GUEST POST: Two Examples Are Better Than One
By Althea Bauernschmidt
Dr. Althea Bauernschmidt @drsilverfox is a professor at St. Bonaventure University where she teaches courses on cognition and memory. She works closely with undergraduates in the Human Memory and Cognition laboratory supervising several research projects focused on student learning.
Once Upon A Time
“Once upon a time a small country was ruled from a strong fortress by a dictator…”
Imagine you are sitting in a classroom and you hear a story about a general trying to overtake a fortress ruled by a dictator. This story describes how there are many roads that lead to the fortress and how the general wanted to send his massive army down one of the roads to overtake the fortress. At a pivotal moment he learns that there are mines on the road that will go off if a large group, like an army, pass over them. However, the mines won’t go off if smaller groups pass over them since they are still roads that workers and farmers use. Undeterred, the general decides to split up his forces so that smaller groups go down different roads but end up converging en masse at the fortress.
Now, after hearing this story you are given a problem to solve. You are told to pretend that you are a doctor faced with a patient who has a malignant tumor in his stomach. You cannot operate on the patient and remove the tumor, but the tumor is going to kill the patient unless it is destroyed. You know that a high intensity ray will destroy the tumor, but at that intensity it will also kill healthy tissue, which will kill the patient. At a lower intensity that is safe for the healthy tissue, it won’t destroy the tumor, which will kill the patient. How can you use the rays to destroy the tumor without destroying the healthy tissue?
Before you attempt to solve this problem, take a moment to think about how you are approaching it. If you are a teacher it may not surprise you to learn that even though the fortress story can help solve the tumor problem, most people will ignore it completely. This scenario is taken directly from a series of experiments on problem solving by Mary Gick and Keith Holyoak (1). They found that unless they prompted students to use the initial story, most ignored it and tried to come up with entirely new solutions to the tumor problem. Only 20% of students who attempted to solve the problem gave the correct answer without that prompt.
This scenario has always intrigued me because it seems so strange that people don’t think to use the story. I’ve done this in the lab like Gick and Holyoak and I’ve used this as a demonstration in my classes every year. Each time I give people the fortress story and the tumor problem I’m surprised that so many don’t immediately see the connection. While I can understand that it’s not immediately obvious – why would a general and a fortress have anything to do with a doctor and a tumor? – what surprises me is that they don’t think it’s weird that the story that I told them out of blue, not 5 minutes ago, could be helpful. As a researcher I often worry that the scenarios I come up with to test learning are too contrived. Students in a psychology experiment are usually suspicious of most things presented to them because they know they are in an experiment. Under these circumstances it should be painfully obvious that everything is related somehow. But even under these circumstances it’s still difficult to get them to see how the two relate. As a teacher I worry that if they won’t use examples to help them solve problems in even the most contrived and obvious circumstances, then what hope do I have that they will use the examples that I give them in class?
To be clear, it’s not like this is a hard problem to solve once you know the trick. Both the story and the problem are solved by using a “dispersion” solution. The general had to split his troops up into smaller forces and have them converge the fortress, and so the doctor needs to split his rays up so that several less intense rays will go through the healthy tissue but converge in a powerful ray on the tumor. And when Gick and Holyoak gave the hint to use the story to solve the problem, about 70% of students were able to come up with this solution. As a teacher I’ve seen this play out, too. I’ve seen students struggle with a question, then given them a hint. “What did we talk about in class yesterday?” or “Remember how we solved the example with hours of TV watched?” More often than not this small prompt causes a lightbulb to switch on and suddenly they know how to solve the problem. So what’s stopping them? Why don’t students use examples to help them, and what can we do to make our examples more effective?
The answer to these questions can be somewhat complicated. It could boil down to a combination of lack of experience, motivation, or innate skill or talent. While those factors undoubtedly influence a student’s ability to solve problems, I’d like to focus on a simple maxim that is easy to use in the classroom: two examples are better than one.
The Devil is In the Details
In a way it’s not surprising that students don’t realize that there’s a connection between the example story and the problem they are solving. All of the surface details are all wrong. By simply hearing the story they haven’t learned the mechanism or process at work that allowed the general to win. The example operates on two levels: the surface details and the structural details. The surface details are the incidentals, the packaging. In our example it’s the general, the fortress, and the roads. The structural details are the relationships among those surface details, the deeper meaning, or the processes at play that are important (2). In our example it’s the dispersion solution. Often we use examples in the classroom to highlight some process, mechanism, or relationship. Our intention as instructors is to flesh out something that is abstract and make it more concrete and relatable for students. However, since we already know that is why the story is important, it’s not as clear to us why our students focus on the irrelevant surface details instead of the structure.
To get students to focus on the important parts of an example – the structural detail – simply give another example with different surface details. When students have two examples to compare and contrast, it’s easier for them to pick out what is similar – the structural details – and therefore important. This bore out in the experiments Gick and Holyoak ran for a follow-up paper (3). In addition to the general and fortress story above, they gave students a second story about putting out a fire wherein using multiple buckets of water from different sides finally puts out the fire. When students were given these two example stories, with different surface details, and then given the problem, they were much more likely to give the analogous solution. Fifty-two percent of students – a substantial increase over the 20% from before – were able to give the analogous solution.
In my best teaching moments I use this in the classroom by making a point to either provide multiple examples, or to structure an activity that encourages students to pick out the process or mechanism that we’re talking about. These activities can be as simple as asking students to explain what just happened. “Why did we get this answer and not some other answer?” “Why was it important to use this method and not some other method?” “What steps did the person in the story follow to achieve their goal?”
In my less than stellar teaching moments I realize that my failure to provide multiple examples, or clearer explanations of my examples, has led my students astray. For example, in my Research Methods course I have students turn in an outline for the introduction of their APA-style paper. Seeing that students were struggling with this, I provided an example of an outline of one of my papers. The entire paper. It had an introduction, a methods, results, and conclusion. I thought it was obvious that my example was there for formatting so they could see how to use simple statements or questions to indicate what the future paragraph would be about. I was surprised when my students handed in bizarre outlines of their introductions that included methods, results, and conclusions. I was deeply frustrated until I realized what had gone wrong. It wasn’t obvious to them how to use this example because APA-style papers were still this strange, new thing that they didn’t understand. They didn’t know what the important parts of my example were so they tried their best to match it on every feature.
Unfortunately for students, but fortunately for my pride, I know that scenarios like the one above are quite common. I’ve heard many instructors complain about how students seem to either not pay attention or understand even after they’ve given an example! The instructor is almost always deeply frustrated by this. After all, they went through all of the trouble of finding a perfectly funny, interesting, or relevant example of the topic they’re covering, but the students don’t seem to appreciate it. While I can’t guarantee that giving multiple examples will magically make all students understand everything, I think that understanding more about how to use examples effectively will help explain some otherwise confusing behavior from students. It will also force you to think carefully about what the principles/mechanisms/theories/processes are that you are trying to teach.
(1) Gick, M. L., & Holyoak, K. J. (1980). Analogical problem solving. Cognitive Psychology, 12, 306-355.
(2) Gentner, D. (1989). The mechanisms of analogical learning. In S. Vosniadou & A. Ortony (Eds.), Similarity and analogical reasoning (pp. 199-241). Cambridge, England: Cambridge University Press
(3) Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1-38.