Course-5 Understanding Disciplines and School Subjects pmd

Reasons for changes
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The rapid advance of knowledge in mathematics makes increasingly greater
demand on an enlightened citizenry.
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The need for more effective articulation from one grade to the next and from
elementary to secondary school.
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The recognition that the traditional mathematics programme, limited mainly to
emphasis on computational skills and divided into traditional compartments
viz. arithmetic, algebra and geometry, is somewhat lacking in a few fascinating
and interesting aspects of mathematics.
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The need for a better understanding of the structure of mathematics and the
mathematical process, its language and methods of proof.
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The need for the utilization of more effective media (technology and aids) for
adapting mathematics learning to the needs of different abilities.
Modern Trends or New emphasis in Mathematics Curriculum:
The following changes have taken place in recent years:
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Concern for the child as an individual and as a learner caused educators to
question
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the grade placement of certain topics in elementary school mathematics.
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A change in emphasis to a more generalized language, formulation of laws and
of Mathematics in integrating algebraic processes in computational work.
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The drill method of teaching was replaced with methods emphasizing "mean-
ing" and explaining the "whys" of the processes as related to computational
procedures.
●
Psychologists emphasized the relatedness of learning and explored the process
of learning pertinent to the development of fundamental mathematical ideas.
They found that there are levels, that is,
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(a)
the level of the concrete or the world of things;
(b)
the level of the semi concrete where experiences are internalized and fit to-
gether;
(c)
the symbolic level where abstractions and generalizations are formulated;
(d)
the level of applications where the generalizations are tested and applied to
situations.
This led them to conclude that certain topics should be introduced much earlier than
was formerly believed.
●
Bruner's hypothesis that any subject can be taught effectively in some intellec-
tually honest form to any child at any stage of development led to an explosion
of new methods based on discovery and problem-solving.
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The study of geometry was expanded far beyond Euclid's elements. The basics
of transformations, vectors and coordinate geometry were included. In algebra
emphasis has now been given to equations by broadening the base to include
ideas such as mathematical sentences, replacement set and solution set. Gener-
alizations, of the properties of the real number system and the introduction of
the algebra of sets, groups, etc., provided an expansion of mathematical ideas
in both depth and breadth. Basic concepts such as function, variable, relations,
etc., gained greater importance.
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The use of computers has further enriched the content and practices in
mathematics education in schools.
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Subject-Centred Approach: This approach to curriculum lays more emphasis
on content in comparison to learners and teaching process. Teachers' role is
very crucial who are expected to transact the curriculum with a view to help
students to learn different subjects.
●
Behaviourist Approach: In this approach, the development of curriculum starts
with a plan, called blueprint. Blue print consists of goals and objectives of
learning of the particular subject. This approach suggests that teacher should
disseminate information in a sequential way and demonstrate how to solve a
problem, how to derive a formula, and how to construct a shape, followed by
independent practice by students. The role of students in this approach is to
repeat what teacher transacted in the classroom.
●
Constructivist Approach: It is based on the premise that whenever a child en-
counters a new experience, he/she can either easily connect it with the existing
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knowledge or can make some changes in the existing knowledge to accommo-
date the new experience.
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Learner-Centred Curriculum: In this approach, the needs and interest of learn-
ers are paramount. The role of student will be that of an active participant in
the learning process, and therefore, it necessitates that the teacher should know
well each child. Learner centred curriculum will definitely help the child to
enjoy Mathematics, to make him realize its beauty, and to remove the fear of
difficulty of the subject. Another benefit of this curriculum is its flexibility.
The new development and thinking in the area of Mathematics can be included
at any time through the modification of the curriculum.
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Activity-Centred Curriculum: This is also very similar to learner centred cur-
riculum. The role of the learner is very important and should be very active.
This is based on the premise that child loves to play and activity will help to
create motivation. When curricular material is presented in terms of activity, it
is known as activity centred curriculum. Learning of the prescribed material
included in the curriculum takes place through appropriate activities.