Humility (and schemas)


Author: Chad Topaz

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In the Introduction, I accused you of sucking. Your cognitive behavioral therapist, who is trying to help you avoid patterns of negative thinking, is very angry at me for saying this. I apologize. I did not mean it, and I should have been more careful with my language. What I meant to say is: you MIGHT suck. Or to frame it more diplomatically, and more positively, the foundational step to being a good teacher is to be open to the idea that you, as a teacher, have something to learn about teaching.

Me telling you that you might suck isn’t personal. As I have already mentioned, I might suck, too. Often, I do.

I’m writing this non-book for a wide range of college level math instructors, from graduate students to senior faculty. By the way, within this range, I myself am somewhere in the middle. At the time I’m writing this chapter, it’s 2015 and I am 40 years old. I first served as a teaching assistant in, I believe, 1998. I first served as a primary course instructor in 2002. I entered a tenure-stream position in 2007. If we count back from my first TA-ship, I’ve been teaching for about 17 years, so I classify myself as mid-career. The main point of this chapter is that regardless of your level of experience, you likely have something you can learn about teaching. I am not excluded from this statement.

To get our discussion going, watch this clip (below). It’s nine minutes long, but it’s worth it. “A Private Universe” was produced by the Harvard-Smithsonian Center for Astrophysics in 1987. In the video, you will see Harvard graduates asked (at their commencement, no less) what causes the change of seasons. They get it wrong. The narrator asks how it is that graduates with some of the best preparation in the world can answer this question incorrectly. I love this video because it demonstrates a key idea that we’ll discuss momentarily, and also because I find it amusing to make fun of Harvard (despite, or perhaps because of, having gone there). Later in the video, you’ll see some high school students for whom instruction on a particular topic has basically no effect on their understanding.

And now we come to some psychological science. Here is the crucial word: “schemas.” (Sort of like when Walter Brooke tells Dustin Hoffman “plastics” in The Graduate.)

We’re going to discuss schemas. In this discussion, whenever I refer to learners and learning, I ultimately want for you to picture YOURSELF (as a learner) and think about YOUR LEARNING (about how to teach). Undeniably, it is also useful to know about schemas because of the insight gained into your students. But for now, I intend for the focus to be on you.

I really like the the explanation of schemas in this classic and highly-cited paper, which itself includes a helpful lit review (if you are in to that sort of thing). Schemas, it says, are “both representations of knowledge and information-processing mechanisms.” If you are already bored, please let me translate. “Representations of knowledge” means that schemas are a bunch of objects or ideas connected by relationships, all in your head. In the world of physics, for example, a simple schema that a learner might have is “gravity is a force that makes things fall towards the Earth.” (I have purposely written something that has an element of truth for some situations, but is not the most general truth.) As for “information-processing mechanism,” this gets at the reason learners make schemas: they are labor-saving devices that make cognition easier. If we had to puzzle out every new experience or fact or decision that we were faced with, our brains would melt. Schemas reduce hard thought to automatic thought.

Though schemas can be useful and efficient, they can also be

  1. wrong, and
  2. hard to change.

When faced with information that contradicts a schema, people are more likely to reject the evidence than to change their schema. To get a better explanation than I could construct myself, I asked my brilliant friend from kindergarten who is a Ph.D.-wielding psychologist and also a ballerina. She said:

More than anything else, human beings want to make sense of the world. If this is taken as a given, it would follow that any explanation is better than no explanation. Also, humans tend to like things to be status quo, probably because for the most part it saves cognitive energy. When we are forced to change, we are forced to think about things in a more conscious, slow-moving way that utilizes more energy, and often adds anxiety or stress to our lives. Most humans really hate this. Put these two things together, and you get sometimes erroneous encoding that tends to stick around over time.

Here’s a concrete example: a study in physics education by Halloun and Hestenes that demonstrates the challenges of schemas. The authors assess students’ basic understanding of physical motion at the start of and at the end of an introductory physics course. As summarized in the abstract, “the student’s initial qualitative, common sense beliefs about motion and causes has a large effect on performance in physics, but conventional instruction induces only a small change in those beliefs.”

Now think about how the idea of schemas applies to you, as a teacher.

  1. Based upon all your life experiences of being taught by other people and teaching others, your brain has put together a picture of how teaching and learning works.
  2. Some aspects of this mental model might be very wrong.
  3. It might be very hard to change your mind about some of this.

To put this all a different way, many teachers teach based on instinct and experience. While I don’t discount those things, they are no substitute for an actual scientific understanding of how human learning works.

If you are an instructor who demands a scholarly approach from your students, you should demand the same thing of yourself in your teaching. Various scholarly fields have published  thousands of papers reporting on empirical studies of human learning: psychology, education studies, neuroscience, sociology, anthropology, and so on. To ignore the main messages of these is to willfully adopt an unscientific approach.

There is an Ig Nobel Prize-winning  paper called “Unskilled and unaware of it: How difficulties in recognizing one’s own incompetence lead to inflated self-assessments” by psychologists Dunning and Kruger. The effect they document is a “cognitive bias wherein unskilled individuals suffer from illusory superiority, mistakenly assessing their ability to be much higher than is accurate.” I urge you: as a teacher, don’t be an exemplar of the Dunning-Kruger effect. Instead, obey some at-this-point-trite-but-still-useful wisdom, as helpfully compiled here:

  • Confucius: “Real knowledge is to know the extent of one’s ignorance.”
  • Socrates: “I know that I know nothing.”
  • Bertrand Russell: “One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision.”
  • Charles Darwin: “Ignorance more frequently begets confidence than does knowledge.”
  • Shakespeare (As You Like It): “The Foole doth thinke he is wise, but the wiseman knowes himselfe to be a Foole.”

When it comes to knowledge, humility is powerful, and not only because a bunch of dead dudes said so rather eloquently. Humility is an active area of research in the field of psychology, and some studies demonstrate that humility can correlate with higher academic performance and higher job performance.

So this is the central plea of this chapter, and it’s advice that I endeavor to follow as well: Recognize your imperfection. Nonetheless, always strive to be a better teacher. Embrace the fact that experts in other fields spend their lives studying human learning, and have a compelling and empirical understanding of it. Listen to them, and work hard to adjust your schemas as necessary. Be humble.

2 Comments Add yours

  1. Trina says:

    This is awesome, my brilliant friend from kindergarten. 🙂


    1. Chad Topaz says:



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