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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.

Back in 2010, I read a charming article in the New York Times about a bunch of neuroscientists bravely disentangling themselves from their technology (email, cellphones, laptops, …) and going into the wilderness (rafting down the San Juan River) in order to get a better understanding of how heavy use of digital technology might change the way we think, and whether we can reverse the problem by immersing ourselves in nature.

The story method (sometimes called the sentence mnemonic) is the most easily learned list-mnemonic strategy, although it is not as widely known as the other simple methods we’ve talked about so far.

As its name suggests, the story method involves linking words to be learned in a story. While this is most obviously useful for learning actual lists, it can also be used for remembering the main points of a passage. In such a case, you need to reduce each point to a single word, which hopefully has the power to recall the whole point.

A Scientific American article talks about a finding that refines a widely-reported association between self-regulation and academic achievement. This association relates to the famous ‘marshmallow test’, in which young children were left alone with a marshmallow, having been told that if they could hold off eating it until the researcher returns, they would get two marshmallows.

Many people, particularly as they get older, have concerns about short-term memory problems: going to another room to do something and then forgetting why you’re there; deciding to do something, becoming distracted by another task, and then forgetting the original intention; uncertainty about whether you have just performed a routine task; forgetting things you’ve said or done seconds after having said or done them; thinking of something you want to say during a conversation, then forgetting what it was by the time it’s your turn to speak, and so on.

Two large-scale international studies have become established to compare countries' performance in the core subjects of literacy, mathematics and science.

TIMSS: Trends in International Mathematics and Science Study

TIMSS is an international study involving 50 countries that assesses math and science achievement at four year intervals. It has been running since 1995. Students are assessed in the 4th and 8th years of school, and in their final year. The next assessment round will be in 2007.

Remembering a skill is entirely different from remembering other kinds of knowledge. It’s the difference between knowing how and knowing that.

I don’t often talk about motor or skill memory — that is, the memory we use when we type or drive a car or play the piano. It’s one of the more mysterious domains of memory. We all know, of course, that this is a particularly durable kind of memory. It’s like riding a bicycle, we say — meaning that it’s something we’re not likely to have forgotten, something that will come back to us very readily, even if it’s been a very long time since we last used the skill.

What do we mean by word-finding problems?

Here are some examples:

  • increasing use of circumlocutions rather than specific terms (e.g., "I wonder where the thing that goes here is")
  • use of empty phrases, indefinite terms, and pronouns without antecedents (i.e., referring to something or someone as "it" or "him / her" without first identifying them by name)
  • increased frequency of pauses

These problems are all characteristic of Alzheimer's, but also, to a much lesser extent, of normal aging.

In the following case study, I explore in depth the issue of learning the geological time scale — names, dates, and defining events. The emphasis is on developing mnemonics, of course, but an important part of the discussion concerns when and when not to use mnemonics, and how to decide.


The Geological Time Scale

Phanerozoic Eon 542 mya—present

  Cenozoic Era 65 mya—present