My first post about “Duke is Missing” focused on wondering. I think of wondering as a good part of *launching* the PoW. Then comes *exploring*… we love to know about all the thinking that goes into working on the problem. Check out this submission to the “Duke is Missing” problem:

i got that dukes body is 24 inches because his tail (18 inches) and his head (6 inches) sum is 24 inches which is equall to his body. so his tail is 6 inches (his head) plus 12 (half his body).

For this one, I keep wondering, “How did you think to choose 24 inches for the body?” As a reader, I’m really curious! I also think the submitter probably did some good thinking, and without writing down what they thought, they can’t get feedback on it, and they might not be able to use their good thinking discover more math, wonder more, or think about how to solve a similar problem.

Some good questions to get to the next level of explanation are:

- What strategy did I use?
- What made me think of that strategy?
- How did I come up with that number — was it a good guess? an adjustment of a previous guess?

What would you ask this student to learn more about their thinking process?

How could writing about thinking help the student improve their math & problem-solving skills?

**Some “Duke is Missing” links** in case you are interested:

- The problem [requires a Math Forum PoW Membership].
- Information about accessing “Duke is Missing” (and all our current PoWs) for two weeks with a free Math Forum trial account.
- Information about becoming a Math Forum Problems of the Week Member. Compare prices – consider starting with a $25 membership giving you access to all of this year’s Current PoWs — and now you can create 36 student logins as well!