A Mixed Method Design
Deductive and Inductive Reasoning
The Raven Paradox - How Hempel's Treatise Led to Questioning of the Inductive Reasoning Process The scientific method
Teaching methods can either be inductive or deductive or some combination of the two. The inductive teaching method or process goes from the specific to the general and may be based on specific experiments or experimental learning exercises. Deductive teaching method progresses from general concept to the specific use or application. These methods are used particularly in reasoning i.e. logic and problem solving. To reason is to draw inferences appropriate to the situation. Inferences are classified as either deductive or inductive. For example, "Ram must be in either the museum or in the cafeteria." He is not in the cafeteria; therefore he is must be in the museum. This is deductive reasoning. As an example of inductive reasoning, we have, "Previous accidents of this sort were caused by instrument failure, and therefore, this accident was caused by instrument failure. The most significant difference between these forms of reasoning is that in the deductive case the truth of the premises (conditions) guarantees the truth of the conclusion, whereas in the inductive case, the truth of the premises lends support to the conclusion without giving absolute assurance. Inductive arguments intend to support their conclusions only to some degree; the premises do not necessitate the conclusion. Inductive reasoning is common in science, where data is collected and tentative models are developed to describe and predict future behaviour, until the appearance of the anomalous data forces the model to be revised. Deductive reasoning is common in mathematics and logic, where elaborate structures of irrefutable theorems are built up from a small set of basic axioms and rules. However examples exist where teaching by inductive method bears fruit. EXAMPLES: (INDUCTIVE METHOD):
A) Ask students to draw a few sets of parallel lines with two lines in each set. Let them construct and measure the corresponding and alternate angles in each case. They will find them equal in all cases. This conclusion in a good number of cases will enable them to generalise that "corresponding angles are equal; alternate angles are equal." This is a case where equality of corresponding and alternate angles in a certain sets of parallel lines (specific) helps us to generalise the conclusion. Thus this is an example ofinductive method. B) Ask students to construct a few triangles. Let them measure and sum up the interior angles in each case. The sum will be same (= 180°) in each case. Thus they can conclude that "the sum of the interior angles of a triangle = 180°). This is a case where equality of sum of interior angles of a triangle (=180°) in certain number of triangles leads us to generalise the conclusion. Thus this is an example of inductivemethod. C) Let the mathematical statement be, S (n): 1 + 2 + ……+ n =. It can be proved that if the result holds for n = 1, and it is assumed to be true for n = k, then it is true for n = k +1 and thus for all natural numbers n. Here, the given result is true for a specific value of n = 1 and we prove it to be true for a general value of n which leads to the generalization of the conclusion. Thus it is an...