Shallowness (not Depth) of Knowledge
Consider the two problems on adding two-digit numbers shown below that are of varying Depth of Knowledge (DOK) levels.
When I gave both of these problems to my then second-grade son (who is fortunately a mini-math geek like his dad), he quickly conquered Problem One with it providing no real challenge. When I showed him Problem Two, he got 98 + 76. This is a great first answer, but it’s wrong.
He knew which four numbers to use but the problem exposed a hole in his understanding of place value and gave me a great opportunity to ask him questions like, “What does the 9 represent? What does the 8 represent? How does having more tens or ones change the sum?”
I’d make the case that the problem on the left is DOK 1 while the problem on the right is DOK 3 (more info here). Recently though, I got some pushback that forced me to think of a new way to articulate the difference between them.