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Embracing confusion as a necessary part of learning (part 1)

April 22, 2011

The NYT has another one of its smorgasboard summaries of lots of recent research into brain science and education, and it’s definitely worth using up one of your 20 to read it, even if the headline leaves something to be desired: Come On, I thought I knew that! . (If you don’t want to burn one of your 20 free articles, here’s a link to my tweet about it).

Here are some great quotes:

Yet overconfidence also develops as a result of the brain’s natural tendency to find shortcuts — and to quickly forget that it used them. In a recent report in the journal PNAS, researchers at Harvard and Duke had college students take what they thought was an I.Q. test. Some got an answer key with the test “to check their answers afterward,” and others did not.

“Studying something in the presence of an answer, whether it’s conscious or not, influences how you interpret the question,” Dr. Bjork said. “You don’t appreciate all of the other things that would have come to mind if the answer weren’t there.

One reason for this has to do with a cognitive quality known as fluency, a measure of how easy a piece of information is to process. The brain automatically associates perceptual fluency, or ease of storage, with retrieval fluency, ease of recall. This is a good rule of thumb for lots of new facts: some people are especially good at remembering directions, others are better with names, still others with recipe ingredients, sports statistics, jokes. But it’s not as good a guide when studying difficult concepts that don’t fall easily into a person’s areas of expertise or interest.

“For example, we know that if you study something twice, in spaced sessions, it’s harder to process the material the second time, and people think it’s counterproductive,” said Nate Kornell, a psychologist at Williams College. “But the opposite is true: You learn more, even though it feels harder. Fluency is playing a trick on judgment.”

The article begins with the research I’d read before that difficult to read fonts actually aids learning. (link goes to original research. nb, this may be the only scholarly work published by a contestant on The Amazing Race). I’m enough of a typography geek to find that studies like this cause me great inner conflict—I obsess over how to properly use an em dash, and I spent a year retraining myself to follow proper typographical conventions and only put 1 space after a period. So I’m not about to go retype all my wonderfully typeset work by changing the font to something like Monotype Corsiva, or god forbid, Comic Sans.

But the bigger point of the research is that putting text in a difficult to read font is confusing to the reader, slowing him down, and causing him to think more about the text, which leads to greater retention.

“The reason that the unusual fonts are effective is that it causes us to think more deeply about the material,” a co-author of the study, Daniel M. Oppenheimer, a psychologist at Princeton, wrote in an e-mail. “But we are capable of thinking deeply without being subjected to unusual fonts. Think of it this way, you can’t skim material in a hard to read font, so putting text in a hard-to-read font will force you to read more carefully.”

Then again, so will raw effort, he and other researchers said. Concentrating harder. Making outlines from scratch. Working through problem sets without glancing at the answers. And studying with classmates who test one another.

And this feeds into a larger question I’ve been asking myself:

Is confusion a required part of learning?

When I first started teaching, I thought my job was just to find the clearest possible explanation for each concept and present that to students. I wanted to pave perfectly smooth and gentle path for my students that led directly to physics mastery. When my students were confused, I would take this as a sign that my lesson needed more work or I needed to work more to develop an explanation, always hoping mywords could cause students to just “get it” in an “ah-ha” moment. But that never happened—this perfect lesson was ever ellusive. And the more I observed my students, i saw that students who really worked through their confusion often came away with a far deeper understanding than their peers who just seemed to “get it.”

My focus on the value of confusion probably started when I saw this wonderful gem of a post by Rhett Allain,learning goes through the land of confusion. And it really got going when I saw this excellent video from Derek Muller that I’ve mentioned before:

The key point in this Derek’s research for me is that the videos that actually lead to more learning student were regarded as “confusing” by students, while the video students saw as “clear, concise and easy to understand” actually had no effect on student learning.

A second post that really got me thinking was Syliva Martinez’s “Kahn Academy and the Mythical Math Cure” which is part 2 of an awesome 4 part critique of Kahn Academy.

In this post, Slyvia describes the traditional way many people see math, as a ladder of skills starting with 2 digit addition, and leading higher and higher through calculus, is deeply flawed and leads to students seeing math as a disconnected set of procedures to be memorized and not understood, while squeezing out all room for creativity in the subject.

She goes on to include a summary of constructivist math teaching as students “construct[ing] new knowledge by combining their experiences with what they already know.”, and she elaborates with a quote:

“…constructivism focuses our attention on how people learn. It suggests that math knowledge results from people forming models in response to the questions and challenges that come from actively engaging math problems and environments – not from simply taking in information, nor as merely the blossoming of an innate gift. The challenge in teaching is to create experiences that engage the student and support his or her own explanation, evaluation, communication, and application of the mathematical models needed to make sense of these experiences.” – Math Forum

Without some confusion, students can easily fall into seeing learning as simply a ladder to be climbed—a set of facts or procedures to be memorized. It is the confusion that pushes them to stop, assess what they know and with proper guidance and motivation, work toward deep understanding.

I think its probably also true that confusion is only valuable in moderation. Too much confusion can easily lead to feeling lost and a sense of dispair that is deeply harmful to learning. But I find that many of my students have a difficult time with any confusion at all. They crave that feeling of everything being explained so it just makes sense, and can quickly fall into a sense of helplessness at the first signs of confusion. So it would seem increasing my students ‘confusion tolerance’ is also necessary.

So it would seem that part of my job as a teacher is to find just the right balance of confusion for students in order to help them to develop deep, connected understanding and free themselves from misconceptions, but at the same time, keep them from being overwhelmed by confusion to the point of hopelessness, and along the way, helping them to increase their overall tolerance for confusion as well. This sounds not unlike the role of a good physical trainer, seeing to find just the right balance of “burn” in a workout to maximize the benefit of the exercise to the athelete, yet not develop discouragement, and over time, increase the athelete’s tolerance for this level of stretching.

This reminds me a quote by Kate Nowak that summarizes this nicely, which I’ve posted before, but bears repeating:

Confusion is ignorance leaving the brain.

which is a a nice riff on the marine corps slogan that “Pain is fear leaving the body”).

In future posts, I’m going to try to explore how to teach students to embrace confusion, and examine what seems to be an interesting possible counter-argument, the series of posts about the Jump Math curriculum in the NYtimes.

23 Comments leave one →
  1. April 22, 2011 9:02 am

    Great post! I think our job as teachers is not only to manage students’ confusion productively, but to make them more at east with confusion. At the end of the day, I want them to desire a level of confusion, because learning is largely about seeking out confusions and taking them on.

    I also think your statement about “wanting to explaining it more clearly” is right on. When a teacher works to explain something more clearly, it’s evidence that the teacher is learning, but not necessarily the students. Not that we are saying that teachers should explain things unclearly, but that those clear explanations need to be targeted toward the resolution of well-designed confusion.

    • April 22, 2011 3:34 pm

      Exactly, I want to focus a post on developing ways of making students easier with confusion—I think a lot of the metacognative work we do in class could help with this. Thanks to some of your prompting, I’m also starting to re-frame some of my efforts to craft better explanations as examples of how my learning is still progressing even after 16 years of studying physics, and thinking about how I might be able to share that with students.

  2. April 22, 2011 10:49 am

    This is something I have been trying to “embrace” with my students. They so much want school/learning to be that ladder of skills and everything is simplistic and understood instantly. There are some true learners in the classroom that revel in the confusion, and you can see they will go far . This reminds me of a quote that i found a few years ago, but cannot remember from whom or the exact phrasing : “The real “Aha” moments in science, the ones that herald new discovery, do not begin with “Eureka”, but rather with “Gee, that’s odd.”

    • April 22, 2011 3:37 pm

      That’s a fantastic quote. I’ve used it often, and the stories of discoveries are littered with examples of embracing confusion. Didn’t Huckel spend 10 years trying to puzzle out the shape of the benzene ring?

  3. April 22, 2011 10:55 am

    Had to go look for the quote. It is from Isaac Asimov :

    The most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka!’ (I found it!) but ‘That’s funny….’

  4. April 22, 2011 11:15 am

    Interesting connections in the article about fonts! I’m looking forward to seeing your thoughts about Jump Math. I’ve read the article, it seems to be a lot about “practicing harder” and having teachers break down everything into smaller and smaller steps – exactly the problem I mentioned with Khan Academy.

    Alfie Kohn wrote in a recent column about research that shows test score gains from direct instruction techniques are short lived

    • April 22, 2011 3:40 pm

      Thanks! I want to do more reading about Jump Math, and I’m no expert in math teaching at the elementary level but I think you’re right—digesting everything down into the smallest bits might rob student of ever being able to take bigger bites on their own. However, I did find the metacognative aspects of the NYT description quite appealing.

  5. Chris permalink
    April 22, 2011 12:00 pm

    Have you thought about (or do you know of) ways to identify or classify different types of confusion among students? Not all confusion is the same; I think that some is productive and other confusion is unproductive. But I don’t know how to identify or characterize the differences.

    • April 22, 2011 3:41 pm

      This is an awesome question, and I need to think more about it. I think it could easily be a blog post. I’m going to try to start keeping a more careful observational record of the confusion I see in my students.

  6. April 22, 2011 1:52 pm

    So is it reasonable to say that because I am always confused in class I could have more meaningful learning than other students? My mechanics professor reads this blog. I am going to use this to try to get a better grade.

    • April 22, 2011 3:45 pm

      I suppose it’s worth a shot. 🙂 I checked out a few post on your blog and really enjoyed it. I’m going to add it to my reader. I think connecting confusion to that pain you feel in a workout really is key. Novice athletes often shun that pain and try to avoid it, while those who have absorbed the mindsets of dedicated athletes know to target right in on the things that are most painful and to use that pain measure their improvement. Still, I’m not sure how good of a motivator this pain metaphor is.

      • April 22, 2011 4:29 pm

        I’m flattered that I have a reader!

        Teachers can relate confusion in science and math to obstacles in other departments. This isn’t a perfect analogy, but authors have “writer’s block” and businesspeople have “growth periods.” Also, we should culture people to understand that pain/confusion/obstacles are a good thing and that the goal in life is not solely to find the easiest or most efficient way to get by.

        When I go to my mechanics professor’s (yes Brian, he is) office hours he always shows excitement for the tiniest progress on my part so that I don’t get discouraged. It still works even though I know what he is doing. In addition to that I think that teachers should embrace confusion in the moment and show students that they also get confused.

        When I feel like I am in a black hole I just remember that many kindergarteners feel like they will never learn how to use scissors, but if they were to give up that early then what would happen?

  7. April 22, 2011 3:12 pm

    JohnG, is Michael Wittmann your Mechanics professor?

    • April 22, 2011 4:41 pm

      Yes he is, do you know him? Can you put in a good word for me? I bet I can get some embarrassing story of him but I don’t know what else I can do in return.

      • April 24, 2011 9:53 pm

        Yeah, I know Michael. He hired me at as a post doc at the university of Maine. I work on the first floor of Bennett. I can only imagine we’ve past each other in the hallways before.

  8. April 23, 2011 9:07 pm

    Love this. Also, the comment about “well-designed confusion” is excellent. So we need a taxonomy of confusions… or at least a rubric for assessing confusion quality? I am thinking of handing this (or an excerpt) out to students next week for conversation. If I can work it in I will let you know how it goes.

    • April 23, 2011 9:15 pm

      Thats a great idea. I think it might be possible for a class to look back over the semester and try to tease out the different types of confusion they felt, or at least I hope this is possible.

      • April 23, 2011 10:40 pm

        That’s my hope too. What questions would you ask? I’m thinking of:
        – Think of a time in school when you felt confused. What caused it? What happened next? How did it affect your learning of that topic? What else did you learn from it (if anything)?
        – Think of a time outside of school when you felt confused. What caused it? What happened next? What (if anything) did you learn as a result?

        • April 23, 2011 11:30 pm

          These questions sound like a good start. I think it will be a challenge for students to critically analyze their confusions, but a very worthy one.

  9. May 5, 2011 11:54 am

    I look forward to future posts on this topic. I’ve been privately exploring the idea of useful student confusion (and the implications for judging college faculty by their student evaluations) for the past few weeks, mostly prompted by the studies on disfluent fonts.


  1. The Science Learnification (almost) Weekly (May 8, 2011) « Science Learnification
  2. What does “I’m confused” mean? « Shifting Phases
  3. Overcoming technophobia with ninja skills « Quantum Progress

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