How Wide and How Deep?

August 4, 2016 at 4:11 am 3 comments

In 2002, William Schmidt described the U.S. math curriculum as “a mile wide, an inch deep,” and it’s been bugging the sh*t out of me ever since.

I mean, I get what he and his co-authors were saying: The curriculum contains too many topics, so they can’t be covered with sufficient depth.

But if a mile is too wide and an inch is too shallow, then what dimensions would be appropriate?

One-inch wide and a mile deep would be problematic, too. That’d be like spending an entire year teaching kids to count to 10.

I suppose we could opt for a square curriculum instead. A curriculum that is a mile wide and an inch deep has an area of 5,280 × 1/12 = 440 square feet, so the conversion would look something like this, with the thin line representing a mile by an inch and the square representing 21 feet by 21 feet:

MileWideInchDeep.png

Sorry, it’s not to scale because of space limitations.

The square curriculum doesn’t feel quite right, either. The only way I know to make this problem tractable is to look at data.

In the late 1990’s, I was a standards weenie. I was fascinated by the variety from state to state. Because I didn’t have a girlfriend (and ostensibly didn’t want one, either), I would read state standards documents for fun. At the time Schmidt coined his phrase, Florida had more than 80 standards in each grade, and Utah subjected students to over 130 standards each year. As I recall, the average state had more than 100 standards at each grade level.

Today, Common Core represents a significant reduction in the number of standards. There are approximately 30 standards per grade for K‑8, and closer to 40 standards per course in high school.

Which means that if the curriculum used to be a mile wide, then the current curriculum is closer to ⅓ × 5,280 = 1,760 feet wide.

But if it’s ⅓ as wide, then it needs to be 3 times as deep. Which means the current curriculum is 1,760 feet wide by 3 inches deep, so it looks something like this:

1760ft_by_3in.png

Doesn’t feel like much of an improvement, does it? And the phrase “3 inches deep” doesn’t inspire confidence that the curriculum now has the depth it needs.

So, I give up. I don’t know what the proper dimensions ought to be. I just know that Schmidt’s phrase was hyperbole for dramatic effect, and it worked.

What do you think are the proper dimensions of the math curriculum?

Here’s a puzzle about width and depth:

How much dirt is in a hole that measures 4¾ feet × 5¼ feet?

And I know a joke about width, but you need to be able to read CSS:

.yomama {
width: 99999999px;
}

 

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3 Questions to Determine if You’re a Math Geek Math of the Rundetaarn

3 Comments Add your own

  • 1. Chris Smith  |  August 4, 2016 at 4:22 am

    Ha ha. I love the way your mind works Patrick!
    There’s no dirt in a hole, however big it is of course🙂

    Reply
    • 2. xander  |  August 4, 2016 at 12:20 pm

      Depends on the material that the hole is in, right? Like, you could take a large block of concrete, take a jackhammer to it, then fill the resulting hole with dirt. There would still be a hole in the concrete, and it would be full of dirt.

      So… uh… define “hole”?

      Reply
      • 3. venneblock  |  August 8, 2016 at 5:01 pm

        My first thought to your question was NC-17, Xander, so I’ll keep it to myself.

        My second thought was, a “hole” is a removable discontinuity in the graph of a function. But that doesn’t really apply here.

        My third and final thought was, a “hole” is an empty space with nothing in it. Google says similarly, “a hollow place in a solid body or surface.” Let’s go with that one, lest the joke be entirely lost.

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The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

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