A segment about the 2020 presidential election primaries on MSNBC News on March 5 caused a flood of comments on Twitter. Here is the tweet that brought the segment into the Twittersphere and started all the ruckus:
Both the guest, a member of the New York Times Editorial Board, and host Brian Williams failed to notice how absurd was the arithmetical claim being made.
If this is the first time you have seen this segment, it likely flew by too quickly to register. Here (right) is the original tweet that started it all.
Curious as to who put out the tweet, I checked her profile. (See below.) [Normally I anonymize tweets, even though they are public, but on this case the tweet was shown on live national television.] She starts out with the claim that she is bad at math. I have no idea whether she is or she isn’t. But that tweet does not show she is. It actually suggests she may be a better mathematical thinker than many – read on.
Many of the comments on Twitter lamented the poor arithmetical skills of the tweeter and the two media figures on the show. In fact, the story went well beyond Twitter. The next day, the Washington Post, no less, devoted an entire article to the gaffe.
The Big Lead took another swipe the same day, pointing out that the tweeter, Mekita Rivas, is a freelance writer and Washington Post contributor, and noting that the math disclaimer on her Twitter bio was a result of her oh-so-public gaffe.
But she was by no means alone. The error was repeated, or at least overlooked, by a whole host of smart media folk: Mara Gay, the New York Times editorial board member who brought it up in her on-camera conversation, the MSNBC graphics department, several producers, host Brian Williams himself, and likely more.
The episode is reminiscent of the numerical error made by a famous New York Times commentator that I wrote about in a post a few days ago (March 3). To be sure, both episodes highlight the clear need, in today’s data saturated and data-driven world, for all citizens to have a reasonably well developed number sense.
For this problem is not, as many critics of Ms Rivas claimed, that she cannot do basic arithmetic. I would not be surprised if she were no worse than most other people, and besides arithmetic skill became in-principle obsolete with the introduction of the electronic calculator in the 1960s, and in every practical sense became really obsolete when we entered an era where we all carry around an arithmetic powerhouse in our smartphone. [There is educational value from teaching basic arithmetic, but that is a separate issue.]
What is most definitely not obsolete, however, and is in fact, a crucial human skill in today’s world, is number sense. What was worrying about the whole Twitter–MSNBC episode is that none of those involved recognized instinctively that the claim in the original tweet was absurd.
The two follow-up news articles I just referred to delve into the absurdity of the error, which comes down to the difference between $1M+ and $1.52.
But this is where it gets interesting. What is it about the statement in the Rivas tweet that led a whole host of smart professionals to not see the error? What led them to not feel in their bones that the amount every American actually would receive from Bloomberg would be “something a bit north of a dollar-fifty” and not a sum “in excess of a million dollars.” This is not a question of calculating; it’s not poor arithmetic. It’s something else, and it’s far more dangerous. Doing arithmetic is something our iPhone can do, quickly, error-free, and with more numbers, and bigger numbers, than we computationally-puny humans can comfortably handle. Understanding numbers, on the other hand, is very much people stuff. Our devices understand nothing.
If a whole group of smart people are so quantitatively illiterate (and that’s what we are talking about) that they don’t instinctively see the Rivas error , how can we as a society make life-critical decisions such as assessing our personal risk in the coronavirus outbreak or the degree to which we should take a candidate’s climate change policies into consideration when deciding who to vote for.
This is why I, and many others in mathematics education, are putting such stress on the acquisition of number sense. Indeed, an article I wrote for the Huffington Post on January 1, 2017 carried the headline Number Sense: the most important mathematical concept in 21st Century K-12 education. I was not exaggerating.
Many of the videos and blogposts on (and referred to on) this website focus on number sense, and discuss how best to ensure no future citizen graduates from high school without adequate number sense. (The Common Core State Standards are designed to achieve that goal, though teaching practices often seem to miss that point, sometimes as a result of inappropriate administrative pressure coming from poorly informed politicians.)
What interested me in particular about the MSNBC example was the nature of the error. It’s similar to the example I discuss at the end of the first of the Blue Notebook videos on this site, in that the way the proposition is worded triggers learned arithmetic skills (more accurately, and appropriately derisive, “test-taking tricks”) that in general are reliable.
Here is the Rivas argument, spelled out:
1. FACT : Bloomberg spent $500 million on TV ads.
2. FACT: The US population is 327 million.
3. (FALSE) ARGUMENT: We are talking millions here. If you take the whole amount and divide it up among the population, everyone gets 500 divided by 327 (millions). Good heavens, that’s more than one million each!
Rivas is doing two smart things here – smart in the sense that, in general, they lead to the correct answer quickly with the least effort, which is what she (and you) likely needed to be able to do to pass timed math tests.
1. First, she says, everything is about millions, so we can forget those six zeros at the end of each number. [GOOD MOVE]
2. Then she says, we have to divide to see how much each person would get. That’s 500 divided by 327, which is around 1.5 (or at least more than 1). [GOOD MOVE]
3. Then finally she remembers everything is in millions. So it’s really $1.5M (or more than $1M). [EXCELLENT. SHE REMEMBERED THE SIMPLIFICATION AND PUT THE ZEROES BACK IN]
On its own, the idea behind each step is fine, indeed can be useful – in the right circumstances. But not, unfortunately, in this coupling! [I’m not saying she went through these steps consciously doing each one. Rather, she was surely applying a heuristic she had acquired with practice in order to pass math in school.]
The trouble is, if someone leaves school having mastered a bunch of heuristics to pass timed math tests – which is how many students get through math – but has not been taught how to think intelligently about numbers (and thereby develop number sense), then they are prone to be tripped up in this way.
Not convinced? Check out the example toward the end of that first Blue Notepad video. It’s a bit more subtle than the MSNBC example I am discussing here; in fact, more than half the people in every audience I have given that example to (under time pressure) get it wrong. The odds are, you would have too. But the overall message about math education is the same.
Ms. Rivas should take that disclaimer off her Twitter bio.
But maybe replace it by one that says, “I need to improve my number sense.” That’s a motto that – by my observation of the news media, social media, and society in general – would well serve the majority of people, including many who are good at “getting the right answer.”