Generalization by pattern discovery

In mathematics to high school, the teacher often teaches how to solve the problem, and we apply abstract knowledge to specific problems.

We spend not much time on how to make the abstract or general knowledge. It is by pattern discovery.

For example, after you see questions Q1 and Q2, you may find how to solve those kinds of questions. After seeing pigeons, sparrows, and swallows flying, you may think that birds fly. These are the pattern discovery. The abstract knowledge that "birds fly" made. This knowledge is sometimes wrong. For example, penguins do not fly even they are birds. However, even if you make a mistake, it is necessary to abstract.

Without an abstraction, when you see a new bird, you think that you do not know whether this bird flies or not because you have not observed it yet. If you do not know anything you have not taught, you can not solve a new problem.

Fig: Concrete information gathering, pattern discovery, pattern application

(1) collection of concrete facts

Doves fly

Sparrows fly

Swallows fly

(2) pattern discovery

Birds fly

(3) application of the pattern

Crows may fly

For this example, it is correct

For another example, "penguins may fly" is incorrect