In grammar instruction, two prevailing ideas guide how one should teach. Inductive and deductive reasoning refers generally to how one comes to an understanding of what is true or probable.
In inductive reasoning, commonly referred to as the scientific method, one makes an observation and tests it against multiple instances of like circumstances. In deductive reasoning, one begins with an accepted truth and discovers multiple instances of it in other instances.
With grammar, we would use inductive reasoning by looking at multiple sentences containing grammatical instances in common and derive a rule from these (sentences with two independent clauses and a coordinating conjunction are routinely divided by a comma; therefore, we might derive a rule that says a comma should always be used in these cases). Alternatively, we would use deductive reasoning by accepting a rule as a given and then finding that every time we have a compound sentence joined by a coordinating conjunction, we should use a comma.
In other words, inductive reasoning builds to truth or rules by aggregating individual instances. Deductive reasoning builds from truth or rules to individual instances. People who learn grammar almost intuitively by being metacognitive about how language works use an inductive approach to grammar, whereas many people need to learn the rules and then apply them deductively.