Teaching Through Insights

Strategies for Insight-Centered Instruction.

Posted Jul 29, 2015

What would it look like to view teaching as a process of creating insights?

I have been thinking about this for the past year, ever since receiving an e-mail from Steffan Elis on July 31, 2014:

“Thanks so much for your book [Seeing What Others Don’t] that I just finished reading. It really opened my eyes to the world of insights and provided some concrete thinking to something that feels like it happens by chance or involuntarily.

I am a teacher and hopefully the awareness of how people gain insights means I can build these principles into my day-to-day teaching to help the children gain insights and make connections/search out contradictions in their learning. In addition, as I think about my role as a leader in school it’ll help me develop the staff I work with to become even better teachers. Very useful summer reading.”

Steffan’s comments got me speculating about the link between insights and education.

Some classroom activities such as vocabulary and arithmetic drills, e.g., memorizing multiplication tables, don’t have anything to do with insights. I am not dismissing multiplication tables — these kinds of operations need to become automatic. But the memorization task is different than the discovery process.

In contrast, approaches such as Problem-Based Learning and the Deweyan program of experiential education do seem like a platform for insights. Decades ago, Lauren Resnick and Robert Glaser, at the Learning Research and Development Center at the University of Pittsburgh, examined the discovery process needed to learn topics such as arithmetic. Science education has long considered concepts such as restructuring and tuning that have their origins in Jean Piaget’s description of accommodation, as well as Karl Popper’s ideas of fallibilism. 

Also, classroom methods such as the use of cuisenaire rods to help young students get a feel for basic arithmetical operations, can be a springboard for discoveries and insights. 

Classroom instructors have long tapped into techniques for encouraging insights even if they didn’t always use that terminology. Here is a well-known example. Deborah Ball, currently the dean of the School of Education at the University of Michigan, was teaching a 3rd grade math class. One of the students, Sean, explained that “6” was both an even and an odd number. Instead of correcting Sean, Ball took his assertion seriously and respectfully, and asked him to explain his comment. Sean said that six was made of three pairs of two. So it contained a two element, making it an even number, and a three element, making it an odd number. Sean’s comment was a healthy sign of an engaged student exploring a possible inconsistency. Ball opened a class discussion of what it means to be an even number, and the class generated a definition of an odd number: there is one left over if it is grouped by twos. Even Sean accepted that definition. The class supported Sean by creating a new category, called “Sean numbers,” for cases like six and ten that had an odd number of groupings of two. The example shows how a teacher, and a class, can diagnose a flawed idea and arrive at a richer mental model. Ball has gone on to create a test for teachers, to help them diagnose the flawed beliefs of students who give incorrect answers.

In this essay I want to explore ways to use recent findings on the nature of insight to articulate a few helpful classroom principles.

Before we get going, let’s review some of the things we’ve learned about insights. I define insights as unexpected shifts in the way we understand things. Our understanding is based on our beliefs, and our beliefs combine to form a mental model of how things work. Insights change that mental model, either by adding new and important beliefs into the mix, or by getting us to discard beliefs that are wrong or misleading. So when we have an insight, it changes the way we understand. The insight can also change our ideas about what actions we can take, the cues we should be noticing, the goals we are pursuing, and the feelings we have.

Further, there seem to be three different pathways to gain insights: by connecting new information to our mental model, by taking contradictory data seriously instead of discarding them, and by finding leverage points and assumptions that are getting in our way.

I also want to bring up some work I did with my colleague Holly Baxter on Cognitive Transformation Theory, which claims that our thinking can become stagnant because we depend on mental models that work most of the time, and protect these mental models by explaining away anomalies and inconsistencies. Instead of evolving our mental models, we hold onto them. As we gain expertise, our mental models become more sophisticated, and also more impervious to change. Too often we treat education as the process of filling a storehouse with more and more information, whereas we also need is to update our beliefs, getting rid of mistaken assumptions. The problem isn’t gaps in our knowledge, but flaws in the beliefs we are depending on. Improving the quality of our mental models depends in part on what we learn, but also on what we unlearn.

Now we can sketch out some ideas about Insight-Centered Instruction.

1. Diagnosis. Teaching isn’t just adding more and more knowledge to what students already know. Early mental models are likely to be buggy — to contain flaws. So teachers need to help young learners subtract from and revise their existing beliefs. And that means being curious about why students get the wrong answers. Wrong answers reveal flawed beliefs, and are an opportunity to diagnose problems. The Sean example above shows how a teacher can use a wrong answer — that six is both odd and even — to deepen the student’s and the class’s understanding. Insight-Centered Instruction is less fixated on getting students to state the right answers, and more patient with incorrect answers, more curious about the reasoning behind them, and more respectful of the student gripped by them.       

2, Unlearning. Teachers can help students unlearn flawed beliefs in a few ways. In the Sean example, the teacher didn’t try to correct Sean but simply invited the class to respond. As a result, Sean abandoned a flawed mental model of odd and even numbers, and other students may have also corrected their beliefs. As long as Sean, and perhaps others, held erroneous beliefs, they were going to have trouble progressing. Another strategy is for the teacher to create cognitive conflict by presenting disconfirming information, letting the students struggle to sort out the inconsistencies, losing faith in the flawed belief as they struggle. Teachers can identify or suggest alternative beliefs, making it less scary to give up a wrong-headed idea. Teachers can use analogs; one science education study addressed the counter-intuitive notion that a table exerts an upward force on a book that is resting on it.  The teachers placed a book on students’ outstretched palms, so the students could feel that they were pressing upward, as a start for thinking about the wooden table. The teachers balanced books on springs, and on wooden planks, and so the idea of a table exerting an upward force became less strange.      

3. Feedback. The notion of feedback is, in itself, not particularly novel to the field of instruction. However, feedback is not very helpful if the learner doesn’t understand it or grasp its connection to the actions just taken, so instructors will be tempted to spell out the implications. But some research suggests that having the teacher provide the feedback can be counter-productive. It can speed up the learning process but slow down the transfer process. Learners may become dependent on having feedback dished out and digested, rather than building skills for finding and interpreting feedback for themselves. This is one of the reasons given for experiential learning in which students do acquire and make sense of their own feedback. In the Sean example, if the teacher had simply corrected Sean she would have left his flawed beliefs intact.

4. Knowledge Shields. These pose an additional difficulty when it comes to feedback. Several researchers have demonstrated the ways that we resist feedback or any kind of information that conflicts with our beliefs. These knowledge shields allow us to preserve our mental models by dismissing the inconsistencies. We may ignore the new data, we may find some minor flaw that lets us reject the data, we may put the data on hold for the time being until we find a way to make sense of them, we may re-interpret the data so that they aren’t so troublesome, we may make a cosmetic change to our beliefs in token compliance with the anomalous data. To make Insight-Centered Instruction work, teachers need to expect that students will use knowledge shields to preserve their mental models. Deborah Ball was not distressed that Sean tried to hold onto his view that six was both odd and even. She didn’t want Sean to succumb to the group pressure to parrot the right answer. She wanted him to genuinely arrive at a deeper sense of what constitutes an odd or an even number.

5. Pathways to insight. My research has uncovered three pathways, and each comes into play in the classroom.

            One pathway is forming connections. Students are often energetic at suggesting connections, most of which are minimally relevant. Rather than discouraging these flights of fancy, teachers might see them as valuable tendencies of engaged learners and discuss how to tell which connections are more fruitful than others.

            A second pathway involves contradictions. Some students are on the lookout for inconsistencies, especially inconsistencies on the part of the teacher. Such behavior can be annoying but the tendency itself is also a sign of an engaged learner. One study found that the best students were alert to anomalies and were stimulated by them, in contrast to unsuccessful students who sought to avoid the conflicting evidence as requiring too much of a cognitive burden. Some teachers will present an erroneous idea and challenge students to shoot it down. Or else teachers can use a student’s erroneous idea, such as six being both odd and even, as a springboard for a class discussion.

            The third pathway is to deliberately try to overcome a barrier, either by discovering assumptions that are trapping us, or detecting leverage points we hadn’t appreciated before. These discoveries are often highly exciting. Actually, all three of the insight pathways can be exciting because the end result, the “aha” moment, has such an emotional charge. One benefit of Insight-Centered Instruction is to take advantage of the insight rush that people experience when they make a discovery.  

6. The Insight Stance (In/Stance). Teachers may be able to boost insights by encouraging students to adopt a stance or mindset that is driven by curiosity rather than a fear of getting a wrong answer. Teachers can help students notice the insights they have, and encourage more of them. Teachers can suggest that students pick up on connections, and on contradictions, and when students get stuck the teacher can help them to re-examine the assumptions they are making.

Notice how Deborah Ball tried to promote an In/Stance in her students. She treated Sean’s wrong-headed comment with respect. She encouraged the class to explore the contradiction to see what could be learned. She approved of the idea of Sean numbers, a useless concept but still a novel discovery that the class had made.

I imagine some seasoned teachers will roll their eyes at the notion of encouraging an active, curious mindset and recoil at the idea of students posing one question after another. An obvious response is to tell them to stop with the questions and just listen to the material in order to get through the lesson. I can sympathize with that impulse, but it makes me uneasy. Skilled teachers seem to be able to encourage productive kinds of curiosity without having to stifle their students. 

Insight-Centered Instruction seems well-suited to topics such as arithmetic and mathematics, and to science. It may also be useful for other areas such as literature, trying to make discoveries about the motivations of people and their varying perspectives. Teachers may find it valuable to work on social insights that address confusions and conflicts. In history class, teachers can challenge classes to sort out why leaders acted in the way they did, and why groups and movements arose or failed to endure.

Teaching does depend on transmitting information and mastering material. Promoting insights is just part of the process. Too many teachers seem to be insensitive to insights and impatient with their students. Insight-Centered Instruction seeks a different balance, one that tries to foster insights when possible and appreciates their value within the educational process.

Good teachers challenge students in the ways I have described. The perspective on Insight-Centered Instruction would have its greatest benefit with less-skilled teachers who lack the patience or the inclination to diagnose problems and resolve them. Insight-Centered Instruction could help these teachers see the value of helping students build richer mental models and adopt a mindset for seeking discoveries.

In the spirit of Insight-Centered Instruction, I encourage readers, especially teachers, to send me their ideas for promoting insights in their students.