Abstraction, intuition, and the “monad tutorial fallacy”

In the past few weeks, I have been reading my calculus textbook and wondering which of the following is true: (1) the book is very badly written, or (2) I am dumb, or (3) all of the above. This wonderful article explains the whole phenomenon with a funny metaphor.

blog :: Brent -> [String]

While working on an article for the Monad.Reader, I’ve had the opportunity to think about how people learn and gain intuition for abstraction, and the implications for pedagogy. The heart of the matter is that people begin with the concrete, and move to the abstract. Humans are very good at pattern recognition, so this is a natural progression. By examining concrete objects in detail, one begins to notice similarities and patterns, until one comes to understand on a more abstract, intuitive level. This is why it’s such good pedagogical practice to demonstrate examples of concepts you are trying to teach. It’s particularly important to note that this process doesn’t change even when one is presented with the abstraction up front! For example, when presented with a mathematical definition for the first time, most people (me included) don’t “get it” immediately: it is only after examining some specific instances…

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About sy2m

a student forever ... never stop seeking knowledge :)
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