A math teacher reads a children’s book

We got this book from the library recently. My daughter Tabitha (4) loves it. For her, the fun is in identifying which fox is which.

But for me, it’s all about the counting. Basic plotline (don’t worry; no spoilers):

The mother goes out to rustle up a chicken for dinner. The wee ones are told to stay behind. They sneak out. Then they worry that someone might get lost. So they decide to count to make sure no one is missing.

This is where it gets good for someone who teaches math for future elementary teachers. One of the foxes (we’ll call her Misty-sorry, I’ve returned the book to the library) volunteers to count. She counts each of the other foxes and only reaches four. This confirms the wee ones’ worst fears. There are supposed to be five, so someone’s missing.

If you have studied CGI, you see the clever dilemma here. I’ll spell it out in gory detail:

(1) Misty has only counted part of the whole. So the fact that she reaches only four is resolved as a Part-Part-Whole/Part-Unknown problem.

(2) Misty misinterprets her result as the answer to a Separate/Change-Unknown problem.

That is, she correctly resolves the computation. Where she errs is in interpreting the conceptual meaning behind this computation.

Lovely.

Of course the first time we read the book, I stopped and asked Tabitha if she knew what the problem was. She didn’t catch my drift. So I reiterated the fox’s counting process and pointed out that (1) she only got to 4, and (2) she takes this to mean that someone is missing. I asked again, What do you think is wrong here?  Where do you think the fifth fox is?

Tabitha replied, It’s her.

I know I am warping my children. But rest assured that our lives aren’t like this 24/7. These are just the interesting bits for my math teaching friends.