Analytic Method:

• It involves breaking up the conclusion into simpler steps and setting up relationships with what is given or known. It applies intuition and inductive reasoning. 
• It is a method of discovery. The solution or proof is arrived at through systematic reasoning.
• It proceeds from the conclusion to the hypothesis. 

If a teacher in Class VII asks her students to draw circles of different radii. She then asks them to calculate the ratio of circumference to diameter. The students find that this ratio is almost the same in the case of each circle (inductive reasoning and method of discovery).

Thus from the above-mentioned points, it is clear that the teacher is using the analytical approach of problem-solving.

• Inductive approach- 
  • Proceeds from the particular to the general; from the concrete to the abstract.
  • It takes care of the needs and interests of children. It is a developmental process.
• Deductive approach-
  • Proceeds from the general to the particular; from the abstract to the concrete.
  • The child is provided with information of facts, principles & theories. 
• Project method-
  • It is based on learning by doing.
  • Children learn through association, co-operation, activity etc.