A lovely third grader pointed to her page.

Her: Is this how you write a quarter?

Me: How many quarters are there in a whole?

Her: Four. How do you write a quarter?

Isn’t that interesting? What do you think is going on here?

• Perhaps they are viewing it as a pie chart, there is 1 part that is “in” the quarter, to 3 parts that are “not in” the quarter.

• Michael Paul Goldenberg

@moron4hire: That’s my take as well, though the pie chart model is only one of several that could lead to the same conclusion: 1 piece of interest, 3 pieces not of interest 1 of 4 total pieces. WIth no previous exposure to the convention for representing fractions, seems reasonable. Until, of course you run into improper fractions, were representing ‘three halves’ with that approach is going to be quite interesting. And with non-unit fractions less than one, you’d have to write, say, ‘three-fourths’ as 3/1. And any fractional equivalent of 1, say five fifths, will be 5/0.

But with NO exposure to the standard way of writing rational numbers, seems like a reasonable, if awkward, attempt.

• mpershan

This kid had exposure to the standard way of writing rational numbers.

• Reasonable to me, too, if you’re thinking of a “one-stop” visual representation of the idea. “one out of four” requires part-whole thinking… 1/3 shows me four entities in all, with 1 on the left and 3 on the right.

• Does she know what other names the fraction she wrote has?

• mpershan

I’ll report back tomorrow. The only other thing I noticed today was that she said that 6/24 was equal to 1/6.

• It occurs to me that to divide a line segment into quarters, I must use three lines. Could it be that when the fraction 1/4 is mentioned she is imagining how to do it. Not just what one quarter is but how do divide something into quarters.
I also wonder about using one fourth rather than one quarter.