I got to see a natural use of logic yesterday – but it was disguised as an ornery kid!

Parenting experts (and magazines) suggest that giving options to kids is a great idea – but only if they’re real. You’re not supposed to

ask your little one if he wants to take a bath when you intend to give him a bath anyway.

Instead, ask him which bathtub he wants to use. Or which towel he prefers when he gets out of the tub. Or even if he wants to take a bath alone or with a sibling.

It’s a clever way of saying, “It’s time for your bath, but you get some autonomy in the activity.”

Kids like this.

### And it’s formal math!

Yup – in formal logic terms it looks like this: *p∪**q*, where *p* and *q* are the options. And that little ∪ means “or.”

For instance, I give K8 the choice of taking a bath alone or with me. So it looks like this:

*p* = Take a bath alone.

*q* = Take a bath with me.

So *p*∪*q* = Take a bath alone or take a bath with me.

### But she’s more clever than I thought!

Yesterday I gave her this option. She responded:

I don’t want to take a bath alone and I don’t want to take a bath with you.

Ornery little thing she is!

But in our formal math lingo, this is

¬*p∩*¬*q*

(Those little thingies in front of *p* and *q* are the “not” part. And the ∩ is the “and.”)

If you look it up (or know formal logic) you can find out that ¬*p∩*¬*q* is exactly the same as ¬(p∪*q*).

She was clearly saying to us that she does not want to take a bath at all!

### Math is built in.

I’ve claimed before that we all have a built in ability to do math. Now it looks like that’s not just with numbers – it’s also with logical processing.

She doesn’t get that she’s doing formal logic, but she understands *in her gut* that saying, “I don’t want to take a bath alone and I don’t want to take a bath with you” is negating the “take a bath” statement.

### Encourage it!

I know it seems like she’s being a snot. And as she gets older it’ll get worse. I’ve seen my niece do it with my sister – play these logical games that feel like back-talk.

But logic is the foundation of learning math. So instead of admonishing children, discuss it with them. Talk about a way to phrase your statements or rules so that there’s no logical loopholes.

Allow them to argue with you on these little things – they’re building skills that will make them into super math thinkers!

### Your turn…

What do you think? Has your child shown natural logic skills? How do you handle it?

And how do I get K8 into the bath now!?

###### You might also like:

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- Math Words – Start Using Them Early
- The Real Place Kids Learn Math
- Counting Isn’t an Inherent Concept

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Just a point of pedantry: it’s only

formallogic when you’re actually working with formulas directly. In this case, it’s just “logic”. But it is, in fact, logic, so the point of the whole article comes across just fine. 🙂On the subject of logic in everyday life, Greg Restall has a great article here

Thanks, Cory, for pointing that out. As a mathematician, I welcome, encourage and appreciate pedantry. 🙂

And thanks for the link!

How about doing a PTA bath?

However, with a three-year-old it would be,”Let’s put your hair up so it won’t get wet[choose a pretty shower cap] then jump into the shower so we won’t get TOO TOO wet, but just take the germs off our hands. Let’s don’t even use soap today. Today let’s do a PTA bath.

Oh, you’ve never done a PTA bath??? Very simple, just soap the hands and get a little bit on our PRETTY (she pats her face) and a smidge on our TINKLE( quick clean on front parts) AND a bit on our booty! (slap hiney with attitude and giggle with her!!!) Pretty soon she will be wet all over, sufficiently washed for the day, and all are happy with the game. Quickly get her out of the shower and give a turkish rub so the water doesn’t stay on her too too long all the time saying “lets get you dry before the water sticks to you too much!”

A quick alternative to a long drawn out bath. Now you have another choice at bathtime, a bath with mommy, by yourself or a PTA bath!

Thanks for the comment, marymoses!

The problem is that our definition of “bath” is that you wash your private parts and your hair. So putting the hair up and washing the PTA doesn’t qualify.

But it’s a nice thought. 🙂

My son talks about making good choices and how making negative good choices really mean making bad choices. He does the same with making negative good choices. Pretty ingenious huh!