METHODS OF
TEACHING MATHEMATICS
.
INTRODUCTION
Different methods of
teaching mathematics have been proposed by different educators. Knowledge of
these methods may help in working out a teaching-learning strategy. It is not
educationally sound for a teacher to commit himself to any particular method. A
teacher should adopt an approach considering the nature of the children, their
interests and maturity and the resources available. The merits and demerits of
various method listed.
Let us
discuss the following methods
1.
Inductive –Deductive Method
2.
Heuristic Method
3.
Analytic –Synthetic Method
OBJECTIVES OF LEARNING THE
METHODS OF TEACHING
w
To identify different methods of teaching
mathematics;
w
To select appropriate teaching-learning strategy
keeping in view the maturity level and interest of children at primary stage of
education;
w
To encourage the activity and the play way
methods to make learning of mathematics more interest and meaningful for
children
Inductive –Deductive Method
Mathematics in the
making is experimental and inductive. Induction is that form of reasoning in
which a general law is derived from a study of particular objects or specific
processes. The child can us measurement, manipulator or constructive
activities, patterns etc.To discover a relationship which he shell himself,
later, formulate in symbolic form as a law or rule. The law, the rule or
definition formulated by the child is the summation of all the particular or
individual instances. In all inductions, the generalization that is evolved is
regarded as a tentative conclusion.
Example
1
Ask pupils to draw
a number of triangles. Ask them to measure the angels of each triangle and find
their sum.
Conclusion
The sum of three
angles of a triangle is two right angles (approximately).
You
can ask children to cut the three corners of the triangles and put them at a
point so that they, form a linear.
Example 2
3+5=8
5+7=12
9+11=20
Conclusion
Sum of two add numbers is an even
number.
In induction the law is accepted
and then applied to a number of specific examples. The child does not discover
the law but develops skills in applying the same, proceeds from general to
particular or abstract to concrete. In actual practice, the combination of
induction and deduction is practiced. The laws discovered by pupils inductively
are further verified deductively through applications to new situations.
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Sl.No
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Inductive Method
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Deductive Method
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1.
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Proceeds from particular to
general; concrete to abstract.
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Proceeds from the general to the
particular, the abstract to the concrete
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2.
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It takes care of the needs and
interests of children. It is a developmental process.
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Facts are thrust upon the child.
The principle of growth is not considered.
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3.
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It encourages ‘discovery’ and
stimulates Thinking.
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The authority decides or gives
the formula and encourages memorization.
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4.
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The generalization or rule is
formulated by the child therefore he remembers it with ease.
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The rule is given to the child.
He does not appreciate its nature and is likely to forget it easily.
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5.
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The how and why of the process is
Made clear through reasoning.
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The process is taken from granted
and accepted without Reasoning.
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6.
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It starts from observation and
direct Experience and ends in developing a Rule in abstract form.
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Does not encourage learning by
doing; it starts with a rule and provides for practice and applications.
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7.
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It encourages child participation
and group work.
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It demands individual learning
and treats the child as a passive recipient.
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.
Heuristic Method
This method can also be named as
the ‘discovery method ‘. It is in contrast to the lecture method. Instead of
merely the teacher telling everything the students finds out everything for
himself. It demands complete self-activity of self-learning on the part of the
student. Through this method, the student learns to reason fir himself. The
teacher is not even required to guide, help or encourage the student. This
method helps in the development of a scientific attitude in the learner. It
develops self confidence, originality, independence of judgement and thinking power in the learner to
make him an even successful student.
Practically speaking, this method in its
extreme form is not appropriate and desirable. The child after all is a child.
He is ignorant about various activities. Most of the things are new to him. He
is needs guidance and in certain situations he may need the teacher’s
assistance at every step. It is true the student should overcome his
difficulties by his own efforts as far as possible, but the teacher’s help
should not be denied when he needs it. Given below is an illustration how do we
go about this method.
Topic: Volume of a cuboid
Class: V
Let the problem be of finding out the volume of a cuboid of
dimensions l cm
b cm
h cm.
The teacher should remember that he
has to elucidate the process from the students. The teacher has to put
questions in such a way that he leads the students to discovery.
Q :
To determine the volume, what is to be done?
Ans. The child should say that they need a
number of unit cubes. Using the cubes, they will make the given solid or they fill up the
entire space of the soild with the cubes. Later they will count the unit cubes.
Q
: How many cubes did you use in
all?
Ans. The child says 18 cubes.
Q: Can you now give me the volume of the
cuboid?
Ans. Yes, 18cu.cm.
Q: Why 18 cu.cm and why not 18cm?
Ans. 18 cubes each of 1cu.cm volume have been
used. So, volume of the cuboid is 18cu.cm.
Despite the fact
that this method allows her learner to become an active participant in the
learning process; creates in the learner a spirit of inquiry; makes the
learner self-reliant; allows the learner
to acquire a real understanding and
clear notion of the subject; it has limitations for its use in primary classes
because of classes being of large size. Resources are being poor and teacher
competence being not satisfactory.
Analytic Method
The word
‘analytic’ is derived from the word ‘analysis’, which means ‘breaking up’ or
resolving a thing into its constituent elements. This method is based on
analysis and, therefore, in this method we break up the problem in hand into
its constituent parts so that it ultimately gets connected with something
obivious, or already known. Therefore, it is the process of unfolding of the
problem or of conducting its operations to know his hidden aspects. In this
process we start with what is to be finding out (unknown) and then think of
further steps and possibilities which may connect with the known and find out
the desired result. Hence in this method we proceed from unknown to known, from
abstract to concrete and from complex to simple. In analytic method, the
argument is that “ To prove that B is true if A is true, it is sufficient to
prove that A is true “
The following example illustrate
how analytic method can applied
Example 1
If
prove that
.To prove this using analytic method, begin from the
unknown.
The unknown is
is true
if
is true
if
if
if
if
if
which is given
to be true
Therefore
In analysis the reasoning is as
follows
C is true if B is true.
B is true if A is true. But A is
true
C is true.
Merits of Analytic Method
s It leaves no doubts in the minds of the
students as every step is justified.
s
It is a psychological method.
s
It facilitates clear understanding of the
subject matter as every step is derived by the student himself.
s It helps in developing the spirit of
enquiry and discovery among the students.
s
No cramming is necessitated in this method as
each step has its reason and justification.
s
It develops self-confidence in the students as
they tackle the problems confidently and intelligently.
s It develops thinking and reasoning power
among the students.
Demerits of Analytic
Method
w It is a lengthy, time consuming method and
therefore not economical.
w
With this method it is difficult to acquire
efficiency and speed.
w
This method may not be suitable for all topics
of mathematics.
w
In this method information is not presented in a
well organized manner.
Synthetic Method
‘Synthetic’ is derived from the word
‘synthesis’. Synthesis is the complement of analysis. To synthesis is to
combine the constituent elements to produce something new. In this method we start with something
already known and connect it with the unknown part of the statement. Therefore,
in this method one proceeds from known to unknown. It is the process of
combining known bits of information to reach the point where unknown
information becomes obvious and true. In synthetic method the reasoning is as
follows “Since A is true, B is true”.
The following example illustrates the
use of synthetic method.
Example 1
If
prove that
In synthetic method, one has to
begin with the known i.e.
and reach the
unknown i.e.
.
Proof:
(known)
Adding
on both sides
we get
(unknown)
i.e.
Thus
beginning with the known, the unknown is reached. But why
is added is not
explained.
In synthetic method the reasoning
is as follows
A is true.
is true and
C is true.
Merits of synthetic Method
1.
It is short and elegant
2.
It facilitates speed and efficiency
3.
It is more effective for slow learners.
Demerits of synthetic Method
1.
It leaves many doubts in the minds of the learner and
offers no explanation for them.
2.
It does not provide full understanding.
3.
It makes the student passive listeners and encourages rote
memorization.
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