Module 5: Synthetic Method

SYNTHETIC  METHOD

In this method we proceed from known to unknown. Synthetic is derived form the word “synthesis”. Synthesis is the complement of analysis. 

To synthesis is to combine the elements to produce something new.  Actually it is reverse of analytic method.  In this method we proceed “from know to unknown.” So in it we combine together a number of facts, perform certain mathematical operations and arrive at a solution. That is we start with the known data and connect it with the unknown part.

v  It leads to hypothesis to conclusion

v  It leads to known to unknown

v  It leads to concrete to abstract

Example :

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

Proof:

To prove this using synthetic method, begin from the known.

The known is a²+b²= 7ab

Adding  2ab on both sides

a²+b²+2ab=7ab + 2ab

(a+b)² = 9ab

Taking log on both sides

log (a+b)²      =       log 9ab

2log (a+b)     =       log 9 + log ab

2 log (a+b)    =       log 3² + log a + log b

2log (a+b)     =       2log 3+ log a+ log b

Thus if a²+b²=11ab prove that 2log (a-b) = 2log3+loga+logb

Merits

Ø  It saves the time and labour.

Ø  It is short method

Ø  It is a neat method in which we present the facts in a systematic way.

Ø  It suits majority of students.

Ø  It can be applied to majority of topics in teaching of mathematics.

Ø  It glorifies the memory of the child.

Ø  Accuracy is developed by the method

Demerits

Ø   It is an unpsychological method.

Ø   There is a scope for forgetting.

Ø   It makes the students passive listeners and encourages cramming

Ø   In this method confidence is generally lacking in the student.

Ø   There is no scope of discovery.

Ø   The recall of each step cannot be possible for every child.