More Willingham - Why Is It So Hard For Students To Understand Abstract Ideas?

In chapter four of Why Don't Students Like School, Dr. Willingham discusses the difficulties students have comprehending abstract ideas and applying them in unfamiliar situations. He says the teachers need to expose their students to many different examples of an abstraction to help them understand it - the mind prefers the concrete to the abstract.

He gives an example of a student who can calculate the area of a table top, but is stumped when it comes to calculating the area of a soccer field. The student needs to solve area calculation problems for tabletops, soccer fields, envelopes, doors, and so on.

Understanding is Remembering in Disguise

The easiest way to understand something new is to relate it to prior knowledge.

Analogies are great for this. Concrete examples are helpful as well. A teacher can try to explain iambic pentameter until she is blue in the face, but the explanation may be useless until the students actually hear the rhythm in the verse.

"Is this the face that launched a thousand ships?

And burnt the topless towers of Illium?"

Come to think of it, that might even not be enough! If the concrete example is not familiar, it may not have the intended effect. (To successfully explain iambic pentameter you might have to begin with a discussion of simple meter using a familiar example like, "Jack and Jill went up the hill...")

Examples must be familiar to be effective. Familiar examples bring old ideas into working memory, so we can "make comparisons we had not made before or think about features we had previously ignored."

But does retrieving and applying old information to an abstraction lead to deep understanding? Does this guarantee that new knowledge and understanding will transfer to the outside world? No.

The next section will concern the issue of shallow knowledge and lack of transfer.