My favorite of all the Depth of Knowledge (DOK) levels, as I define them in these matrices for elementary and secondary mathematics, is DOK 3. I’ve always found it challenging to give a short and sweet reason as to why I felt that way… until I heard Bushnell’s Law.

This “law” was created by Atari founder Nolan Bushnell and was used to describe his ideal video game. He said:

All the best games are easy to learn and difficult to master. They should reward the first quarter and the hundredth.

When I first heard his law, I thought “That is exactly why I love DOK 3!!” Yes, I realize how nerdy that is, but I’ve learned to embrace it. To explain what I mean, try solving the problem below:

Using the digits 1 to 9, at most one time each, place a digit in each box to make a sum that is as close to 1000 as possible.

This is the kind of problem that takes people many attempts to figure out. So, when you’re ready to see the answer to this problem, head over to Open Middle.

Easy To Learn
Beginning this problem is fairly straightforward. Just place the nine digits in their own box and find the sum. As a result, every person begins with success. So, this problem is “easy to learn.”

Difficult To Master
However, you quickly realize that randomly choosing digits won’t be effective in the long run and so you have to think strategically by using your conceptual understanding of place value. For example, lets say you get a sum of 1044, how do you change your digits so that you don’t get even farther from 1000? So, this problem is also “difficult to master.”

Conclusion
I used to describe DOK 3 problems like the one you just tried by saying they had a very low floor (so that anyone can attempt them) but very high ceilings (so that they challenge even the most advanced students). That wasn’t so bad, but there is something elegant about describing them as “Easy to learn and difficult to master.”

What do you think? How do you describe problems like these? Let me know in the comments.