An approach is a theory about language learning or even a philosophy of how people learn in general. They can be psychologically focused such as behaviorism or cognitivism. They can also be based on older philosophies such as idealism or realism.
Approaches are fuzzy and hard to define because they are broad in nature. An example of an approach that leads to a method would be the philosophies of scholasticism, faculty of psychology, or even perennialism. Each of these philosophies encouraged the development of the mind in the way of a muscle. Train the brain and a person would be able to do many different things. These philosophies have impacted some methods of language teaching as we will see below.
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https://drive.google.com/open?id=1lGEy9s8nier_HLnrukir6o56ukNAY8kL