil of a certain age
and what type of topics will be most suitable for the development of such
logical thinking. Logic will help in maintaining the link and sequence of
topics found useful and meaningful for the child.
3) 3. Principle of correlation: While organizing the content in mathematics
the principle of correlation should always be given due weightage. Correlation
may be of different varieties. The following types of correlation must be kept
in mind while organizing curriculum in Mathematics:
I.
Correlation
of Mathematics with the problems of everyday life.
II.
Correlation
of Mathematics with other subjects.
III.
Correlation
between different branches of Mathematics.
IV.
Correlation
between different topics of a particular branch of Mathematics.
V.
Correlation
with craft or work experience.
For correlating subject-matter we
must know the following:
Ø Day to day life activities of the students.
Ø The nature of topics included in other
subjects at the same stage.
Ø The topics included in different branches of
the subject e.g., Arithmetic, Algebra, Geometry etc.
Ø The sequence of topics of the same branch of
the subject.
Ø The nature of work experience or projects
undertaken by the students.
4) 4. Concentric approach:
This is a system of organizing a
course rather than a method of teaching. It is therefore better to call it
concentric system or approach. It implies widening of knowledge just as
concentric circles go on extending and widening. It is a system of arrangement
of subject-matter. In this method the study of the topic is spread over a
number of years. It is based on the principle that subject cannot be given an
exhaustive treatment at the first stage. To begin with, a simple presentation
of the subject is given and further knowledge is imparted in following years.
Thus beginning from a nucleus the circles of knowledge go on widening year after
year and hence the name concentric approach.
Procedure:
A topic is divided into a number of
portions which are then allotted to different classes. The criterion for
allotment of a particular portion of the course to a particular class is the
difficulty of portion and power of comprehension of students in that age group.
Thus it is mainly concerned with year to year teaching but it its influence can
also be exercised in day-to-day teaching. Knowledge given yesterday and should
lead to teaching on following day.
Merits
of Concentric approach:
Ø This method of organization of subject-matter
is decidedly superior to that in which one topic is taken up in particular
class and an effort is made to deal with all aspects of the topic in that
particular class.
Ø It provides a frame work from science course
which is of real value to students.
Ø The system is most successful when the
teaching is in hands of one teacher because then he can preserve continuity in
the teaching and keeps the expanding circle concentric.
Ø It provides opportunity for revision of work
already covered in a previous class and carrying out new work.
Ø Since the same topic is learnt over many
years so its impressions are more lasting.
Ø It does not allow teaching to become dull
because every year a new interest can be given to the topic. Every year there
are new problems to solve and new difficulties to overcome.
Drawbacks:
·
For the
success of this approach we require really capable teacher. If a teacher
becomes over4 ambitions and exhausts all the possible interesting illustrations
in the introductory year then the subject loses its power of freshness and
appeal and nothing is left to create interest in the topic in subsequent years.
·
In case
the topic is too short or too long then also the method is not found to be
useful. A too long portion makes the topic dull and a too short portion fails
to leave any permanent and lasting impression on the mind of the pupil.
