I. Working memory

The capital of Lithuania is Vilnius. Now I’m going to quiz you. Tell me, what’s the capital of Lithuania?

“Vilnius, of course,” you reply. “You just said so.” Let me ask another question, then: what’s the capital of Lithuania?

“It’s still Vilnius.” OK, but here’s another one for you: what’s the capital of Lithuania?

“Vilnius. What’s the point of this?”

That’s a great question. Why would I ask you the same thing over and over again? Is it going to help you learn? No, you learned the answer in the first sentence of this article.

Ah, but maybe it’s going to help you remember! That’s a much trickier issue, and we’re going to have to bring in some scientific evidence about how learning and memory work. I’ll give you the punchline right now: it barely helps you remember at all! The answer to my question is already in what psychologists call your working memory, the very-short-term thoughts that we have immediate, reliable access to. It’s what you use when you do math in your head. That means that when I ask you for the answer, it takes almost no effort to recall. Your brain doesn’t make new connections, and barely strengthens the ones that exist. In a day or a week, you’ll have forgotten.

So why do we practice piano this way?

II. Best Practices

You know what I’m talking about. You take a difficult passage, practice it over and over until you have it perfect, but then the next day… your progress, gone! Your time, wasted!

It’s not just piano either. This approach is so common it has its own name in the research literature: blocked practice. Many of us had “drills” in school that looked exactly like this. We cram the night before a test by reading the same things over and over and repeating them to ourselves. And it just barely works well enough that we keep doing it, without ever realizing there’s a better way.

So if you can’t easily learn or memorize something for the long-term just by drilling all at once, what does work? The answer that researchers in teaching and learning have found is that to take something you’ve learned and make it into long-term memory, you need to practice recalling that thing from long-term memory. This makes perfect sense—you should always practice the skill you want to improve, and in this case it’s recall from long-term memory, not recall from working memory!

When applied over long timescales for the sake of secure memorization, this technique is called spaced repetition. In a spaced repetition approach, you aim to review material just before you would forget it, so you’re practicing the skill of long-term recall the best you can. As you do this, you go longer and longer between reviews, and in the end you spend much less time for better security of memory. It’s a hugely important topic for any learner, especially pianists and other musicians, and I go into more detail here. For now, though I want to talk about another application of this principle.

It’s called interleaved practice, as opposed to the “blocked practice” I had you do earlier.

III. Interleaved practice

The idea here is simple. Rather than drill yourself on the capital of Alabama twenty times, then the capital of Alaska twenty times, and so on in alphabetical order, you could mix it up. Alabama, then Alaska, then Arizona, then… and when you finish, go back to Alabama, and repeat twenty times. That way, you’re never recalling from working memory. Most people can only hold only about seven items in working memory; hence the title of Miller’s classic 1956 paper on the subject, “The magic number seven, plus or minus two.” So by putting so many other things to recall in between repeated questions, you’re forcing the relevant knowledge out of working memory.

This way, you successfully practice the long-term recall that you wanted to practice. For the really long term, you work up to reviews separated by days or weeks with spaced repetition. But when you’re learning, not just memorizing, it’s important to frequently clear your working memory to make sure your gains will last.

An even better approach is to randomize the order of the fifty states. With the above method, you can always remember “Juneau comes after Montgomery” rather than associating Juneau with Alaska. This makes your memory more fragile. (It’s also, sadly, exactly how we practice piano, and often results in preventable memory lapses.) By forcing yourself to recall things at random, you build stronger connections.

(By the way, what’s the capital of Lithuania?)

This is a well-studied effect, and it shows up in many domains, from motor to cognitive skills (Rohrer and Pashler, 2010). The studies reported in “The shuffling of math problems improves learning” (Rohrer and Taylor, 2007) show exactly what the title claims. Students’ tested performance was “vastly superior” after they had practiced problems that were mixed randomly compared to when the problems were blocked by type.

Even more importantly, the authors were able to distinguish between the effects of spaced repetition—that is, the mere fact that similar problems were further apart in time when they were randomly mixed—from the effects of interleaved practice (which they call mixed practice)—that is, specifically having a variety of problems in between similar problems. What did they find?

While blocked practice proved superior to mixed practice during the practice session, subsequent test scores were much greater when practice was mixed rather than blocked.

In other words, blocked (or massed) practice will feel productive and successful at the time—but for long term gains, you need to mix up your practice. The authors attribute this success to the way that mixed practice forces the students not just to know how to solve a given problem, but to know which solution procedure to apply. They reinforced this conclusion in their 2010 paper. When similar practice problems are blocked, students are able to just apply the same procedure over and over again. But when they’re mixed, students have to dig into their longer-term memory or review the material again to figure out which technique to apply.

IV. What does this mean for how to practice piano?

Piano is more complicated than geography trivia. I’d say it’s even more complicated than solving math problems. If you can only hold seven things in working memory, what are they? Individual notes, runs, chords, phrases? It could be any of these, depending on your level of mastery. (This is known as chunking in research on expertise.) But in any case, even a small section is likely to have more than you can hold in working memory. And when you’re sight-reading, how well does anything enter your working memory at all? Does it just flow from your eyes to your fingers?

There are also layers upon layers of learning any piano passage—the notes, the fingering, the gestures, dynamics, rubato, the way it fits into the rest of the piece, tempo, all of which you master in degrees and in subtly linked ways. One could argue that this makes it unclear whether the same principles of learning should apply for such a complex skill. But I’d take the other side—all of this complexity means that we have to be even more conscientious and deliberate in applying what we know. Because of this complexity, there’s less research on applying these ideas to musical practice, but results suggest that these lessons transfer well. For example, Stambaugh 2009 found similar results for randomized practice with flautists. This shouldn’t be surprising—when I practice the same thing over and over, it feels like I’m just telling myself “do what I did last time.” But when I interleave my practice, it feels like there’s a much more complex recall process going on in my head, and more deliberate commands sent to my fingers.

No two musicians are the same, so you’ll have to figure out a practice routine that works for you. Here’s what one practice routine designed with the research in mind looks like:

• Divide your piece into small phrases or passages that you can practice individually. Make them small enough that you can see progress in a minute or two of focused work on each.
• Don’t divide your practice session into long blocks, one for each passage.
• Instead, divide your practice session into short intervals where you select a passage at random to practice. Make the intervals short enough that you can revisit passages multiple times during the practice session, so that you’re really engaged in interleaved practice. Breaking up your practice in this way has the additional benefit of keeping your focused attention on goal-directed skill-building, for better deliberate practice.
• Make sure you don’t just practice these sections in isolation, of course! Practice the transitions, and practice starting in random places. This will help you develop performance cues robustly throughout the piece and will help prevent memory lapses.
• Cycle between section-by-section practice and “integrative” practice in which you combine what you’ve been working on.
• If you practice for hours at a time, consider breaking that up into smaller sessions—and make sure you visit the same pieces of music in each session.

Similar methods are also observed in case studies of expert musicians, under the name “work and runs.”

Personally, I break up my pieces hierarchically: first, into large, thematic sections, like the exposition, development, and recapitulation of a sonata. This is important even in more traditional practice methods, just for understanding the music. Then I take each large section and divide it into subsections, short enough that it takes me about 3 minutes to make substantial progress on one. This can be as short as three measures or as long as a page, depending on the difficulty and complexity. Then, when I go to practice, I set a repeating timer for 3 minutes, and select a large section at random. From that section, I play the subsections for around 3 minutes at a time, in a random order. Then I consider the section as a whole, for a longer period of time, and try putting the sections together. Then I rinse and repeat for each large section. If I have time, then I’ll go through the whole thing again, for even better interleaving.

My actual practice sessions, of course, usually aren’t so rigid; I’ll skip or move on early from subsections I feel I’ve mastered, or take slightly longer than 3 minutes on a hard subsection or revisit it more often. It’s important to be flexible, and to try many different things to see what works for you.

I also do this all with Piano Practice Assistant, where I’ve customized the settings for my own use. I encourage you to give it a try, and play with it for a while. If it doesn’t work for you, email me at greg@pianopracticeassistant.com with your feedback and I’ll refund you.

V. Pop quiz

If you’ve made it all the way to the end of this article, I have a question for you: what’s the capital of Lithuania?

References

Miller, George A. (1956). The magic number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review, 63, 81-97.

Rohrer, Doug and Pashler, Harold. (2010). Recent Research on Human Learning Challenges Conventional Instructional Strategies. Educational Researcher, 39, 406-412.

Rohrer, Doug and Taylor, Kelli. (2007). The shuffling of math problems improves learning. Instr. Sci., 35, 481-498.

Stambaugh, Laura A. (2009). When repetition isn’t the best practice strategy: Examining differing levels of contextual interference during practice. International Symposium on Performance Science. 567-572.

Taylor, Kelli and Rohrer, Doug. (2010). The effects of interleaved practice. Applied Cognitive Psychology, 24, 837-848.