The Number Field

A common mathematical phrase is necessary and sufficient , for example: having exactly three sides is a necessary and sufficient condition for a polygon to be a triangle. Sometimes you see the terms switched up, as in: having four sides is a necessary but not sufficient condition for a polygon to be a square--because every square has four sides, but there are lots of other shapes, e.g. rhombuses, kites, parallelograms, and rectangles, that have four sides and are not squares.

As parents, I think that sometimes we take too much credit, because we often think that there is a strict causal relationship between the conditions we create for our children and the resulting outcomes. In other words, we think that we've created necessary and sufficient conditions, when most of the time we have only done the bare minimum of providing some (but not all) of what's necessary.

Elena has started to be independently polite. After more than a year of instructing her to say "please" and "thank you," she seems to understand their proper usage and will often say them on her own. We get more cute thank yous than pleases, but she still responds quickly when we need to prompt her to say please. If we take too long to respond to a request, she has started to catch on to the power of the whiny, manipulative please. I suppose that's somewhat unavoidable.

Two other niceties, "sorry" and "you're welcome" have also entered into Elena's vocabulary. We only occasionally instruct her to say sorry, such as when she's cuddling with Jenny and elbows her (and Moonbeam) in the stomach. However, Jenny and I say "I'm sorry" a lot, maybe too much, and Elena now says sorry a lot. She says sorry when she feels sad, even if it wasn't her fault at all. We're only starting to work on "you're welcome," but she's already starting to use the term properly.

I have one contrived training situation in which it's very hard to get Elena to be polite. She's very possessive of her favorite blanket, and it's almost always nearby. When I'm playing with her--these days she likes wrestling (aka wrasslin')--she leaves it lying around, and sometimes I pick it up. This instantly causes her to start shouting "MY BLANKEY, MY BLANKEY!" and not want to do anything until I release the blanket to her control. At that moment, she isn't receptive to my suggestion that if she'll just say "please," I'll be happy to give it back to her.

Jenny thinks that I shouldn't employ this tactic, because it's too close to the heart--we wouldn't let other kids play with the favorite blanket. I think that in this controlled environment, it's a good way to teach her how to share. I always say that I know the blanket belongs to her, and I'll give it back, but it's important to be polite. She has a baby brother on the way, and sharing will be more important when he comes around than it is now. I'm always open to suggestions other than this one, especially since Jenny thinks it's too much.