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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.

This post is the second part in a four-part series on how education delivery is changing, and the set of literacies required in today’s world. Part 1 looked at the changing world of textbooks. This post looks at the oral equivalent of textbooks: direct instruction or lecturing.

On my walk today, I listened to a downloaded interview from the On Being website. The interview was with ‘vocal magician and conductor’ Bobby McFerrin, and something he said early on in the interview really caught my attention.

I have spoken before, here on the website and in my books, about the importance of setting specific goals and articulating your specific needs. Improving your memory is not a single task, because memory is not a single thing. And as I have discussed when talking about the benefits of ‘brain games’ and ‘brain training’, which are so popular now, there is only a little evidence that we can achieve general across-the-board improvement in our cognitive abilities.

Flashcards are cards with a word (or phrase) on one side and its translation on the other. You can buy ready-made flashcards, and these can certainly be helpful, particularly if you're inexperienced at learning another language. However, it is more effective if you make them yourself. Not only will the cards be customized to your own use, but the activity of selecting words and writing them down help you learn them.

Subliminal learning achieved notoriety back in 1957, when James Vicary claimed moviegoers could be induced to buy popcorn and Coca-Cola through the use of messages that flashed on the screen too quickly to be seen. The claim was later shown to be false, but though the idea that people can be brainwashed by the use of such techniques has been disproven (there was quite a bit of hysteria about the notion at the time), that doesn’t mean the idea of subliminal learning is crazy.

Alzheimer's disease currently affects one in 10 people over age 65 and nearly half of those over age 85.

More than 19 million Americans say they have a family member with the disease, and 37 million say they know somebody affected with Alzheimer's.

In the United States, the average lifetime cost per Alzheimer patient is US$174,000. (These figures are from the U.S. Alzheimer's Association).

There is a very common form of forgetfulness that is not really a failure of memory. When we get in our car to drive to place A and find ourselves instead on the road to the more familiar place B, this is not a failure of memory. When we clear the table and find ourselves putting the margarine in the dishwasher or the dirty plate in the fridge, this is not a failure of memory. When we go into a room intending to do one thing and do something else instead, this is not, really, a failure of memory.

Children’s understanding, and their use of memory and learning strategies, is a considerably more complex situation than most of us realize. To get some feeling for this complexity, let’s start by looking at a specific area of knowledge: mathematics.

Children's math understanding

Here’s a math problem:

Pete has 3 apples. Ann also has some apples. Pete and Ann have 9 apples altogether. How many apples does Ann have?

This seems pretty straightforward, right? How about this one:

Montessori education

Maria Montessori (1870-1952) was an Italian physician. After working with retarded children in a psychiatric clinic attached to the University of Rome, she applied the ideas she had developed to children in a slum district in Rome. This was the first Casa dei Bambini ("children's house"). It opened in 1907. Two years later she set out her methods and principles in a book, which was translated as The Montessori Method in 1912.