of the tea-ceremony problem, depicted to show the analogy to the discs-and-pegs problem."/>
FIGURE 1.10: The tea-ceremony problem, depicted to show the analogy to the discs-and-pegs problem.
Source: © Greg Culley.
Your first thought upon reading this problem was likely “Huh?” You could probably tell that you'd have to read it several times just to understand it, let alone begin working on the solution. It seemed overwhelming because you did not have sufficient space in working memory to hold all of the aspects of the problem. Working memory has limited space, so thinking becomes increasingly difficult as working memory gets crowded.
The tea-ceremony problem is actually the same as the discs-and-pegs problem presented in Figure 1.8. The host and two guests are like the three pegs, and the tasks are the three discs to be moved among them, as shown in Figure 1.10. (The fact that very few people see this analogy and its importance for education is taken up in Chapter 4.)
This version of the problem seems much harder because some parts of the problem that are laid out in Figure 1.8 must be juggled in your head in this new version. For example, Figure 1.8 provides a picture of the pegs that you can use to help maintain a mental image of the discs as you consider moves, whereas the tea ceremony version provides no such support. And in the tea version, the description of the rules that govern moves is longer and therefore occupies so much space in working memory that it's difficult to plan a solution.
Aristotle said, “The pleasures arising from thinking and learning will make us think and learn all the more.”5 You've seen that this view is too optimistic. It's successful learning that's pleasurable and that will keep students coming back for more. We've seen that one of the factors in successful learning is having the right information in long-term memory. In the next chapter, we examine that need more closely.
Summary
People's minds are not especially well suited to thinking; thinking is slow, effortful, and uncertain. For this reason, deliberate thinking does not guide people's behavior in most situations. Rather, we rely on our memories, following courses of action that we have taken before. Nevertheless, we find successful thinking pleasurable. We like solving problems, understanding new ideas, and so forth. Thus, we will seek out opportunities to think, but we are selective in doing so; we choose problems that pose some challenge but that seem likely to be solvable, because these are the problems that lead to feelings of pleasure and satisfaction. For problems to be solved, the thinker needs adequate information from the environment, room in working memory, and the required facts and procedures in long-term memory.
Implications for the Classroom
Let's turn now to the question that opened this chapter: Why don't students like school, or more accurately, why don't more of them like it? Any teacher knows that there are lots of reasons that a student might or might not enjoy school. (My wife loved it, but primarily for social reasons.) From a cognitive perspective, an important factor is whether or not a student consistently experiences the pleasurable rush of learning something new, of solving a problem. What can teachers do to ensure that each student gets that pleasure?
Be Sure That There Are Problems to Be Solved
By problem I don't necessarily mean a question addressed to the class by the teacher, or a mathematical puzzle. I mean cognitive work that poses moderate challenge, including such activities as understanding a poem or thinking of novel uses for recyclable materials. This sort of cognitive work is of course the main stuff of teaching – we want our students to think. But without some attention, a lesson plan can become a long string of teacher explanations, with little opportunity for students to solve problems. So scan each lesson plan with an eye toward the cognitive work that students will be doing. How often does such work occur? Is it intermixed with cognitive breaks? Is it real cognitive work that can lead to the feeling of discovery and not just retrieval from memory? (Think especially about questions posed during whole-class instruction – research shows it's easy for teachers to slip into a pattern of asking lots of fact-retrieval questions.) When you have identified the challenges, consider whether they are open to negative outcomes such as students failing to understand what they are to do, or students being unlikely to solve the problem, or students simply trying to guess what you would like them to say or do.
Respect Students' Cognitive Limits
When trying to develop effective mental challenges for your students, bear in mind the cognitive limitations discussed in this chapter. For example, suppose you began a history lesson with a question: “You've read that 35 nations united to expel Iraq from Kuwait in the First Gulf War, the largest coalition since World War II. Why do you suppose so many nations joined?” Do your students have the necessary background knowledge in memory to consider this question? What do they know about the relationship of Iraq and neighboring countries that ended up joining the coalition prior to the war? Do they know about how Iraq brought their dispute with Kuwait to the Arab League before the invasion? Do they know about the significance of oil to the world economy and the forecast economic consequences of the invasion? Could they generate reasonable alternative courses of action for those countries leading the invasion? If they lack the appropriate background knowledge, the question you pose will quickly be judged as “boring.” If students lack the background knowledge to engage with a problem, save it for another time when they have that knowledge.
Equally important is the limit on working memory. Remember that people can keep only so much information in mind at once, as you experienced when you read the tea-ceremony version of the discs-and-pegs problem. Overloads of working memory are caused by such things as multistep instructions, lists of unconnected facts, chains of logic more than two or three steps long, and the application of a just-learned concept to new material (unless the concept is quite simple). The solution to working memory overloads is straightforward: slow the pace, and use memory aids such as writing on the whiteboard to save students from keeping too much information in working memory.
Clarifying the Problems to Be Solved
How can you make the problem interesting? A common strategy is to try to make the material “relevant” to students. This strategy sometimes works well, but it's hard to use for some material, and your struggle to make it relevant to students is usually obvious. Another difficulty is that a teacher's class may include two football fans, a doll collector, a NASCAR enthusiast, a horseback riding competitor – you get the idea. Mentioning a popular singer in the course of a history lesson may give the class a giggle, but it won't do much more than that. I have emphasized that our curiosity is provoked when we perceive a problem that we believe we can solve. What is the question that will engage students and make them want to know the answer?
One way to view schoolwork is as a series of answers. We want students to know Boyle's law, or three causes of World War I, or why Poe's raven kept saying, “Nevermore.” Sometimes I think that we, as teachers, are so eager to get to the answers that we do not
