I think Polarbear already gave some wonderful advice. I'll add my own perspective and experience:
Mathematics is its own language. Some children are native speakers of that language, and some are learning it as a second language. When you know math as a second language, you translate every math problem into your native language and solve it there. When you know math as a native language, you solve math problems without the need to translate your thought process into your spoken/written language.
When you ask a student to explain their answers in a language other than math, you are asking them to approach math the way MSL (Math as a Second Language) students approach it. Performing this unnecessary translation is an unnatural hindrance to mathy students, who often resist. It's analogous to asking a child to explain how they walk or catch a ball, and has about as much bearing on the actual performance of the task.
Personally, when I was in elementary and middle school, explanations weren't considered as important as they are today. It wasn't until I was in algebra that my teacher really wanted me to focus on showing my work and explaining my thought process. She wanted to make the point that my intuition wouldn't hold up to the more complicated problems, and we made a deal: I would try to solve a problem of her choice in my head in under a minute. If I solved it, I wouldn't have to show my work to get full credit, if I failed to solve it, an explanation would be required. In under a minute, my problems were gone. Perhaps there is some demonstration of rare mathematical insight that your child could perform for his teacher that would convince him/her that understanding a problem and being able to explain it in English to other people is not the same thing.
I've grown up to be an engineer, and when I think about math, I can't say I hear a lot of english buzzing around my head. I tend to think in pictures, but not where arithmetic is concerned. That's just recall.
Last edited by DAD22; 09/11/13 07:22 AM.
