My life is split into 2 parts. One side of my life is spent at home and on the computer. I write and I read a lot. My social media feed and my social life is made up of mainly educated folks. The other part of my life is spent as a math teacher. I teach geometry in an urban high school.
When I’m around friends and writing on the internet, I take it for granted that everyone will understand me when I’m talking about probabilities and basic numeracy. But when I’m at school, I’m frequently reminded that many people do not have a strong understanding of basic mathematics.
Even at 16, many students still have trouble understanding the difference between fractions, decimals, and percents. I wouldn’t be surprised if many people did not know how to use a mortality rate to find the number of people who will die in a particular population (e.g. if we have a population of 150 people and a mortality rate of 4% then how many people die?).
We are in a very weird situation right now where the only way you can understand the pandemic — and all of the intricacies of the largely statistical arguments about it — is if you have a strong understanding of math. Unfortunately, when we actually look at American numeracy, we find that a large portion of people are unlikely to grasp what’s going on. As measured by the OECD, US adults have “very poor [skills] in numeracy”.
“ In numeracy, only 8% of adults score at Level 4/5, below the average of 13%. By contrast, 19% of adults in Japan and Finland achieve the highest levels of proficiency. At the other end of the performance spectrum, nearly one in three adults in the United States scores below Level 2 in numeracy. The average score in the United States (253 points, corresponding to Level 2) is higher than that in only two comparison countries (Italy and Spain) and similar to that in France. One in four adults (26%) scores at Level 3 and one in three adults (33%) scores at Level 2.”
To put these levels in context, being at level 2 requires the basic manipulation of whole numbers, common decimals, and simple statistics. This is arguably the lowest level of numeracy you’d need to make informed decisions about the pandemic. If “nearly one in three Americans” are below that level and another 35% are at that level, well over 50% of Americans may be educationally unprepared to understand Coronavirus.
I think it’s important to note how unprecedented this situation is.
Think back on the major disasters that Americans have dealt with in the last 100 years. Consider what it would actually take to understand the situations. We haven’t had a true American pandemic since 1918. The primary catastrophes are natural disasters, wars, terrorism, and economic crashes. In all of those situations, someone’s decision does not necessarily need to be informed by any numbers. They may be told how many folks have died and they may be told who the enemy is. But the number of available actions is pretty limited and their decisions are unlikely to require a high-level of numeracy.
Now we have Coronavirus. A lot of us assume that we understand basic probability. But even small mathematical mistakes can have big impacts on how we think about the risk.
Let’s take an important example: “is coronavirus just a bad flu?” Ask the average American, how could we evaluate this claim? One hopeful response would be to compare mortality/death rates. That’d be a good first step, but there are many other important factors that would be required to evaluate the claim well. A lot of these factors like R-nought, recovery time,and doubling time all require some background understanding of exponential numbers that most people are unlikely to know.
But for the sake of the argument, let’s pretend that the only thing you’d need is mortality rate. What math would you need to understand these claims and what common mistakes would people make?
The mortality rate of the seasonal flu is .1% and the estimates for the mortality rate of COVID-19 range from .5 to 4%. In order to compare mortality rates we would just have to divide the COVID-19 rates by seasonal flu rates to find that Coronavirus death rates range from 5-times-worse-than-the-flu to 40-times-worse-than-the-flu. But it’s not clear how to translate that into specific actions, and many people make the mistake of switching the dividing numbers to find that COVID-19 is actually safer than the flu (.1/.5 = .2, “oh it’s .2% better”)
The trouble is that rates are communicated in so many different ways and many people make common evaluation mistakes. Take 1%. We could communicate that as 1/100, .01, 1 in 100, or, the original, 1%. But which one would we use if we wanted to find the actual number of deaths?
Say we wanted to find the number of deaths in country of 327 million. To make it more realistic, let’s also factor in the infection rate. If 40% of people get the infection with a 4% mortality rate, then how many Americans will die? First owe have to convert the percents to decimals. Most people forget this and get radically incorrect numbers. The answer for total deaths is 327000000 * .4 * .04 = 5232000. Even if you avoided all the common mistakes and got to that number (which is a vastly oversimplified overestimate), it’s still difficult for a lot of folks to understand how bad that actually is.
On top of all of this, how do I understand all of the well meaning (but, frankly, confusing) graphs that are being passed around the internet?
To sum it up, it is very difficult to understand the true risks of the Coronavirus. It is even harder to make an informed decision about how to react when so many of us are under constant pressure to stay healthy, stay fed, and still make rent during the beginning of a possible recession. On top of all this, US distrust of the media is at an all-time high, and there’s been a lot of misinformation making its way through many major outlets. It’s not enough for us to just assume that citizens will fall back on the “good” advice of the media.
We still need citizens who understand the math well enough to assess risk independently. I don’t know what that means for our education system. It’s unbelievably hard to improve it. But this ought to motivate us even more to possibly reform the math curriculum in ways that maximizes our collective understanding of probability, risk, and data.