Friday, May 20, 2011

Module 1: Inductive Method

INDUCTIVE METHOD

ü  Inductive approach is advocated by Pestalaozzi and Francis Bacon
ü  Inductive approach is based on the process of induction.
ü  In this we first take a few examples and greater than generalize.
ü  It is a method of constructing a formula with the help of a sufficient number of concrete examples. Induction means to provide a universal truth by showing, that if it is true for a particular case. It is true for all such cases. Inductive approach is psychological in nature.
ü  The children follow the subject matter with great interest and understanding. This method is more useful in arithmetic teaching and learning.
Inductive approach proceeds from
  • Particular cases to general rules of formulae
  • Concrete instance to abstract rules
  • Known to unknown
  • Simple to complex
Following steps are used while teaching by this method:-
(a) Presentation of Examples 
        In this step teacher presents many examples of same type and solutions of those specific examples are obtained with the help of the student.
(b) Observation
After getting the solution, the students observe these and try to reach to some conclusion.
(c) Generalization
          After observation the examples presented, the teacher and children decide some common formulae, principle or law by logical mutual discussion.
(d) Testing and verification
              After deciding some common formula, principle or law, children test and verify the law with the help of other examples. In this way children logically attain the knowledge of inductive method by following above given steps.



Example 1:
Square of an odd number is odd and square of an even number is even.


Solution:
Particular concept:
12 = 1                     32 = 9                     52 = 25 equation 1
22 = 4                     42 = 16                   62 = 36 Equation 2   
General concept:
From equation 1 and 2, we get
Square of an odd number is odd
Square of an even number is even.

Example 2 :
Sum of two odd numbers is even
Solution:
Particular concept:
1+1=2
1+3=4
1+5=6
3+5=8
General concept:
In the above we conclude that sum of two odd numbers is even

Example 3 :
Law of indices am x an =a m+n
Solution:
            We have to start with a2 x a3         =       (a x a) x (a x a x a)
                                                          =       a5
                                                                         =       a 2+3                   
                                      a3 x a4           =       (a x a x a) x (a x a x a x a)
                                                          =       a7
                                                                         =       a 3+4
                                Therefore      am x an    =       (axax….m times)x(axa …n times)
                                      am x an          =       a m+n
MERITS
Ø  It enhances self confident
Ø  It is a psychological method.
Ø  It is a meaningful learning
Ø  It is a scientific method
Ø  It develops scientific attitude.
Ø  It develops the habit of intelligent hard work.
Ø  It helps in understanding because the student knows how a particular formula has been framed.
Ø  Since it is a logical method so it suits teaching of mathematics.
Ø  It is a natural method of making discoveries, majority of discoveries have been made inductively.
Ø  It does not burden the mind. Formula becomes easy to remember.
Ø  This method is found to be suitable in the beginning stages. All teaching in mathematics is conductive in the beginning.

DEMERITS
Ø  Certain complex and complicated formula cannot be generated so this method is limited in range and not suitable for all topics.
Ø  It is time consuming and laborious method
Ø  It is length.
Ø  It’s application is limited to very few topics
Ø  It is not suitable for higher class
Ø  Inductive reasoning is not absolutely conclusive because the generalization made with the help of a few specific examples may not hold good in all cases.



Applicability of inductive method
Inductive approach is most suitable where
Ø  Rules are to be formulated
Ø  Definitions are be formulated
Ø  Formulae are to be derived
Ø  Generalizations or law are to be arrived at.

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