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Option 1 : Deductive method
Deductive method:- In this method, the teacher uses the established formula, principle, or generalizations to solve the problem. The students proceed from general to particular, from abstract to concrete. In other words, the facts are deduced or analyzed by the application of the established formula. Hence, the formula is accepted by the students as a duly fact. Characteristics of the deductive method:
- Here first a generalization or a rule will be accepted and then according to it problem-solving or examples will be taken.
- Here the students move from unknown to known and abstract to concrete.
- This method is followed for teaching geometry at the upper primary level because geometry has a lot of axioms, postulates, and theorems that cannot be proven individually each time. After all, it takes more time.
- So the axioms will be first declared as a truth or a rule to the students and according to that axiom, the students learn the remaining concept.
- The deductive method will not take more time than the inductive method because here the established formula or generalization is first accepted then problems or solved according to it.
Hence the deductive method is used most commonly in mathematics classrooms for geometrical proofs.
| Inductive Method | In this method, one proceeds from particular events to generalized conclusions. A formula or generalization is arrived at through a convincing process of identifying the similar elements and the conditions of these similarities in several concrete cases. |
| Proof by contradiction | Proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. |
| Proof by counter-example | This proof structure allows us to prove that a property is not true by providing an example where it does not hold. |
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