I have an idea for a course that’d be appropriate for high school or college. The basic idea is to try to distill and bring together a set of knowledge, skills, and habits that allow people to think critically about quantitative information.
I’d call this course Quantitative Skepticism, which I think captures the sense of what I’m talking about pretty well, although it isn’t very catchy. I’d be tempted to call it Calibrating your Bullshit-o-meter, but I don’t think that would fly with many parents.
Anyone reasonably interested in their community, nation or the world is going to have to come to terms with numbers.
Facts, Questions, Claims
We all need to understand quantitative facts, like Facebook has 500 million users, which only make sense in how they relate to other quantitative facts. Is that a lot for a website? For the world? There were 30,797 fatal crashes in 2009. Is driving safer than flying?
Quantitative Questions range from very personal, like “how much to I need to save to be able to afford a vacation next year?” to big, world-changing questions like, “how much would it cost to eliminate world hunger?”
Lastly, we all need to be able to evaluate quantitative claims. This affects who you vote for, “this new law will create 5,000 new jobs in the US,” and where you put your money, “buying a new refrigerator could save you 10% on your electricity bill.”
Estimation
At the core of the course would be what physicists sometimes call “Fermi Questions,” after Enrico Fermi who used them extensively in his teaching at the University of Chicago to train people to think quantitatively. These are estimation questions which ask you to find a route to an unknown quantity by considering things you do know and the relationships between them.
The classic example is “how many piano tuners are there in New York City?” And, you work your way there by thinking about how many people live in NYC, what proportion of them have pianos, how often they need to be tuned, etc to get some idea of the demand for piano tuning. Then you think about how many pianos a tuner can do in a day, and multiply out all your estimates to get the final answer. This interesting thing is the process: what starting facts are helpful, and how to you form a logical chain of connections between them and your question. Maybe in the age of Google, you can just look this one up by searching the business listings, so we’d need some modern examples.
At its core, this involves
- Core numbers you need to know or be able to find. Understanding what kinds of things are most useful as starting points is the key thing to teach in the course: populations, physical constants, metrics at the community, national, or world level.
- Relationships between quantitative facts. There are main types of relationships: conversions and proportions. Conversions are things like how many people are there in an average household? Proportions are fractions of populations or probabilities, like what fraction of an average person’s income is spent on food?
- Sources and reliability. Where do you get basic facts from and how do you know how good your sources are. What is the uncertainty in your base facts and relationships?
Connections
There would be really great opportunities to tie a course like this to both STEM and humanities.
The basic mathematics of estimation are often no more advanced than multiplication, but there are plenty of ways to tie it in to other topics like calculus, statistics and geometry. Science ties nicely into relationships via physical or biological laws and core numbers.
Critical reading of quantitative claims dovetails nicely into economics, politics, history and journalism. These fields are a great source of interesting questions to investigate as well.