NOTE: This is one of a series of ten blog posts on cognitive biases that have applications in education.
Over the last year I have become extremely interested in learning about how aspects of behavioral economics and psychology affect our ability to be effective educators. Specifically, humans’ ability to make sense of the world is sometimes inhibited by quirks, called cognitive biases, that may prevent us from making the choices we would like. I want to share what I’ve learned using a series of blog posts that describe a cognitive bias and the implications it has in terms of working with teachers and students.
I’ll begin with one of the most common biases in education…
Throughout my career pluralistic ignorance has been a problem for me. Graduating from UCLA with a degree in mathematics, I did not yet realize how superficially I understood mathematics. Early in my teaching career I received professional development that helped me make connections between concepts and think more deeply. I came to realize that I had been more of a math robot who could solve problems yet didn’t really understand how or why it worked. I thought that perhaps I was the only one who felt that way and alternated between feeling too embarrassed to admit it and confused as to whether understanding why math worked even mattered. What I certainly didn’t realize until some time later was that almost every teacher feels insecure about something they teach. Keeping my thoughts and fears to myself wasn’t going to help anybody.
For example, dividing fractions is a math concept people often have a superficial procedural understanding of. Most frequently, teachers instruct students to change the division to multiplication and use the reciprocal of the fraction on the right, often referred to as “invert and multiply.” How many can explain why invert and multiply works or provide a context for why 2/3 divided by 1/6 is 4? I certainly couldn’t when I had graduated from college and it didn’t even occur to me that I should be able to. However, now that I do understand, I realize how it strengthens my ability to make sense of mathematics. The reality is that many teachers have similar gaps in their understandings, yet they don’t get help. There are a lot of reasons for this, but one may be that they don’t want to be the one to tell the emperor about his clothes, just in case they are the only one who can’t see the clothing.
When you work with teachers, lead by example and be upfront about areas where you have weaknesses. I’ll go first. I was shocked when I learned, after graduating from college, that there was a reason for the variety of area and volume formulas. It may sound like I’m joking, but it never occurred to me that there was a reason for them. It was as if I believed that a magical math fairy came and bestowed formulas upon each shape. Then one day someone showed me that you can find the formula for the surface area of a cylinder by taking a regular piece of paper and turning it into a tube. It blew my mind to see how simple it was: the tube has a circle on each end and a big rectangle (the tube unraveled) which has the dimensions of the height by the circumference. Hence, the formula is simply the area of the two circles plus the rectangle. I don’t know if I was more surprised by the fact that there was a reason for the formula or that I was a grown man by the time I realized it. Again, you are not the only one who has weaknesses, and you are never going to make progress without acknowledging that and working to improve them. Your colleagues will appreciate you being brave and taking the first step towards making this a conversation people feel more comfortable having.
Implications for working with students
What are we really expecting from students when we ask them, “Does everyone understand?” or “Any questions?” There were probably many times I asked those questions where my students would have loved to collectively state, “Yeah, actually we are totally lost and need you to explain that to us in another way.” The reality though is that few of the students want to be the one to raise their hand and state that they don’t understand. They likely view themselves in the minority, even when they are not. Instances of pluralistic ignorance such as this impede learning.
To address this concern, consider being brave again and take the lead. State up front that there are going to be times in this class that despite all you are trying to do to make learning easy for students, they are still going to be confused. Tell them that you would rather them learn than have everyone pretend that everything is alright. I remember my high school science teacher who did this by telling us that whenever we have a question, at least a few other people probably have that same question, so you are helping others when you ask questions.
Keep in mind an important test that will happen in this process. Students may feel liberated by this policy and ask more questions than you are used to. Be careful as your emotions and body language may convey feelings that you may not realize. If you ask for questions but show frustration, you won’t get very far.
What other examples of pluralistic ignorance have you seen in education? What other strategies are there for dealing with this?