*The Daily Show* gave us a twofer last night. Neither one of these is any kind of lengthy inquiry. They’re interesting examples of math used to make sense of political debate (in one case) and distort it (in the other).

In the first case, you have this exchange:

Romney: Across the nation, over twenty millions Americans still can’t find a job or have given up looking. In 1985 I helped found a company. At first we had 10 employees. Today there are hundreds.

Stewart: You created hundreds of jobs in just twenty-six years? At that rate you’ll have the whole country employed in â€” hold on â€” 4,000,000 years.

In the second case you have Stewart pretty well embarrassing himself with this wacky scaling:

Both clips would have stalled out at “interesting” but I censored out their interest â€” bleeping out Stewart’s (obv. imprecise) calculation of “4,000,000 years” in the first; blurring out the 2.9% in the second â€” making them perplexing instead.

**The Goods [Romney]**

Download the full archive [10.6 MB], including:

- Question Video
- Answer Video

**The Goods [Health Care]**

Download the full archive [15.3 MB], including:

- Question Video
- Question Photo
- Answer Video

Many thanks to my flinty-eyed reader Joshua Schmidt for making sure I didn’t miss last night’s episode.

**2011 April 16**: As of this writing, Bain Capital has 375 employees, which is completely germane to the problem. Huge ups to Emily’s resourcefulness.

## 16 Comments

## Benji

April 14, 2011 - 7:36 am -I watched this episode last night and thought about both of those problems. The one that hurt the most was that graphic. C’mon John. C’mon buddy. He might as well have put two clowns holding the percents on the screen.

## Jason Dyer

April 14, 2011 - 7:49 am -One general issue with using bleeping for these things is related to the standard-student objection to word problems about Joe’s age compared to Tom’s: why don’t I just ask Joe? In other words, a piece of information we’d know if this information is encountered in reality was removed, and it feels artificial.

Here if encountering one of these videos normally we’d hear the entire thing; there would be no need to recreate information. Since Stewart’s number in the first clip is wrong no matter how I calculate it (at least presuming “hundreds” to be >=200), I think leaving the bleep out and asking if his answer is accurate is a more interesting and natural question.

I’d use the unedited health care clip for the same reason. I’d start with feeling out if anyone senses something is wrong, and only work on recalculating the percent of the second bar after they decide it’s worth pursuing. Blurring the image out forces the question on them.

## Corey

April 14, 2011 - 9:49 am -I love these questions and as a Chemistry teacher they are great because they help the students get comfortable with large numbers. . .

The Household survey that contributes to the unemployment report recently listed 13.5 million as unemployed.

It would be good to look at a range of possible answers to how many jobs Romney’s company did make over 25 years. All in all, looking at those estimates, on the low side (just over 200) Stewart’s within one order of magnitude. Which would satisfy Fermi.

Another good question might be: How many jobs would of Romney created if it would take 4 million years to make 13.5million jobs? Bonus points if they take population growth estimates into it.

## Joshua Schmidt

April 14, 2011 - 10:22 am -When I was working this out with my seniors, I had to agree with Jason. First of all, the Romney number is just wrong. No matter how we scaled it, 4 million just couldn’t be right at all. Secondly, the graph itself was one that students were trying to figure it out as soon as I put it on the board.

With problems like this, I feel very happy when students ask questions as soon as I put them on the board. I just started doing WCYDWT, but I am starting to feel the students willing to engage with any Math that’s on my screen. The next step in my opinion, is that they are willing to engage this type of Math when THEY see it in the real world. That’s my biggest hope.

## Matt McCrea

April 14, 2011 - 10:44 am -I’m with Jason on this one as well. An equally strong consequence of making them figure out if there’s something fishy with it is it starts to develop a self-checking sense in doing problems. I appreciate the ability to set bounds at the beginning of the problem, but there’s also something to having students be able to self-check their own answers for reasonableness.

## Dan Meyer

April 14, 2011 - 5:38 pm -I’ve gone back and forth on this one a bit lately and I’d appreciate it if you guys would press me some more.

First, the largest reason students hate the problem about Joe and Tom’s age isn’t that you could just ask Joe his age (though that

isirritating) it’s that the operation doesn’t follow naturally from the premise. Just like special right triangles don’t follow naturally from dog bandanas.Second, the reveal of the answer (or in this case “the answer”)

in the mediaitself is important. The students knows that the answer exists outside of the authority structure of the class â€” teacher, teacher’s edition, etc. The fact that the answercannot be messed withby the teacher is motivating and generative.Third, what are the implications of the uncensored approach? Consider an analogy to the ticket roll problem. Would you recommend here that I uncensor the image (removing the black box), show the students the answer, and encourage the students to check to make sure the answer on the label is correct? Kind of like watching a balloon deflate, I’d expect.

So do we take the reverse approach here on account of the

incorrectnessof the answers? (The answer for the ticket roll being correct.) If you’d censor the correct answers (the ticket roll) and uncensor the incorrect answers (Stewart’s graphs), I’m not sure you’d get this outcome you expect â€” where students develop a sense of incorrectness in the media. You’re signaling the incorrectness in several ways, not the least of which is you’re playing a clip that has a very obvious mathematical moment in it. It isn’t the same as a student at home watching the entire show.Walk me through it a little more.

## Joshua Schmidt

April 14, 2011 - 7:03 pm -You know I hadn’t thought about the idea of this being in the context of an entire curriculum. Simply put, if you reveal this answer, but you don’t reveal the previous answers gives away the fact that the answer itself is incorrect (or mostly incorrect in the Romney example). However, there is a certain level of intrigue in proving authority figures wrong (teachers or John Stewart) that make students feel smart. Maybe I won’t get the desired outcome immediately, but I feel that the cost benefit analysis of boosting student ego is sometimes worth the loss of the authenticity of the creation of the math.

I think it’s interesting to talk about the “reveal” of the answer not being able to be messed with. To be honest, your teaching style totally discredits that. You have already messed with the video itself, you have been doing it for the entire year (depending when you do this video), by video editing. A video with a hidden reveal is altered, just like your jump shot videos are altered. If you leave the video as is, then the students are creating a answer to a question that they have to create. If you create the reveal, the students already know the question, they are only searching for an answer, which creates a more linear problem. However, you are absolutely correct in that this is NOT the same as a student who sits as home watching the entire show (which is what I am always hoping to emulate) where they would question in context. However, I don’t have any ideas on how to handle that currently.

## Jason Dyer

April 15, 2011 - 7:18 am -In the particular case of the Stewart clips you aren’t hiding the answer, even; you’re hiding the fact that the show got the wrong answer. To me the main interest in the clips (especially the second one for a stats class) is spotting there’s a problem in the first place, not in the mathematics.

Regarding the general idea of removing information: clearly the answer going to have to get left out in any problem. It’s just a matter of if the answer is a natural thing to remove in the context. The tickets don’t bother me (one could always take the label off if it was a problem) but adding a gap to an audio track does.

Perhaps a better comparison would be with your Office video involving the bouncing cube. By stopping the video before the answer is revealed, you’re realistically placing the student in the scenario of being the character in the story in anticipation; that’s fine. If for some reason the answer was shown in the middle of the story and a blur was required, the immersion element is removed and the feel of realism is broken.

In essence you’re trying to create a storytelling-type anticipation among the students based on either “what just happened” or “what will happen next”? Forming a gap in the middle with a bleep just strikes me as an artificial way of doing it (at least I, personally, have no anticipation of ‘what was in the bleep?’ the same way some other WCYDWTs affect me).

## Dan Meyer

April 16, 2011 - 7:38 am -You still get that WTF moment, though. You get it after the students have worked out the answer, justified their work to each other, and they’re ready for catharsis … that doesn’t come. You’re flipping the confidence of

the entire classaround on itself. You’re aren’t just making an appeal to the few students who spotted the discrepancy in advance.Point being, with my approach you get both. You get the guessing, the intuition. You get the extra motivation (however slight) to figure out what’s concealed. And then you get the WTF moment, only it’s distributed across the entire class.

I agree. This is a separate, lower class of WCYDWT problem, meant only to upgrade this textbook problem:

Which isn’t to say there aren’t better ways to upgrade it than others.

## Joshua Schmidt

April 16, 2011 - 11:24 am -I still am with Jason, I don’t have the anticipation of the answer to this problem the way that I did before. However, once you get the students to fill out their answer, you get a really good argument on what defines “hundreds”. It’s obvious Stewart’s answer is exaggerated at the very least, but I have a group of students who would rather prove an expert wrong than simply get their own answer correct.

Plus, I love the moment to play the entire clip and say, “What do you think?” It’s better than me giving them the question. While some other classrooms have students who are ready to create their own questions with WCYDWT, mine are not. We are creative infants, and I like the baby steps of this problem.

## Emily VA

April 16, 2011 - 1:39 pm -(1) When I used the State of the Union problem (https://blog.mrmeyer.com/?p=9258) for a lesson, I did what Jason and Joshua suggested — gave the students the real thing, unedited, and asked them to think through what might be suspicious about it. It was interesting to hear them think about a host of interesting questions you could ask — for starters, you could think about countries other than the US and China in that example — before narrowing it down to the one I wanted them to focus on. I think both approaches have their place, depending on which skills you’re working on that day — skeptical consumption of media and prioritization of questions vs. specific mathematical reasoning for a given question.

(2) Does it add anything to actual look up what the current employment figures for Romney’s company are? (Bain Capital: 375 according to their website http://www.baincapital.com/Team/Default.aspx )

## Dan Meyer

April 16, 2011 - 7:17 pm -Yes! Big winner!

## Jason Dyer

April 16, 2011 - 7:43 pm -Point being, with my approach you get both. You get the guessing, the intuition. You get the extra motivation (however slight) to figure out whatâ€™s concealed. And then you get the WTF moment, only itâ€™s distributed across the entire class.I get you. I just would rather trade off for the extra learning objective of students spotting errors in a natural scenario (which I feel is one of the primary reasons for all this “math education” stuff).

I’m also with Joshua in that the bonus multiplier for my students of thumbing it at The Man is high. I realize this may depend on your school environment.

## Joshua Schmidt

April 16, 2011 - 8:57 pm -Emily, great find! I think that gives an answer to how far off the estimate is. Students are always more interested when their is a “right” answer. Although I as a Math teacher don’t always value one answer over another, the students always want a correct assumption.

## Gary D

February 1, 2012 - 7:11 am -Revisited these problems today. Romney’s still relevant (for a little while at least!)

An extension on this would be to compare linear and exponential growth. Assuming Bain were increasing employees at a linear rate, how long would it take to employ 20 million…

The current company would have to havegrown from 10 to 130 employees in 26 years, for an increase of 5 employees per year for linear growth to employ 20 million in 4 million years. Not quite hundreds, but maybe that’s what the Daily Show math people were thinking…

## Gary D

February 1, 2012 - 7:14 am -Oops – should be an increase of 130 employees, growing from 10 to 140.

Measure twice, post once.