By providing opportunities for gifted students to think logically the teacher will enable them to organise their thoughts, draw conclusions and make generalisations with greater care and accuracy. Students should be provided with activities that will promote the use of inductive and deductive reasoning.
Inductive reasoning is not logically valid but used as part of the discovery process whereby students reach a conclusion supported by special cases: for example, a general principle is true because the special cases you have seen are true (the shop all the products in the shop are unhealthy). However just because some of the products in the shop are unhealthy, doesn't mean there is guaranteed proof that the shop does not stock health products. To develop inductive thinking, regular opportunities to engage in these types of activities should be provided.
Deductive reasoning is logically valid and it is the fundamental method in which mathematical facts are shown to be true. In deductive thinking activities students are encouraged to recognise certain facts and deduce conclusions based on their reasoning.
Deductive reasoning involves the left hemisphere of the brain and includes activities such as reading, spelling and number calculations. Activities such as recognising patterns, generalising and some kinds of inductive reasoning appear to involve the right hemisphere. The connecting link between the two hemispheres gets more use during the kinds of thinking which draw inferences, reason by analogy, recognise cause and effect, use spatial perception, recognise relations, and ask and answer such questions as "What would happen if...?"
Logical/Deductive reasoning activities
These activities may be done separately or incorporated into the learning program. For each of these activities students could work on their own, in pairs or small groups, students to devise their own patterns, sequences, codes, statements and questions for the rest of the class or group to solve. Students could then create a class book to showcase their outcomes.
Deductive and Inductive Thinking [PDF]
A concise overview of the differences between the two forms of logical thinking - "top-down" vs. "bottom-up".
Mission: Critical
A "virtual lab", capable of familiarising users with the basic concepts of critical thinking in a self-paced, interactive environment, includes arguments and exercises for induction and deduction.