Analytic Method Synthetic Method

Analytic Method Synthetic Method

Analytic Method:

It proceeds from unknown to known. ‘Analysis’ means ‘breaking up’. 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.

Procedure:

Example: If (ac- 2b²)÷ b = (c²-2bd) ÷d  prove that   a/b=c/d,

Solution start from unknown i.e. to solve this problem we have to start from

(ac- 2b²)÷ b = (c²-2bd) ÷d   after calculation

 We get the answer a/b=c/d

Example:

If a²+b²=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 3² + 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 a²+b²+2ab =9ab is true

Then  a²+b²=7ab which is known and true

Thus if a²+b²= 7ab  prove that 2log (a+b) = 2log3+loga+logb

Merit of Analytic Method

• It is logical method. It leaves no doubts and convinces the learner.
• It helps student in understanding and strengthen the urge to discover facts.
• Each steps has the  its reason and justification. So, no fixed steps is required.

·         It is a method of discovery.

·          It is a process of thinking (exploration).

·          It pulls apart or breaks up the statement under solution.

·         It answers satisfactorily and question that may arise in the mind of pupil.

·          The students can recall and reconstruct easily any step if forgotten.

·          It develops originality.

Demerit of Analytic Method

·         It is lengthy method and laborious.

• It is difficult to acquire efficiency and speed
• It may not be applicable to all topics equally well.

·         It is slow, round-about and involves trial and error. 

Synthetic Method

Synthesis means building up separate element and their combination.It proceeds from the known to the unknown facts. It is opposite of analytic.

Procedure:

Example: if  a/b=c/d, prove that ac-2b²/b=c²-2bd/d

Solution:  start from known i.e. to solve this problem we have to start from

a/b=c/d ;  subtract both side by 2b/c

and get the answer ac-2b²/b=c²-2bd/d . it is unknown

Merit Synthetic Method

• It is short method, it glorify memory, it suit the teachers and it follow the same process as given in the text book.

·          It is a method of present­ation of discovered facts.

·          It is a product of thought.

·          It is short and concise.

·          It puts together or synthesizes known facts.

·         Once forgotten, it cannot be recalled.

·          It is quick, straight forward and does without trail and error.

·          It does not satisfy doubts and questions arising in the mind of the leaner.

·          It is a special device; it is a method for the crammer.

·         It is not that easy to recall or reconstruct any forgotten step.

·          It develops memory.

·          It is informal.

·         It is simply informational.

·         There is no heuristic approach in it.

·         It is the follower of analysis.

Demerits Synthetic Method

•    It is not a psychological method.
•  There is a scope for forgetting.
• It makes the students passive listeners and encourages cramming.
• In this method confidence is generally lacking in the student.
• There is no scope of discovery.
• The recall of each step cannot be possible for every child.

Difference between Analytic Method & Synthetic Method

No.	Analytic Method	Synthetic Method
1	Analysis means breaking up into simpler elements.	Synthesis means building up separate element and their combination
2	It proceeds from the unknown to the known facts.	It proceeds from the known to the unknown facts.
3	It is a method of discovery.	It is a method of present­ation of discovered facts.
4	It is a process of thinking (exploration).	It is a product of thought.
5	It is lengthy and laborious.	It is short and concise.
6	It pulls apart or breaks up the statement under solution.	It puts together or synthesizes known facts.
7	It can be rediscovered.	Once forgotten, it cannot be recalled.
8	It is slow, round-about and involves trial and error.	It is quick, straight forward and does without trail and error.
9	It answers satisfactorily and question that may arise in the mind of pupil.	It does not satisfy doubts and questions arising in the mind of the leaner.
10	It is a general method; it is a method for the thinker and discoverer.	It is a special device; it is a method for the crammer.
11	The students can recall and reconstruct easily any step if forgotten.	It is not that easy to recall or reconstruct any forgotten step.
12	It develops originality.	It develops memory.
13	It is informal.	It is informal.
14	It is formational.	It is simply informational.
15	It is based on heuristic lines.	There is no heuristic approach in it.
16	It is fore-runner of synthetic.	It is the follower of analysis.

Conclusion: Since analysis is a lengthy method, it needs the help of Synthesis for the removal of doubts. Synthesis is the complement of the analysis method. both the method are interdependent. Teachers should offer help for the analytic form of the solution and that synthetic work should be left for the students.