Younger students first encounter mathematical reasoning through observing similarities and differences between objects. As they develop and practise various types of inductive and deductive thinking, they move towards more formal reasoning and the writing of proofs.
Same and different
The use of the questions "What is the same?" and "What is different?" encourages mathematical reasoning.
Visualisation is a powerful mechanism.
One approach to stimulating students' reasoning skills is to focus on the truth of propositions.
If-then statements are used in deductive reasoning.
What is deduction?
Students need to learn that conjecture is not the same as proof.