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.
Yes! This is beautiful!
I don't even know how to tell my kids how to "show your work" on something like subtraction. How did I get the answer to 7 - 4 = 3? Well, because 7 - 4 = 3. As DS used to write, "because it is the answer". And no amount of drawing apples or coloring circles is going to make it any easier. It's just going to annoy the pig.
DS is currently up to about 50% on showing his work in 8th grade math, from the looks of last night's homework. He had approximately every other step written down -- and it was mostly legible, which is something.
