Mathematics teachers use variety of methods and techniques in his/her daily classroom teaching in order to make his/her teaching more interactive and operative. Teachers and student interact with each other with in the school, so to develop this interaction; an educator uses new teaching substantial, procedures, strategies and approaches of teaching to make learning pertinent and beneficial. Till now so many methods and techniques has been launched but a mathematics teacher select only most relevant one keeping in view the topic, contents and needs of the learner. To grip or fully command on the content of mathematics it is too much necessary for an educator to use various relevant methods in the mathematics classroom at elementary level. It has been observed so many times that learners solved so many problems very rapidly by using a different methods, technique or formula to which they have already learnt in the classroom but unfortunately they have no idea about the basic logic that how this problem have done. Initially there was only the deductive approach of Aristotle to find a solution for a problem but later is the inductive reasoning of Francis Bacon was introduced to solve the mathematics problem. It is perhaps the oldest and the most basic method of teaching as well as learning mathematics. All other methods in mathematics utilise this method in different degrees. This is a combination of two methods of induction and deduction.

1. INDUCTIVE-DEDUCTIVE METHOD
K.THIYAGU,
Assistant Professor,
Department of Education, Central University of Kerala

2. Inductive Approach
Pestalozzi Francis Bacon

3. Inductive approach proceeds from
Particular General
Concrete Abstract
Known Unknown
Simple Complex

4. Inductive Approach / Method
Steps…

5. Appearance / Presentation of Examples
Teacher shows lot of examples of same type and
solutions of all those specific examples are
obtained with the help of the student.
Step # 1

6. Observation/ Reflection
After solving so many specific examples the
students detect and observe these and
try to reach some conclusion.
Step # 2

7. Generalization (Simplification)
The educator and students resolve some common
rules, laws, formulae or principle
by logical mutual discussion.
Step # 3

8. Testing and verification (Authentication)
Students test and prove the law, rule or principle
with the help of other suitable specific examples.
Step # 4

9. Inductive Approach / Method
Examples

10. Particular :
• Case 1 : 12 = 1
• Case 2 : 32 = 9
• Case 3 : 52 = 25
Take all the above Cases
General Concept:
From Cases 1 to 3, we have to
make a generalization
SQUARE OF AN ODD NUMBER
IS ODD
Example # 1(a)
Particular :
• Case 4 : 22 = 4
• Case 5 : 42 = 16
• Case 6 : 62 = 36
Take all the above cases
General Concept:
From Cases 4 to 6, we have to
make a generalization
SQUARE OF AN EVEN NUMBER
IS EVEN.
Example # 1(b)

11. Particular Cases:
• Case 1 : 1+1=2 (Odd + Odd = Even)
• Case 2 : 1+3=4 (Odd + Odd = Even)
• Case 3 : 1+5=6 (Odd + Odd = Even)
• Case 4 : 3+5=8 (Odd + Odd = Even)
General Concept:
In the above we conclude that
SUM OF TWO ODD NUMBERS IS EVEN
Example # 2

12. Inductive Approach - Merits
• Enhances self confident
• Promotes a meaningful learning
• Enhancing the Scientific method of
learning
• Develops scientific attitude.
• Develops the habit of intelligent
hard work.
• Does not burden the mind. Formula
becomes easy to remember.
• Suitable in the beginning stages.

13. • Not suitable for all topics.
• Time consuming and Laborious method
• Application is limited to very few topics
• Not suitable for higher class
• 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.
Inductive Approach - Demerits

14. Applicability of
Inductive method
Most Suitable Where
• Rules are to be formulated
• Definitions are be
formulated
• Formulae are to be derived
• Generalizations or law are
to be arrived at.

15. Deductive Approach /
Methods

16. Deductive approach proceeds from
General Particular
Abstract Concrete
Unknown Known
Complex Simple

17. Deductive Approach / Method
Steps…

18. Clear recognition of the problem
Step # 1

19. Search for a tentative hypothesis
Step # 2

20. Formulating of a tentative hypothesis
Step # 3

21. Solving the problem
Step # 4

22. Verification of the result
Step # 5

23. Example # 1
Find a2 X a10 = ?
Solution:
General :
From the law of indices,
it is known that
am X an = am+n
Particular:
Hence a2 X a10 = a2+10 = a12
(here m = 2 and n = 10)

24. Find (102)2 = ?
Solution:
General Law:
We know that (a+b)2 =a2+b2+2ab
Particular:
(100+2) 2 = 1002 + 22 + (2 x 100 x 2)
(in this case a = 100 and b = 2)
= 10000+4+400= 10404
We can also multiply 102 with itself to get the same result
(for verification of the correctness of the earlier result)
Example # 2

25. Deductive Approach - Merits
• Short and time saving method.
• Suitable for all the mathematical topics
and concepts
• Useful for revision and drill work
• Enhance the power of learner’s memory
• Provides sufficient practice in the
application of various mathematical
formulae and rules.
• Speed and efficiency

26. • Not a psychological method.
• Not easy to understand
• Not suitable for beginners.
• Encourages cramming.
• More emphasis on memory.
• Students are only passive listeners.
Deductive Approach - Merits

27. Applicability of Deductive Approach
• Suitable for giving
practice to the student
• very useful for fixation
and retention
• provides adequate drill
and practice.

28. Inductive
Approach
Deductive
Approach
Inducto-
Deductive
Approach

29. Licensed under