Defining a Half

Despite all the difficulties students traditionally have with fractions, even young children seem to use the concept of "half". So I ask a few six-year-olds to define "half".

To my surprise and delight, they were able to think about this question and construct answers. Of course, no one had yet tried to tell them the answer to this question, so they had to think.

The answers weren't bad, but they were not correct. If you are hoping for the correct answer, don't bother. If you are planning on teaching the correct answer, you are missing the point of how to teach math. Give them the problem. Let them think. That helps develop their mental models. Be happy with them, so they will think for you again. When the time comes to learn the correct definition (if there is a correct definition), they will be better prepared to learn it.

Elsewhere I describe how to properly do definitions. I suspect that is not a reasonable goal for six-year olds. Just let them try their best, and give them time to try to put things into words.

Extending the Discussion

I could extend the discussion of half a little. (I was acting like someone who didn't know the answer, not like an examiner who was testing them.) I think I asked about quarter and thirds.

I also asked if half was a number. If they had answered yes, I would have asked how come when you count (1,2,3......) you don't get to half? They dodged that bullet by saying that half wasn't a number.

So I asked them, if half wasn't a number, how come you could have more than half and less than half? I could not understand their answer to that, but they were thinking, so I was happy. I am not sure how much sense the question makes either, but you can't knock success -- it made them think.