80 mph

My brother showed me this video --- can't remember if we've ever posted it here.

What I love about it is that the girlfriend actually comes up with a guesstimate that's pretty close to correct, which reminded me of something I once read about the difference between really good math students versus the "works hard" variety.

To wit: the really good students devise elegant and efficient solutions and proofs. The 'works hard' students go on wild goose chases.

Works-hard students do get to the answer or the proof eventually, but the process isn't pretty. (Speaking as a person who has spent a lot of time teaching herself math, I relate.)

The process may not be pretty, but it can be funny.



Another thing: this exchange is a brilliant example of "inflexible knowledge" in action. The young woman isn't transferring the meaning of "per hour" to a different phrasing of the same situation.

Speaking of inflexible knowledge, in Atlantic City this weekend we had a semi-galling episode of Failure to Transfer. My father-in-law has been deaf for years, and Ed and I -- and Andrew -- have had iPads for at least two. We use Andrew's iPad to communicate with him via typing (Andrew types, too). Yet it had never occurred to us that we could do the same for Ed's dad.

Two years to make the connection!

Immediately after I'd had the blinding revelation that iPads work for old people with hearing loss as well as young people with autism, we began plotting and scheming how to get an iPad for Ed's dad (would he use it?? Which one should we get?? The big one?? The little one that would take up less space on a dinner table?? Etc.)

It took me a good 5 minutes to figure out that Ed's dad does not need an iPad. He can talk.

We had a chuckle over that & then an hour or so later Ed raised the subject again.

We have spent a LOT of years living with people who can't talk.

The Benign Cousin to Rote Knowledge

I'm savoring these Willingham articles. Just one more to go, then I will read his book.

It's not only helping me with my own learning process, but I feel armed to help my kids study with specifics about what works best.

(cross-posted on Perfect Score Project)

severely fragmented knowledge

Looking through the SAT prep posts, I found this problem that, just 12 days ago, I couldn't begin to do.

If 20 percent of x equals 80 percent of y, which of the following expresses y in terms of x?

(A) y = 16% of x
(B) y = 25% of x
(C) y = 60% of x
(D) y = 100% of x
(E) y = 400% of x

The Official SAT Study Guide 2006
ISBN-13: 978-0874477184
p. 550

Today it seems simple and obvious.

This is a classic case of inflexible knowledge. I've practiced solving many, many literal equations over the past few years, a skill I learned and practiced in high school, too. I had no trouble doing it then, and I've had no trouble doing it now.

So, in theory, I 'know' how to do this problem.

And yet when I encountered a literal equation involving percent, I was mystified.

What fresh hell is this?


from cranberry:

Funny, I didn't need to set up a formal equation for this. If 20% of x = 80% of y, y must be four times as small as x. Thus, 25% of x.

That's the kind of thing years of doing bar models does for you.

Not that cranberry has spent years drawing bar models.