practice

Transfer refers to the ability to extend (transfer) learning from one situation to another. For example, knowing how to play the piano doesn’t (I assume) help you play the tuba, but presumably is a great help if you decide to take up the harpsichord or organ. Similarly, I’ve found my knowledge of Latin and French a great help in learning Spanish, but no help at all in learning Japanese.

Transfer, however, doesn’t have to be positive. Your existing knowledge can hinder, rather than help, new learning. In such a situation we talk about negative transfer. We’ve all experienced it. At the moment I’m experiencing it with my typing -- I've converted my standard QWERTY keyboard to a Dvorak one (you can hear about this experience in my podcast, if you're interested).

Teachers and students do generally hope that learning will transfer to new contexts. If we had to learn how to deal with every single possible situation we might come across, we’d never be able to cope with the world! So in that sense, transfer is at the heart of successful learning (and presumably the ability to transfer new learning is closely tied to that elusive concept, intelligence).

Here’s an example of transfer (or lack of it) in the classroom.

A student can be taught the formula for finding the area of a parallelogram, and will then be capable of finding the area of any parallelogram. However, if given different geometric figures, they won’t be able to apply their knowledge to calculate the area, because the formula they have memorized applies only to one specific figure — the parallelogram.

However, if the student is instead encouraged to work out how to calculate the area of a parallelogram by using the structural relationships in the parallelogram (for example, by rearranging it into a rectangle by moving one triangle from one end to the other), then they are much more likely to be able to use that experience to work out the areas of a different figure.

This example gives a clue to one important way of encouraging transfer: abstraction. If you only experience a very specific example of a problem, you are much less likely to be able to apply that learning to other problems. If, on the other hand, you are also told the abstract principles involved in the problem, you are much more likely to be able to use that learning in a variety of situations. [example taken from How People Learn]

Clearly there is a strong relationship between understanding and transfer. If you understand what you are doing, you are much more likely to be able to transfer that learning to problems and situations you haven’t encountered before — which is why transfer tests are much better tests of understanding than standard recall tests.

That is probably more obvious for knowledge such as scientific knowledge than it is for skill learning, so let me tell you about a classic study [1]. In this study, children were given practice in throwing darts at an underwater object. Some of the children were also instructed in how light is refracted in water, and how this produces misleading information regarding the location of objects under water. While all the children did equally well on the task they practiced on — throwing darts at an object 12 inches under water — the children who had been given the instruction did much better when the target was moved to a place only 4 inches under water.

Understanding is helped by contrasting cases. Which features of a concept or situation are important is often only evident when you can see different but related concepts. For example, you can’t fully understand what an artery is unless you contrast it with a vein; the concept of recognition memory is better understood if contrasted with recall memory.

Transfer is also helped if transfer implications are explicitly pointed out during learning, and if problems are presented in several contexts. One way of doing that is if you use “what-ifs” to expand your experience. That is, having solved a problem, you ask “What if I changed this part of the problem?”

All of this points to another requirement for successful transfer — time. Successful, “deep”, learning requires much more time than shallow rote learning. On the other hand, because it can apply to a much wider range of problems and situations, is much less easily forgotten, and facilitates other learning, it saves a lot of time in the long run!

Distributed practice more effective than massed practice

It has long been known that spacing practice (reviewing learning or practicing a skill at spaced intervals) is far more effective than massed practice (in one heavy session). An interesting example of this comes from a study that aimed to find the best way of teaching postmen to type (this was at the request of the British Post Office). The researchers put postmen on one of four schedules:

• an intensive schedule of two two-hour daily sessions
• one of two intermediate schedules involving two hours a day, either as one two-hour session, or two one-hour sessions
• a more gradual schedule of one hour a day

The researchers found quite dramatic differences, with the one-hour-a-day group learning as much in 55 hours as the four-hour-a-day group in 80. Moreover, the gradual group showed greater retention of their skills when tested several months later.

Research has also demonstrated that people commonly over-estimate the value of massed practice, and tend not to give due recognition to the value of spacing practice. This particular study confirmed this, by finding that, notwithstanding their superior performance, the gradual group were the least happy with the program - for though they learned much more quickly in terms of hours, it took them many more days (80 hours at four hours a day is 20 days, but 55 hours at one hour a day is 55 days).

Micro-distribution practice

What about practice over much shorter intervals? Say you are learning vocabulary in a foreign language - is it better to repeat a word twice in rapid succession, or to space out the repetitions?

On the basis of the distribution principle, the answer is clear. Go through your list once, then repeat it. That way, every item will be maximally distant from its own repetition. But the distribution principle isn't the only memory principle at work here. The other principle is that of generation - that if you produce the word for yourself, this will strengthen the connection better than having the word given to you. And your likelihood of being able to successfully recall the word is greater if you test it earlier.

So you have two opposing principles at work here: one says maximise the time between repetitions, the other says minimise it. Which wins? Well, neither. They're both at work, so you need to take both into account, like this:

• the first time, test a new word after only a brief interval (your own experience is best here, to tell you what length of interval is best for you)
• on successive recalls, gradually increase the interval (your aim is to find the maximum interval at which you can reliably recall the word)
• if you fail to recall the word, shorten the interval; if you succeed, lengthen it

Distributed practice in skill learning

The distribution principle also applies to skill learning, although people are probably even more reluctant to apply it. Practicing a skill in a concentrated block seems to give better performance, and indeed it does - at the time. The problem is, it doesn't lead to better long-term learning.

Part of the problem is that it makes you over-estimate how well you have learned the skill. But most of that learning will fade quickly. To learn the skill properly (i.e., for over the long term), you are best, not simply to distribute your practice, but also practice the skill in the context of a variety of different tasks. For example, if you were learning to type, you could hammer away at one combination of keys (say, asdf) thirty times, then you could move on to another sequence (jkl;) and repeat that thirty times, and so on. But it would be better if you mixed the sequences up.

It is thought that practicing in this way works better because it requires you to repeatedly retrieve the motor program corresponding to each task. It also requires you to differentiate the skills in terms of their similarities and differences, which may be assumed to result in a better mental conceptualization of those skills.

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

Practice, practice, practice

Practice is the key to mastering a skill. One of the critical aspects is assuredly the fact that, with practice, the demands on your attention get smaller and smaller. Interestingly (and probably against common sense), there appears to be no mental limit to the improvement you gain from practice. Your physical condition limits how much improvement you can make to a practical skill (although, in practice, few people probably ever approach these limits), but a cognitive skill will continue to improve as long as you keep practicing. One long-ago researcher had two people perform 10,000 mental addition problems, and they kept on increasing their speed to the end.

How to get the most out of your practice

While practice is the key, there are some actions we can take to ensure we get the most value out of our practice:

• Learn from specific examples rather than abstract rules
• Provide feedback while the action is active in memory (i.e., immediately). Try again while the feedback is active in memory.
• Practice a skill with subtle variations (such as varying the force of your pitch, or the distance you are throwing) rather than trying to repeat your action exactly.
• Space your practice (maths textbooks, for example, tend to put similar exercises together, but in fact they would be better spaced out).
• Allow for interference with similar skills: if a new skill contains steps that are antagonistic to steps contained in an already mastered skill, that new skill will be much harder to learn (e.g., when I changed keyboards, the buttons for page up, page down, insert, etc, had been put in a different order — the conflict between the old habit and the new pattern made learning the new pattern harder than it would have been if I had never had a keyboard before). The existing skill may also be badly affected.
• If a skill can be broken down into independent sub-skills, break it down into its components and learn them separately, but if components are dependent, learn the skill as a whole (e.g., computer programming can be broken into independent sub-skills, but learning to play the piano is best learned as a whole).

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.

Worked-out examples are also used in small-group settings, either by working on the example together, or by studying the example individually and then getting together to enable those who understood to explain to those who didn't. Explaining something to another person is well-established as an effective method of improving understanding (for the person doing the explaining -- and presumably the person receiving the explanation gets something out of it also!).

Metacognitive differences between high and low achievers

An interesting study comparing the behavior of high and low achieving students who studied worked-out examples cooperatively found important differences.

High achievers:

• explained things to themselves as they worked through the examples
• tried to construct relationships between the new process and what they already knew
• tended to infer additional information that wasn't directly given

Low achievers on the other hand:

• followed the examples step-by-step without relating it to anything they already knew
• didn't try to construct any broader understanding of the procedure that would enable them to generalize it to new situations

Other studies have since demonstrated that students taught to ask questions that focus on relating new learning to old show greater understanding than students taught to ask different questions, and both do better than students who ask no questions at all.

Learning to ask the right questions

An instructional method for teaching mathematics that involves training students to ask metacognitive questions has been found to produce significant improvement in students' learning. The method is called IMPROVE -- an acronym for the teaching steps involved:

• Introduce new concepts
• Metacognitive questioning
• Practise
• Review
• Obtain mastery on lower and higher cognitive processes
• Verify
• Enrich

There are four kinds of metacognitive questions the students are taught to ask:

1. Comprehension questions (e.g., What is this problem all about?)
2. Connection questions (e.g., How is this problem different from/ similar to problems that have already been solved?)
3. Strategy questions (e.g., What strategies are appropriate for solving this problem and why?)
4. Reflection questions (e.g., does this make sense? why am I stuck?)

A study that compared the effects of using worked-out examples or metacognitive questioning (both in a cooperative setting) found that students given metacognitive training performed significantly better than those who experienced worked-out examples (the participants were 8th grade Israeli students). Lower achievers benefited more from the metacognitive training (not surprising, because presumably the high achievers already used this strategy in the context of the worked-out examples).