Monday, November 8, 2010

Section Three Summary

Section Three (chapters four and five)

Chapters four and five explain why students struggle understanding abstract ideas and how practice can help.

According the Willingham, the goal of education is to teach students how to transfer knowledge to the world outside the classroom. To do this, students must understand abstract ideas. However, the mind prefers concrete ideas, so students need many concrete examples. Learners look at new information and compare it to old information, and since most of what students know is concrete, concrete examples help students make sense of the abstract.

One way to make comparisons is through analogies. Analogies help students relate the unknown to the known. However, it's not the quantity of the comparisons that help students understand abstractions, it's the quality. The comparisons have to be familiar to the student, and most of what students know is concrete -- hence the need for concrete examples to understand abstract ideas. As Willingham said on page 92, "Every new idea must build on ideas that the student already knows."

In chapter four Willingham contrasted shallow knowledge with deep knowledge and surface structure of problems with deep structure. With shallow knowledge students have some understanding of the material but their understanding is limited. They may see the parts but not the whole, and they may be focusing only on the simple surface structure of a problem. Students with deep knowledge can apply their knowledge in many different contexts and see the whole problem and how that problem changes when one part is altered. Students with deep knowledge understand abstractions and transfer that knowledge to new problems because they recognize that analogy between different problems.

Willingham stressed the importance of emphasizing deep structure in problems. Teachers can do this through the types of assignments and assessments they create and through daily questioning in the classroom. However, Willingham also assured his readers, "Shallow knowledge is much better than no knowledge at all, and shallow knowledge is a natural step on the way to deeper knowledge."

In chapter five Willingham explained how a store of factual knowledge and regular practice help students learn by clearing up space in their working memories. Practice that is spaced out over time help mental processes become automatic so the working memory can focus on more complex processes. Practice also helps with transfer and long-term memory.

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