Posts tagged ‘standards’

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:


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:


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

It’s Not About the Standards

Dear Indiana,

It’s not about the standards.

I’m very glad that you have abandoned the Common Core, “designed [your] own standards” and, according to Gov. Mike Pence, “done it in a way where we drew on educators, we drew on citizens, we drew on parents.” This sounds familiar. Where have I heard such rhetoric before? Oh, that’s right… the NGA and CCSSO sang the praises of a similar process when the Common Core standards were developed.

And I love what you’ve done with your new standards! Look at this gem from the proposed Indiana standards for Grade 6:

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

You radicals, you! What a deviation from the Common Core State Standards for Grade 6! To wit:

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

How dare those pundits who called your new standards nothing more than a “warmed-over version” of the Common Core! I don’t think that’s true at all. Rather, I think they are better described as a “still-warm version,” since you didn’t let Common Core’s body get cold before pilfering verbiage.

But there are differences, to be sure. Like with ratios, where you ask students to know the three notations of a/b, a:b, and a to b. Well, bully for you! Chart your own course! Spread your wings!

Personally, I cannot wait for the new Indiana standards to be passed on April 28, and your school districts can once again adjust their curriculum, and teachers can change their lesson plans, in preparation for the new standards. Won’t that be fun, just two years after they started adjusting curriculum and changing lesson plans to prepare for Common Core? Perhaps they’ll get to do it again in 2017, when the political winds shift and his constituents decide that Governor Pence needs a different job.

Indiana - Uncommonly HighAnd by the way, Governor Pence, I’d like to commend your cheeky use of the phrase “uncommonly high” to describe the new Indiana state standards. Bravo! What better way to trumpet your DOE’s good work than to sound like a Keebler elf at a NORML rally?

I cannot wait until that becomes the new state motto and starts appearing on license plates.

But I digress, so let me return to my point.

It’s not about the standards.

It’s not about whether students solve quadratic equations by plugging numbers into the quadratic formula or by completing the square. It’s not about whether students should graph quadratic functions with a calculator or by hand. It’s not even about whether or not students should learn about quadratics.

It’s about effective teaching and student learning.

It’s about a common discussion regarding what needs to happen in math education.

It’s about teachers from Wisconsin and California and Vermont and Alabama engaged in dialogue as professionals, in a community where their opinions matter and they are not merely enacting a pacing guide created to fulfill state mandates.

When I travel to New Orleans in a few weeks for the National Council of Teachers of Mathematics Annual Meeting, there’ll be conversations between educators from different states. And sure, some of those conversations will be about effective strategies and exceptional classroom activities. But most of them will be comparing the classroom ramifications of political decisions.

  • Oh, you get to teach math on a block schedule? That’s what our teachers wanted, but our administrators wouldn’t go for it.
  • I would LOVE to have a SMART Board in my class. But our school board voted for new football uniforms instead of more technology.
  • Well, maybe you thought it was good, but our district doesn’t teach adding fractions until Grade 7, so I’m not sure anything covered in this workshop will be relevant to me.

Don’t get me wrong, Hoosiers. I’m not mad at the state of Indiana. Hell, I love auto racing, Larry Bird, and corn. Instead, I’m frustrated at the state of education. How did we let things come to this?


Ed U. Kader

March 25, 2014 at 1:59 am Leave a comment

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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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