Posts tagged ‘curriculum’

How Wide and How Deep?

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;
}

 

August 4, 2016 at 4:11 am 3 comments

Why Did Vi Hart Go to Khan Academy?

I love Vi Hart. And with over 300,000 subscribers and 25 million views on her YouTube channel, I’m clearly not alone.

Vi Hart - WikipediaBut perhaps you don’t know who she is. Maybe you’ve been living under a rock. Maybe you’re still using dial-up. Or maybe you’ve just been posing as a mathy folk, only visiting this blog because you think the author is hot. (Of course, you’d be correct in your assessment, but you shouldn’t let hot authors guide your tour through the blogosphere.)

If you don’t know who Vi Hart is, you can check out her Binary Trees video below (from her now famous Doodling in Math Class series).

Pretty awesome, huh?

In the video, she makes the following statement:

…if the [math] curriculum wasn’t so appalling and the teaching methods weren’t so atrocious, you wouldn’t have to entertain yourself with these stories and games.

She also implies that many math classes are

…fuzzy, unfocused, and altogether not very good.

Some educators don’t like these videos. Some don’t like that a brash, young woman is criticizing what they do and how they do it. Some find her statements offensive.

Not me.

I think she’s spot on.

Too many math classrooms still look like the math classrooms of yesteryear, devoid of excitement and technology and filled with endless hours of meaningless practice.

But here’s where I have trouble. On the About Vi page of her site, she says:

I am now a full-time mathemusician at Khan Academy! It’s pretty exciting.

If she is truly opposed to appalling curriculum, why would she work for a company that creates the video version of a 1950’s textbook?

Maybe I’m being too harsh. But I don’t think so. Though she now creates recreational math videos for Khan Academy that are awesome, the vast majority of videos on the site are nothing more than math lectures of topics that probably should have been removed from the curriculum years ago. When I asked a colleague his thoughts, he had this to say:

Vi’s videos show such polish and cleverness, while Khan’s were so obviously made by someone who just took an exercise from a textbook and sat down at a computer and improvised. About the only thing [Khan Academy] has going for it is that it’s free. I suppose it can have some good use in getting kids an opportunity to learn and practice skills they need, but having them practice skills for no particularly good reason… it’s just reinforcing everything that’s wrong with math education.

In her Binary Trees video, Vi Hart makes fun of the boring presentation of exponential functions that typically occurs in math classes. Yet the Khan Academy video Exponential Growth Functions uses the same examples and “atrocious teaching methods” that would be found in many of the math classes that are “fuzzy, unfocused, and altogether not very good.”

So, what’s up, Vi? How can you rail against bad teaching but then go to work for a place that delivers bad teaching in spades? Your work is amazing, and you had such an opportunity. I hope your intent is to make change from within rather than assimilate.

How do you feel about Vi Hart’s move to Khan Academy? And what do you think about Khan Academy in general?

February 19, 2013 at 2:55 pm 24 comments


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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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