When students observe patterns in worked examples and then derive a general…

Concept

Methods of teaching mathematics are classified by the direction in which the reasoning travels. The inductive method moves from the particular to the general: learners work through specific instances, notice the regularity common to them, and only then state the general rule or formula. The deductive method travels the opposite way, from the general to the particular: an established rule is stated at the outset and is then applied to individual problems.

Application

The classroom sequence described in the question runs in this order:

1. Worked examples of addition and subtraction are placed before the students — these are the particular instances.

2. The students observe what recurs across those examples, that is, they detect the pattern.

3. From that pattern the students themselves frame the general rule for addition and subtraction.

The particular cases come first and the general rule emerges at the end as the students’ own conclusion. Reasoning that runs from particular instances to a general rule is the inductive method.

Cross-check

Contrasting the sequence with the other methods on offer:

• Deductive method: the rule for addition and subtraction would be announced first and the worked examples would follow as practice of it. Here the rule is the endpoint, not the starting point, so the direction is reversed.

• Rote learning of rules: the rule is supplied ready-made and fixed by repetition. No pattern is examined and nothing is derived, whereas the question has the students derive the rule themselves.

• Memorizing formulas only: a finished statement is committed to memory for recall. There is no set of instances to generalise from and no generalisation step at all.

Result

The teacher is applying the inductive method — pattern first, rule afterwards.