Articles

The use of worked examples

We're all familiar, I'm sure, with the use of worked-out examples in mathematics teaching. Worked-out examples are often used to demonstrate problem-solving processes. They generally specify the steps needed to solve a problem in some detail. After working through such examples, students are usually given the same kind of problems to work through on their own. The strategy is generally helpful in teaching students to solve problems that are the same as the examples.

Graphic summaries are summaries that reorganize the text. Two examples of graphic summaries are outlines and graphic organizers.

In an outline, topics are listed with their subtopics in a linear format, like this:

Children learn. It’s what they do. And they build themselves over the years from wide-eyed baby to a person that walks and talks and can maybe fix your computer, so it’s no wonder that we have this idea that learning comes so much more easily to them than it does to us. But is it true?

There are two particular areas where children are said to excel: learning language, and learning skills.

Elaborative interrogation is a strategy to help you remember meaningful information. The idea behind the strategy is that relevant prior knowledge is not always readily activated when you are trying to learn new information, and sometimes help is needed to make the right connections. The strategy requires you to go beyond the information given to you and to construct reasons for the relationships between bits of information.

Michael Gove is reported as saying that ‘Learning facts by rote should be a central part of the school experience’, a philosophy which apparently underpins his shakeup of school exams. Arguing that "memorisation is a necessary precondition of understanding", he believes that exams that require students to memorize quantities of material ‘promote motivation, solidify knowledge, and guarantee standards’.

I was listening on my walk today to an interview with Edward Tufte, the celebrated guru of data visualization. He said something I took particular note of, concerning the benefits of concentrating on what you’re seeing, without any other distractions, external or internal. He spoke of his experience of being out walking one day with a friend, in a natural environment, and what it was like to just sit down for some minutes, not talking, in a very quiet place, just looking at the scene.

As we all know, we are living in a time of great changes in education and (in its broadest sense) information technology. In order to swim in these new seas, we and our children need to master new forms of literacy. In this and the next three posts, I want to explore some of the concepts, applications, and experiments that bear on this.

The thing to remember about Ericsson’s famous expertise research, showing us the vital importance of deliberate practice in making an expert, is that it was challenging the long-dominant view that natural-born talent is all-important. But Gladwell’s popularizing of Ericsson’s “10,000 hours” overstates the case, and of course people are only too keen to believe that any height is achievable if you just work hard enough.

The much more believable story is that, yes, practice is vital — a great deal of the right sort of practice — but we can’t disavow “natural” abilities entirely.

We forget someone’s name, and our response might be: “Oh I’ve always been terrible at remembering names!” Or: “I’m getting old; I really can’t remember things anymore.” Or: nothing — we shrug it off without thought. What our response might be depends on our age and our personality, but that response has nothing to do with the reason we forgot.

Recently a “Framework for Success in Postsecondary Writing” came out in the U.S. This framework talked about the importance of inculcating certain “habits of mind” in students. One of these eight habits was metacognition, which they defined as the ability to reflect on one’s own thinking as well as on the individual and cultural processes used to structure knowledge.