Shallow Knowledge

We have all been in classrooms where we ask a question about the previous day's lesson and get an answer that's an exact duplicate of what we said or wrote on the board. You wonder if the student really understood what he's saying. The student has just demonstrated rote learning, but not true understanding. In fact, rote learning means there is no understanding.

Willingham calls limited understanding "shallow knowledge." Shallow knowledge is information tied to an analogy or example that cannot be used to create further analogies or examples. He uses the example of "Carpe Diem." You can tell a student it means, "Seize the day," figuring the student understands that concept. However the student can know the translation without knowing it's true meaning. In fact, it's possible the student, if the saying hadn't been written down, might have interpreted "Carpe Diem" to mean "Cease the Day!" We have all seen examples of student test responses that hilariously demonstrate this kind of misunderstanding. The students' knowledge is truly "shallow."

"Deep knowledge," on the other hand, is knowledge that can be applied to many different contexts. This is the aim of good teaching. Unfortunately deep knowledge does not always come easily. Many students only look at the surface structure of problems when trying to apply knowledge.

For example, if a student can calculate the this problem:

Jayne is reseeding her lawn. The lawn is 20 feet wide and 100 feet long. She knows that lawn seed costs $10.00 per bag, and that each bag will will 1,000 square feet.

How much money does Jayne need to seed her whole lawn?"

but not this problem:

Jon is varnishing his tabletop, which is 72 inches wide long and 26 inches wide. The varnish he needs costs $8.00 per can, and each can will cover 2,300 square inches.

How much money does he need to buy the varnish?

it is because he can't see past the superficial difference between the problems. If he can't see that both problems have the same deep structure, he can't see they require the same steps for their solution.

So how do we lead our students to deep knowledge and understanding?

1. Ask students to compare different examples. You can guide students to discover deep similarities, while skimming over superficial differences.
2. Ask questions that require students to demonstrate deep understanding. This goes far beyond quizzing them about factual knowledge. For example, a student may be able to follow the arithmetical procedure of "borrowing", but may not be able to explain why it works. Lacking the deeper understanding of place value and regrouping may cause the student to have trouble later on as math becomes more complex.
3. Set appropriate benchmarks (Bloom's Taxonomy) for your student's level of understanding. Let the students know of your expectations for deep understanding.