Our culture looks on inability to read as a grave disability, but treats inability to do arithmetic as a minor weakness—something people admit without embarrassment and even laugh at. This doesn’t show causality, but as Jo Craven McGinty writes in her June 11, 2021 Wall Street Journal article “What Are the Odds? Even Experts Get Tripped Up by Probabilities,”

According to the research of Ellen Peters, an expert in decision making at the University of Oregon and author of “Innumeracy in the Wild,” the lack of skill can have consequences for your wallet and your health. People who are less numerate adopt fewer healthy behaviors; they are 40% more likely to have a chronic disease; they end up in the hospital or emergency room more often; and they take 20% more prescription drugs, but are less able to follow complex health regimens.

Our culture pays even less attention to statistical illiteracy than it does to general innumeracy. Part of the problem is that the traditional math curriculum hasn’t changed in a long time, and has its roots before the rise of modern statistics. We should be integrating a little bit about probabilities into the math curriculum even in grade school. And at the advanced high school level, my view is that AP Statistics is more important than AP Calculus. My son took that advice, and never regretted it as he went on to graduate Phi Beta Kappa in Economics at Ohio State University.

A lot needs to be done to help people understand probabilities better—especially small probabilities. Here is an example of the sort of thing that might help, from Jo Craven McGinty’s article:

Dr. Anagnostopoulos, who has helped develop a probability-based dice game called Borel, offered this example.

“Let’s assume that the risk for a certain group of people was that 1 in 50,000 would get a clot after having the vaccine,” he said. “If instead you were told you need to roll six dice and get all of them to be a one, would it be easier for you to make a decision?”

The odds of simultaneously rolling six ones, he said, are also 1 in 50,000. 

People’s lack of understanding of probabilities is an important issue for “Cognitive Economics.” Let me mention three things of interest for economics research:

1. In Behavioral Economics, it is always important to know whether what people say that violates the standard axioms is due to nonstandard quirks of their genuine preferences or to difficulties in understanding things cognitively—which might be accompanied by standard preferences. (It matters for Normative Behavioral Economics, for example.) I have noticed that a large fraction of the evidence against expected utility theory involves choices with small probabilities that people may not understand. I consider it an important agenda to reexamine the evidence and isolate what evidence against expected utility theory remains when looking only at choices that had a 50/50 probability. I don’t trust the typical person to intuitively understand any probability more complex than a 50/50 probability. (Talking about rolling six dice and getting six ones could help, but I still worry about people’s level of understanding.)

2. My University of Michigan colleague Bob Willis found that, in the Health and Retirement Study, a simple index based on how often someone rounds a probability they are asked for to 0, 50% or 100% can predict many things, including their portfolio choices. Someone’s level of probabilistic sophistication predicts a lot!

3. For someone (or some team) with the right qualifications who is willing to do a very ambitious survey experiment, I could see myself collaborating on this:

   • There is a way to make correctly reporting probabilities incentive-compatible.

   • Using true/false quiz questions for which an experimental subject reports probabilities that they got it right, it should be possible to train them to report probabilities more accurately.

   • Randomizing this intervention, one could then look at what the effects of this probability training were:

     • effects on survey responses (say being more informative about important probabilities in their life)

     • effects on how they play experimental games

     • effects on their real life (as judged by a follow-up survey)

   • I think it would be possible to do all of this on MTurk

   • It would require some nontrivial programming.

Math education in general needs a lot more attention. And within math education, early statistical education especially needs a lot more attention. If you are aware of good things for statistical education on free websites, please let us know in the comment section!

Other Posts about Learning Math and Doing Math

I wrote a follow-up column "How to Turn Every Child into a "Math Person" that gives links to some of the reactions to "There's One Key Difference Between Kids Who Excel at Math and Those Who Don't" and many resources for math learning. Here are some links to posts on math learning that didn't make it into that column:

• Math Camp in a Barn

• Fields Medal Winner Maryam Mirzakhani's Slow-Cooked Math

• Barbara Oakley: How We Should Be Teaching Math

• Jessica Lahey: Teaching Math to People Who Think They Hate It

• My Advice to Qatar: Make Math Education a Research Grand Challenge

• Laura Overdeck: Math for Pleasure

• Jethra Spector: Using Miles and Noah's Math Column in the Classroom

• Warren Henning: A Software Engineer’s Adventures In Learning Mathematics (link)

• Laura Overdeck: Street Math

• 21 GIFs That Explain Mathematical Concepts | IFLScience (link)

• Muhammed Chaudhry: College Success Starts in Math Class (link)

• Evidence that Bedtime Math Boosts Kids’ Math Performance

• Examining the Statistics in “Math at Home Adds Up to Achievement in School” by Talia Berkowitz, Marjorie Schaeffer, Erin Maloney, Lori Peterson, Courtney Gregor, Susan Levine and Sian Beilock

• Gabrielle Emanuel: Houman Harouni's New Book on the History of Math Education (link)

• Jenny Anderson: Teaching Kids Philosophy Makes Them Smarter in Math and English (link)

• Jenny Anderson: The best way to learn math is to learn how to fail productively (link)

• Calculus is Hard. Women Are More Likely to Think That Means They’re Not Smart Enough for Science, Technology, Engineering and Math

• A Mathematician Has Created a Teaching Method That’s Proving There’s No Such Thing as a Bad Math Student (link)

• You, Too, Are a Math Person; When Race Comes Into the Picture, That Has to Be Reiterated

• Math Learning for Kids Who Have a Tough Time

• Jo Boaler and Lang Chen: Why Kids Should Use Their Fingers in Math Class

• Gabriela D'Souza on Failure in Learning Math

• Why Thinking Geometrically and Graphically is Such a Powerful Way to Do Math

• Preparing the Ground for Mathematical Creativity

Also, here are some Twitter discussions on math learning:

• Genes vs. Hard Work in Learning Math

• Noah Smith's Tweetstorm on Making Everyone a 'Math Person'

• The Vicious Self-Fulfilling Prophecy That You Can't Do Math

• Tweets about How to Turn Every Child into a "Math Person"

Finally, on learning more generally, don’t miss:

• The Most Effective Memory Methods are Difficult—and That's Why They Work