Estimation is more than rounding.
Most of the time we don’t teach this, but it is.
Tabitha (8 years old) had a homework assignment the other night that asked her to imagine she had $100 to spend in a catalog, and to make a list of things she would like to buy from that catalog. She found the latest American Girl catalog and got to work.
There was a table to fill out with three columns.
- Description of item
- Actual cost of item
A couple minutes later she asks, What’s the estimate if it costs five dollars? Should I write $5.01?
She has discerned that estimate means write down a number that is not the exact value.
But that’s not what estimation is about at all. Estimation is about finding a number that makes sense, and not worrying about whether it’s the exact value or not.
The image below seems to be going nuts on the Internet today (despite my exhortations to the contrary! Oh, Internet! When will you learn to listen to me?)
“Is this reasonable?” is a great estimation question. Rounding is one way to answer the question. But if a kid can quickly find a number that makes sense and it happens to be a precise number, then we probably haven’t asked a good estimation question. Rather than mark it wrong because the kid didn’t round, we should ask this kid a more challenging question next time.
What does a good estimation question look like? What would be more challenging?
I’m glad you asked.
Estimation 180. Thinking of a number that makes sense is much more interesting when you have to bring your knowledge of the world to bear.
Is 75 inches a reasonable answer for the difference between the father’s height and the son’s? Is 75 centimeters reasonable?
Oh! And here’s the first in a nice sequence about numbers of pages.
Here are two questions we can ask about educational technology.
The differences between them are important.
- Is the activity this technology supports more intellectually stimulating than what children would otherwise be doing?
- Is the activity this technology supports more intellectually stimulating than what children should otherwise be doing?
I will confess, here, now and publicly that I hold (for example) Khan Academy to the latter standard.
And, it seems to me, the typical defense of Khan Academy is that it should only be held to the former.
What made this difference especially salient for me was a recent article in the New York Times, which describes (among other things) a waffle-cutting app on the iPad. (See video at this link.)
Now, it seems to me that the children in the study were telling the researchers that there is something inappropriate about the activity when the 2-year old was trying to taste the waffle, and the 4-year olds needed to be coerced into not tap, tap, tapping everything on the screen.
But if we imagine a perfected version of the app, optimized for the ways 4-year olds interact with electronics, then we can ask those two questions about the idealized waffle-cutting app.
If kids are cutting virtual waffles in a daycare environment that otherwise provides little to no math talk, then perhaps this app would be an improvement. But I cannot really imagine an app that would be better than having children cut real waffles and talk about the nature of their activity with sympathetic adults as they do so.
I cannot imagine a virtual waffle app that is better than what 2—4 year olds should be doing, which is talking math.