The word “analytic” is derived from the word “analysis” which means “breaking up” or resolving a thing into its constituent elements. The original meaning of the word analysis is to unloose or to separate things that are together. In this method we

**break up**the unknown problem into simpler parts and then see how these can be recombined to find the solution. So we start with what is to be found out and then think of further steps or possibilities the may connect the unknown built the known and find out the desired result. It is believed that all the highest intellectual performance of the mind is Analysis.

v It is derived from the word analysis, its means breaking up.

v It leads to conclusion to hypothesis

v It leads to unknown to known

v It leads to abstract to concrete

*Example:*
if a

^{2}+b^{2}=7ab prove that 2log (a+b) = 2log3+loga+logb**Proof:**

To prove this using analytic method, begin from the unknown.

The unknown is 2log (a+b) = 2log3+loga+logb

Now, 2log (a+b) = 2log 3+ log a+ log b is true

If log (a+b)

^{2}= log 3^{2 }+ log a + log b is true
If log (a+b)

^{2}= log 9 + log ab is true
If log (a+b)

^{2}= log 9ab is true
If (a+b)

^{2}= 9ab is true
if a

^{2}+b^{2}=7ab which is known and true
Thus if a

^{2}+b^{2}= 7ab prove that 2log (a+b) = 2log3+loga+logb

*Merits*
Ø It develops the power of thinking and reasoning

Ø It develops originality and creativity amongst the students.

Ø It helps in a clear understanding of the subject because the students have to go thorough the whole process themselves.

Ø There is least home work

Ø Students participation is maximum

Ø It this method student’s participation is encouraged.

Ø It is a psychological method.

Ø No cramming is required in this method.

Ø Teaching by this method, teacher carries the class with him.

Ø It develops self-confidence and self reliant in the pupil.

Ø Knowledge gained by this method is more solid and durable.

Ø It is based on heuristic method.

*Demerits*
Ø It is time consuming and lengthy method, so it is uneconomical.

Ø In it, facts are not presented in a neat and systematic order.

Ø This method is not suitable for all the topics in mathematics.

Ø This does not find favour with all the students because below average students fail to follow this method.

Ø Every teacher cannot use this method successfully

So this method is particularly suitable for teaching of Arithmetic, algebra and Geometry as it analyses the problem into sub-parts and various parts are reorganized and the already learnt facts are used to connect the known with unknown. It puts more stress on reasoning and development of power of reasoning is one of the major aims of teaching of mathematics.

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