muffins and math

I did something weird today. I made muffins for breakfast today. To make things even weirder, I made regular, full sized muffins instead of mini-muffins. Both girls were crowding so close around the bowl that I could barely squeeze in to mix and pour. Fine, if the girls are going to shove so close, I'm going to throw some math in.

Me: "Sparkle, how much is two times six?"
Sparkle: "Twelve."
This was easy for her as her math program introduced simple multiplication to her months ago.
Me: "Without counting, can you tell me how many muffins there are?"
Sparkle: "Twelve."
Sounds good, but I am suspicious.
Me: "How did you know?"
Sparkle: "Because that's the answer to the math problem you just said."
Arg.
Me: "What does the math problem have to do with the muffins?"
Sparkle: "I don't know."
Really? How can you stand there and see the muffins and not get it?
Me: "So how do you know that there are twelve muffins?"
Sparkle: "I just know that there are twelve. That's what two times six is."
Me: "So what does two times six have to do with the number of muffins?"
Sparkle: "I don't know. Fine, there aren't twelve muffins."
Sigh. Retracting her answer is easier for her than explaining it.
Me: "I'm not saying that there aren't twelve muffins. In fact you're right, there are twelve muffins. But how does two times six relate to the number of muffins, as opposed to say 10 + 2?"
Sparkle: "Ten plus two is twelve. There are twelve muffins."
Me: "Ten plus two means there's a group of ten objects and a group of two objects and you put the groups together."
Sparkle: "Yeah."
Me: "Do you see a group of ten muffins and a group of two muffins?"
Sparkle: "No."
Me: "So, ten plus two is not a useful representation of number of muffins. But two times six is. Do you know why?"
Sparkle: "No, I don't know."
... and on and on. Arg.

The conversation goes nowhere. I go finish my morning routine and shoe the girls off to do theirs while the muffins bake. After we are done and the oven beeps, I take the muffins out of the oven.

Me: "Sparkle, look, how many muffins are in this tray?"
Sparkle: "Six."
Me: "How many muffins are in the other tray?"
Sparkle: "Six."
Me: "How many trays of six muffins are there?"
Sparkle: "Two"
Me: "So there are two sets of six muffins. Two groups of six muffins is two times six. That's what multiplication is."
Sparkle: "Oh! I get it. Ask me again."
I pretend that we haven't had this aggravating conversation.
Me: "Sparkle, what does two times six have to do with the number of muffins?"
Sparkle: "There are six muffins in this tray and six in that tray. That's two sets of six. Two times six is twelve."

Ah. Finally. The poor girl can do the arithmetic and is starting to memorize her math facts, but she still doesn't really get it.

Sorry I don't have a picture of the muffins. We ate them for breakfast. They were oatmeal raison muffins. Sparkle and I each ate three muffins. Glitter ate two. How many muffins were left to snack on later in the day?