Comparison of Analytic and Synthetic Methodsof mathematics

Synthetic

1. It synthesizes various elements to get the desired results.

2. It proceeds from the known to the unknown.

3. It is product of thought.

4. It is a method for the learner.

5. It encourages memory work.

6. This method is logical.

7. Only a few things are learnt.

8. Things once forgotten cannot be easily recalled.

9. It is an unscientific method.

10. The teacher loses touch with the class.

11. The ‘why’ of every step is not explained?

12. It is a concise and elegant method.

13. In this method, we apply deductive reasoning.

14. No opportunity is provided for independent work. The Students taught by this method, lack self-confidence.

15. Synthesis follows analysis. The facts discovered through analysis, are put systematically by synthesis.

Analytic

1. It analyses a problem into its simpler units.

2. It proceeds from the unknown to the known.

3. It is process of thinking.

4. It is a method for the discoverer.

5. It encourages reasoning.

6. This method is psychological.

7. Many things are learnt.

8. The facts forgotten can be rediscovered.

9. It is a scientific method.

10. The teacher carries the class with him.

11. Each step is explained with a ‘why’.

12. This method is lengthy-Steps may not be systematic.

13. In this method, we apply inductive reasoning.

14. Here the students learn through their own attempts. The method develops confidence in the students.

15. Analysis is the fore-runner of synthesis. Problem is first analysed for discovering the solution.

From the above comparison, it is clear that analytic and synthetic methods are complementary. One is incomplete without the other. If we follow synthetic method alone, our approach will be dogmatic. We shall not understand the process of discovery.

If we follow only analytic method, the things will not be put in a systematic form. Application of conclusions may become difficult. So both the methods must go side by side. Analytic method serves the purpose of clarifying the reasons for the steps taken in the construction of synthetic proof.

So it should come in the beginning. Analytic method is a logical way to develop a proof which is not evident at first sight. When the steps are properly understood, we should proceed synthetically.

That will give a logical proof of the mathematical principle in question. So analysis should be followed by synthesis. The best approach is analytic-synthetic approach.