Why Feelings Matter to Data Literacy: Understanding The 20 in 20% Chance

What is Data Literacy?

“Data literacy” is a buzzword in contemporary education, and refers to our ability to use numbers (particularly statistics) to make good decisions. We often assume that because numbers are objective and feelings are not, we can best achieve rational outcomes by disregarding feelings and intuition entirely. But in this post, I want to convince you that emotion and intuition can be features not bugs in our mathematical thinking.

To begin, imagine that you are planning on walking to the nearby community pool. You check the weather forecast and it says, “20% chance of rain.” In light of this information, do you go to the pool? If you’re like me, you probably acknowledge that in this case, it seems like a mild risk, and therefore choose to go. But what exactly is happening here? Neither you nor the weather forecaster can see into the future or actively shape future weather conditions. So how exactly are you evaluating risk in this situation?

The Context of Numbers

To answer that question, let’s ask another question: what does 20% mean, in this context?

Since none of us know what the future holds, this number must be telling us about something we do know something about, namely our past and present. When we say there is a “20% chance of rain,” what we are really saying is that “Given our historical records of past weather conditions, in 20 cases out of 100 when the weather conditions were similar, it rained.” 20 times out of 100 times is a relatively small number, and getting caught in the rain is not the end of the world. So even though we’re still only guessing at what might happen, we feel pretty confident about going to the pool, and reasonably so. Notice that in this example, we are deciding what goals or desires we care about, and deciding what outcomes we can live with, meaning that we are not simply thinking abstractly but are involving our whole selves in our deliberation, emotions and intuition included.

The Factor of Risk

Now let’s consider another hypothetical: flying on an airplane. If I told you there is a 20% chance that the plane you’re about to board will crash, would you still choose to get on the plane? The first thing you should be wondering here is how I arrived at the 20% estimation. Remember that I can’t see the future so 20% can’t be based on insight about what will happen. Is my number rooted in studying past crashes? Are records of plane crashes really the same kind of thing as records of weather conditions? Is this prediction based on the airline, the kind of aircraft, the weather conditions while flying, the length of the flight? In asking these questions, I am trying to sow doubt; more precisely, I am trying to undercut your trust in my prediction, your feeling that this prediction is credible and weighty. In assessing my claim, intuition should be playing an important role here, in suggesting to you whether or not you should be content to accept my claim at face value. To the extent that your intuition is sharply attuned, your ability to reason well will actually be strengthened, and you will be motivated to analyze my claims and the evidence or lack thereof behind those claims.

In almost every instance, our intuition (and subconscious reactions) is faster than conscious reasoning. And in situations where we need to act quickly and decisively, the power of intuition can literally be life-saving. Nevertheless, feelings are not always helpful guides, and just as we need our emotions to help shape our reasoning, we also need our reasoning to shape our emotions. To see this in action, let’s assume that the 20% estimation for plane crashing is reasonable enough for you to use in your decision-making. You could say to yourself, “80 times out of 100, the plane makes it to its destination just fine. 80 is a large number. I feel comfortable.” But of course, given how ratios work, it’s equally true to conceive of this information as stating that “in 1 out of every 5 times, the plane crashes.” The point here is that I’ve just said the same thing two different ways, but I suspect it feels different. Any skillful rhetorician knows that saying 1 in 5 results in a very different feeling than saying 20 times out of 100, and if you don’t interrogate your immediate reaction when you read that rhetorician, you can be misled or even deceived.

Consider that the numbers in both hypotheticals are exactly the same, and yet most of us are much more likely to risk the negative outcome in the pool example than the plane example. Why? To answer that “why” question requires something more than numbers. Numbers can tell you about probable outcomes, but numbers alone cannot tell you what you should value, nor can numbers tell you what risks are worth tolerating or what outcomes justify greater or fewer amounts of risk. And that means that we will always need to combine our number-sense and mathematical thinking with other sources of wisdom and knowledge if we are going to make good choices.

Helpful Questions to Ask

Here are a few questions to ask when you encounter “20% chance of” examples in your everyday reading or decision-making. These are also great questions to have your students talk through as they work through word problems or engage in research for papers:

1) How do I feel about the numbers I am seeing?
2) Do I know why I am feeling the way that I am feeling? / Why am I feeling this way?
3) Do I think I have compelling reasons to feel what I am feeling?
4) Is this an instance where my feelings are helping me achieve clarity or an instance in which they are making it more difficult to think clearly?

Recommended Reading

This approach to data literacy accords well with an approach to math education entitled Culturally Responsive Mathematics Teaching. CRMT asks us to reject the image of students that see them as blank slates waiting to be filled with facts and answers and to instead affirm students as explorers who are active in their own learning.

Blog post: The Importance of Improving Math Culture

How do we cultivate data literacy in students? Alex Edmans considers this very question in his TED TALK.

Blog post: Building Data Literacy [TED Talk]