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