Should You Visualize the Score when Playing by Memory?

 

I've heard people say that they try to visualize the written score when playing by memory. And I've heard people advise doing that. I've also heard people say that you should even write out the piece, by memory, to help with visualization (Wow, that would be terribly time-consuming.) I don't believe that this will help with memory in the long term.

It seems like people who have photographic memories would have zero problems with memory slips when performing. I know someone who has a photographic memory, but he still has memory slips just due to nerves. It's possible to lose your place in the score while just visualizing it, and the fear of this causes the slips. More importantly, his playing is not very musical. I suspect that the involvement of the visual cortex of the brain to such a great degree detracts from the auditory and the emotional parts of the brain. 

I would imagine that trying to visualize just parts of the score, versus all of it, would be even worse, because you'd have to remember to jump to doing the visual in just those parts, and if you forgot to do that, you might have no back-up plan. I say I "imagine" because I never ever visualize the score. By the time I'm ready to play in performance, I have been playing by memory for months, and how the actual score looks is long forgotten.

Remember, the score is just a visual representation of the music, not the music itself! Before the composers set the music down in writing, they heard it all in their minds. Music notation is a wonderful thing, giving access to a whole world of music. But the goal should be to go past the notation and fully internalize the music. So how do you do that?

As you've heard me say in previous posts, the development of the ear is the number one job for the musician. The best musicians are the ones with the best ears. Even if you already have a good, or even great ear, there are ways to improve it. I've had students ask me if they should go to the internet for programs which, for example, play intervals and have you identify them. You can do that yourself, at the piano, just by playing two notes (one in each hand, so you can't feel the interval) with your eyes closed. That would just be for beginners who want to improve their ear. For the more advanced player, transposing the pieces you are working on, or simpler pieces if necessary, is the most powerful tool for making your ear work harder and thus get stronger. Transposing means you are moving the music to another place (another key), but keeping all the relationships the same. That is the essense of hearing and knowing a piece, to be able to hear all the relationships.

Remember, the transposing needs to be by ear, not by eye, which would mean just calculating each note's distance from the original one.

Another often-overlooked way to improve your ear is to sight-sing. Choirs often require that their members be able to sight sing. If you can see an interval and sing it, that means your ear knows it. To practice this, you'd need to take music with which you are not familiar, otherwise you'd already just sing it from memory.

Even if you try to visualize the score and are successful at it, you'd have to start again from scratch on every new piece. But if you develop your ear, it is there for you at all times, in everything you play.

So many people just focus on "learning the notes" of what they are playing, and perhaps mastering the physical techniques as well. But if you want to play by memory (which I hope you do), then you need to get the piece into the deep levels of the "wiring" in your brain. This means really knowing how it sounds. You may think, "of course I know how it sounds," but if you can't transpose it to another key, then you don't really know it. I believe ear and memory are essentially the same thing.

Don't Count On It

 

Once again I find myself wanting to write about rhythm. Without rhythm there would be no music. 

I am still amazed at how many people, even some who have been playing the piano for a few years, are just stumped by rhythm, and others who ignore it almost entirely.

If you are improvising (solo), you can theoretically ignore rhythm. There is no such thing as NO rhythm. But you could have a rambling, unsteady, incoherent rhythm, and, I suppose, if it doesn't bother you and no one else is listening, then who am I to say it's not good. But if you improvise with or for others, you will find no one will want to be your partners or your audience. And if you continue this way, focusing just on "the notes," your improvising will not improve.

Now we will address the more common situation, playing music from written musical notation. If you tried to teach yourself, you may have had no idea how to go about learning to read and hear rhythm. If you had a teacher, she/he should have given you the training and tools to hear the rhythm, and to understand the rhythmic notation. However, intellectual understanding is not enough; you must connect the hearing and understanding to a deep knowledge in your body to be able to actually play them. Sadly, many teachers and many books and many "methods" don't really do this. It has to be taught in a way which engages the physical, not just the mental. Knowing the "math" of rhythm is not enough.

So for hundreds of years teachers and pedagogues have searched for tools that could help with the learning of rhythm. Unfortunately, the one most commonly used is "counting," which is a blunt instrument indeed. As you are probably aware, counting involves saying (out loud) the number of the beat (e.g. one-two-three-four), and when the beat divides in two, adding a syllable between the beat (e.g. one-and-two-and etc.). If the beat divides further, more syllables are added. Proponents of this method insist you must count at all times. 

There are SO MANY problems with this, yet I am going to attempt to list them all.

1. Counting is basically putting the cart before the horse. Or perhaps it's more of a "catch-22." If you can hear the rhythm, you don't need to count or put any other words to it. If you really can't hear it, no amount of counting will help you, because you can still just say those numbers in the wrong rhythm and not even realize it. We all have a pulse within us, 24/7, moment of birth until moment of death, so I firmly believe everyone can hear (and replicate) a steady pulse. No need to say "one two three four" to hear it. (Yes, there are those few who are challenged to clap to the beat when hearing music, but they are a small minority and could improve with proper training.) Let's say our beat is a quarter note, and when the beat divides you have eighth notes. It is still like a pulse, just twice as fast. Same thing if it divides again. The problem is, of course, that actual music has these in different and ever-changing patterns. So, if your counting isn't 100% consistent, and even, it will still be a mess. With my method, I break down the more complex rhythms into a simpler ones, then "fill in" more of the "divisions" step by step, until the whole thing is fleshed out. I realize this may be unclear just from the description, but suffice it to say that, like many things we do, we start with the basic structure and add details litte by little. That being said, if the student is attempting to play a piece with really complex rhythms and is getting lost in it, then they may not be ready for that particular piece, and I would assign simpler pieces (rhythm-wise) and work up to the complex ones.

2. The system of counting began hundreds of years ago, when music was not nearly as complex as it is now. The system never really came up with an adequate method of using numbers and words when the beat divides in three instead of two or four, which is quite common. Teachers have devised all sorts of words to supposedly help with this problem, but again, it's entirely possible to say these words in a different rhythm than the one you intended. Counting is completely useless for non-standard divisions of the beat (see my post on this topic) such as five or seven, which may not have been used by early composers, but is very common in all the composers of the Romantic era and everything since then.

3. Counting is pathetic when it comes to jazz or pop. The idea of counting was formulated when the most "stressed" notes fall ON the beat. Thus, the other syllables such as the "and" and uh" are not as stressed. But what about syncopation, where the most "important" notes (or words, if it's a song) are occuring OFF the beats. Counting becomes very awkward. It was just never imagined that there would be a need for a system to accomodate this type of music.

4. Counting is totally useless for poly-rhythms, for example one hand playing in duplets (normal eighth notes) and the other in triplets. You obviously can't be saying both at once. Proponents of counting would just tell you to play each hand separately as you count, then put them together. I can assure, it's the putting them together that is the challenge. No amount of counting is going to help "wire your brain" to hear two different rhythms at once. (See my post on this topic.)

5. Counting is too slow. You can really only do it if you are playing fairly slowly. If you have to count "one-ee-and-uh two-ee-and-uh" for sixteenth notes, you can't say it fast enough for a lot of music that would actually have sixteenth notes.

6. Since counting itself is unreliable, the use of the metronome was introduced. Theoretically, having the metronome tick away in a steady pulse is supposed to help you with the rhythm. But as we have seen, the pulse is not the problem. It's all the stuff that happens within the beat that makes it complicated. Use of the metronome, making yourself a slave to an external machine, is never going to give YOU a good sense of rhythm, or help you play with rhythmic vitality. If you somehow manage to use it and get all your rhythm "correct," it will be lifeless and dull. By the time you wean yourself off it, it will be too late. Your habit of playing without any rhythmic nuance and subtelty will be too entrenched. Once again, some proponents of the metronome insist you use it almost all the time.

7. You can't really be listening to your own playing if you have to constantly hear the chatter of all those numbers and syllables. Our goal is to strengthen the connection between ear and body (arms, hands, etc.). Inserting mental and verbal activity such as counting is a distraction and is going to impede your progress.

8. Proponents of counting never do say when you can finally stop doing it! I've read the blogs and articles of many counting enthusiasts, and I have yet to find one who tells you when you don't need it anymore. Should you wean yourself off or go cold turkey? I hope you realize that concert pianists and other highly accomplished players DO NOT COUNT in their practicing. Many probably never did. If their their early teachers insisted on it, they just stopped doing it because they learned to hear the rhythm and simply realized they didn't need to count.

9. And finally, I want to point out that the people who play the most complex rhythms, such as African and Latin drummers, and many jazz musicians, never learned to play with counting nor with the metronome.

There are so many people who advocate using counting and the metronome, sternly warning you that you would ignore this at your peril! So you may be inclined to think there must be some truth in it if so many people believe it. I hope this post has convinced you otherwise. Our understanding and our methods have evolved over the years in almost every field of endeavor -- sports, science, medicine, to name a few -- yet piano methods seem largely stuck in the 1700s. If you still want to follow those methods because you are comfortable with them, or any other reason, and think you will someday play with beauty, fluency and mastery, I would say: DON'T COUNT ON IT!

Making Your Own Song Arrangements

 

You've read in my previous posts that I encourage students to play music other than classical music, at least a little, even if they are mostly interested in classical. It has a lot of skills to teach you.

When beginners start with me (and even not-so-beginners), I always start with playing by ear. They pick out the melodies for familiar songs such as Happy Birthday, Silent Night, Amazing Grace, and so on. I teach them about chords, starting with major triads, but they need to learn all twelve, not just the ones which fall all on white keys (which I've seen many students do). They harmonize the songs with the chords (just three chords for those songs), by ear, but with my guidance as necessary. We continue on to more songs, finding ones that require more chords.

Not only do you need to use your ear to determine which chords to select, you need to use your ear to tell you where they come. This will build your sense of rhythm and your understanding of musical architecture. Many people think the chord is one that has the melody note in it, but this is not necessarily the case. The musical architecture is more important here. You may not quite understand what I mean by architecture, but just for starters, read my post "Going Away and Coming Home."

Soon after, they learn all twelve minor chords, then augmented and diminished traids, then 7th chords, eventually learning all five kinds of 7th chords. At this point they know 108 chords. It is important to stress here that you must learn the chords by learning how they are built, not reading them from a book or chord chart. If you learn them by reading them or other methods which just show you which keys to play, you will never really know them well. It's the difference between giving you a fish and teaching you how to fish. If you currently have a teacher who cannot teach you this, or thinks it is not important, I strongly suggest you find a new teacher. (One of my current students had a previous teacher who told him that "the learning curve was too steep" to learn all about chords! Isn't that what a teacher is supposed to be helping you with?)

You originally learn all the chords in root position, but later your must also learn to play the inversions with ease. This means the notes of the chord are re-arranged. It is the equivalent of a whole egg vs. a scrambled egg. You must know the "egg" first, then you can scramble it.

In addition to being able to play dozens, if not hundreds of songs, you will be getting a lot of ear training and a lot of experience with chords. Not to mention that most people find this fun and satisfying. They can sit down at the piano and play for friends and family at a social gathering, playing music which many people may recognize and really enjoy.

The next step would be to play from "fake books" (also called "real books") where the melody is written in standard musical notation but the chords are written with symbols, which of course I taught them when the learned the chords. With this approach, you can learn and play many songs you might not have been able to figure out by ear. (Which doesn't mean you shouldn't still try.) You would continue playing the chords blocked (meaning all the notes at once) in root position in the left hand. This arrangement sounds perfectly fine, although it lacks something that a more complex and elaborate arrangement would have.

The next step, therefore, is moving the chords to the right hand, which frees up the left hand to play in the lower registers of the piano, which gives more richness to the arrangement, as well as being able to add some rhythmic interest. To put the chords in the right hand means that the melody note must always be at the top (the highest note). If it were not, we wouldn't identify it as the melody. (You don't want to "bury" the melody note inside the chord.) That means the chord tones will fall underneath the melody note. Therefore, many, if not most, of the chords will end up being an inversion (as opposed to root position). It takes a while (for many students) for the hand to just find those chords quickly, but eventually it will.

The left hand arrangement will differ if it is a slow, lyrical song, vs. an upbeat faster song. It is beyond the scope of this post to describe the myriad things the left hand can do. But even if it is simple, having chords in the right hand and even just one note (probably the root of the chord) in the left, will give you  a very pleasing result. And remember, if you can do this, without having read the chords in notation, from a book, it means you really know your chords.

Even if you think you want to play 100% classical music, I believe it's wise to devote some time to doing this as well. I've had many people come to me for lessons, and they may play a Chopin Nocturne, but when I ask them to play a simple rendition of Happy Birthday they can't do it. They ask to see the sheet music! Or I will point to a place in their classical piece and ask what chord it is, and they don't have a clue. Even though I've seen it dozens of times, I'm still shocked when this happens. Chords are one of the building blocks of our music. If you play clarinet or any single-line instrument, you don't have many opportunities to learn about harmony (chords), unless you go to a good music school or conservatory, in which case you absolutely are required to learn them. But as pianists, we are virtually never NOT playing chords. So it behooves you to at least understand what you are playing, but even better, to achieve mastery of it.

Are We Having Fun Yet?

 

When people contact me to inquire about starting piano lessons with me, they often say "I'm just doing this for my own enjoyment," to which I reply, "what other reason is there?"

All of my students are adults. Some are total beginners, and many are returning to the piano after an absence. Either way, it is quite clear to them that they aren't going to become concert pianists or make a career of music. This is virtually impossible. (I say "virtually" because there was the case of a man who was a doctor by profession, was struck by lightning on the golf course, and when he woke up in the hospital he had an overwhelming desire to devote his life to music. He became a composer and conductor with a succesful career. But I'm sure you don't want to be struck by lighting to achieve this result for yourself!)

Having fun is goal number one. Yes it's going to be work and effort to make progress and play really well. There are days that will be frustrating and even discouraging. But it will all be ultimately worth it if the majority of the time you find it to be FUN.

Hearing a piece of music come to life under your hands can be very exciting. Opening up a page of music and playing it through is very gratifying. Improvising and/or playing with others can be a great experience. So what are the things that prevent your piano studies from being fun? Here are the main ones.

1. Turning your practice sessions into drudgery. Many people believe that drudgery, endless repetition, and grueling or boring exercises are just part of the territory in learning to play the piano. Not true!! Playing scales, arpeggios or other "finger exercises" for hours is not the way to learn, and certainly not the way to learn to play with emotion and expression. Yet many teachers still will tell their students to do these things. Some repetition is needed, but it must be very targeted to solve an actual problem.

2. Having too limited a "diet." A woman came to see me last week who had been studying piano on and off for several years. She told me she had played almost all the Clementi Sonatinas, as well as some Haydn and Mozart, but not much else. Nothing written in the last 200 years. Since she didn't know anything else, she may not realize what potential fun she is missing out on. But someday she may realize it, and then it will be lot of time lost. In addition to a wide range of classical music, I urge my students to also play some jazz, pop, and Broadway, as well as to improvise. All of these will make you a better pianist, not to mention being fun.

3. Adherence to a rigid method or routine. There are a large number of "methods" (e.g. Suzuki) or curriculums (e.g. ABRSM -- Associated Board of the Royal Schools of Music), and others developed by schools or individuals, too numerous to list here. In Suzuki there must be a strict following of the methods and there is no room for individual differences. In APRSM, there is a curriculum of exercises and pieces which must be practiced and learned in the prescribed order, followed by exams which must be passed before moving on. I really believe this is absurd. Every student is different. Some have a good ear but can't sight-read, others the reverse. Some have good coordination but cannot play with emotion, others the reverse. I find some students keep practicing things they can already do reasonably well, just out of habit, but then ignore other aspects of playing because no one "told" them to do it. I tailor all my lessons to each individual, working more on their weaker areas, but still continuing to improve their stronger ones. Most importantly, all students do not play the exact same music. Before assigning a piece, I want to make sure they enjoy the sound of it. If not, we choose something else that will develop the same skills. You wouldn't expect a doctor to give the same exact medical advice to every patient. Learning to play the piano is not a "one-size-fits-all." Following a rigid plan or schedule makes it easier for the teacher because they don't have to put a lot of thought into each lesson, but it's not better for the student.

4. Bad teachers. By this I mean a teacher who insists you do all of the above mentioned items. Or it could just be the teacher is cold, critical, un-caring, or seems bored with teaching. Or they could be un-professional, unrealiable (e.g. cancelling a lot of lessons). Some are just unqualified: they can't play well themselves and can neither demonstrate nor explain the many aspects of music theory, technique, etc., and wave their students' concerns off with statements like "you don't really need to know that." I have had many students describe their previous teachers as doing all of the above. The relationship with the teacher is critically important. The teacher must be very invested in the student's progress, yet also kind and caring. They need to be "friendly" but not be "casual" about the lessons or expect you to be their friend. Sadly, there are a great number of incompetent and un-kind teachers out there.

I'm sorry if I paint a bleak picture. Of course there are many excellent teachers as well. But sometimes the student has to kiss a lot of frogs before finding the prince.

Hands Crossed

If you are at the level where you are playing advanced or moderately advanced classical pieces, you may have encountered passages where one hand crosses over the other. A notable example is the third movement of Beethoven's Sonata Opus 53 ("Waldstein"), where the left hand crosses over the right to play the main melody. It continues this way for quite a few measures, and returns again every time the main theme returns. The right hand is busy with an arpeggiated chord pattern, so it's more practical for the left hand to cross, than it would be to keep switching which hand plays the chord pattern. It sounds much more smooth as well. 

Perhaps the very first time you try this you find it slightly awkward, but soon you will be used to it and will have no problem, assuming the piece is at the right level for your general abilities. The first time I suggest it to my students they think I am kidding --- or crazy. But then they find it is a fun challenge.

Although Beethoven and the other composers probably would not have known this, crossing the midline of your body with your arms has benefits for the brain. You probably know that the left hemisphere of the brain controls the right side of the body, and vice versa. This is an over-simplification (the brain is far more complex than that), but in general it is true. So when the right half of the brain is sending signals to the left hand at the piano, but the left hand is not where it usually is, but in fact is now on the opposite side, the brain has to develop additional pathways to accomplish the task. If you do an internet search on benefits to the brain of crossing hands, you will find numerous scientific articles which confirm this. It's not just a theory but is borne out by many tests and studies. And who doesn't want a bigger, better brain? It benefits every area of your life, and certainly is important for aging well.

The Waldorf School, a private school for children, has all its students learn a string instrument, such as violin or cello. Of course they want the children to experience the joys and benefits of playing music, but they specifically select string instruments because moving the bow over the strings involves crossing the midline of the body, which has the benefits mentioned above. Unfortunately, brass and wind players do not get this opportunity. Nor do singers.

It is now recommended that parents do games and exercises with their babies and young children that involve crossing the midline with their arms (or legs) to advance brain development.

If you find that you rarely, if ever, have a piece which involves crossing the hands, you can still get all the benefits by simply playing with hands crossed on your own. Select a passage from a piece you are working on that is not too technically difficult, and just cross hands, meaning you will play the left hand's part with the right hand, and vice versa. (You would not be playing each hand's own part but just in a higher or lower register. They each have to play the part they are not familiar with.) Of course you can read the music, and of course you can go slowly. Each hand has no muscle memory for the part it is playing, so it feels like learning it from scratch. However, your ear knows the sound of the music, so it will be assisting you. Don't worry about mistakes; you'll have lots of them. Just continue on.

After you have done this, go immediately to playing it in the normal way, and see if it doesn't feel easier. Don't wait for a later time; do it when the new neural pathways are "fresh." 

To take things one step further, use the hands-crossed method on a passage you are having trouble with. If you have tried other forms of creative problem solving (that is, not just playing it over and over) and it still hasn't improved as much as you hoped, play it hands crossed, and then immediately afterwards play it normally.

I can't promise that every technique I talk about in the blog will work for absolutely everyone, 100% of the time. But I do know that they work. Hands crossed is another tool to have in your toolbox. 

Can Pianists Have Nice Nails?

 

You may think this is a trivial subject, but you will see that it is not.

Even if you are male and have no interest in having longer nails, read on.

When I was a young piano student, my teachers always insisted that I keep my nails trimmed very short, almost no visible white part at all. As a teenager, I was envious of my friends who had longer, lovely manicured nails. If I dared to let them grow a bit, I would get a lecture from my teacher. Alas....

But the reason for needing to have your nails very short is a bogus one. It stems from the idea that you must curve your fingers when you play. Some books say to curve your fingers as if holding a tennis ball. With this curvature, you end up playing on the tips of your fingers. If the nails protrude past the finger at all, they will produce a clicking sound on the keys.

This idea of curved fingers is another example of what I call "300-year-old ideas." It originated with the harpsichord. The harpsichord has a completely different action than the piano. Even then, the idea really had no basis in reality, but they believed it was required to achieve the right sound. And so the idea persisted right up until today, where most teachers will still tell you to curve your fingers.

If your fingers are curved, how can you play an octave or larger? Or a large chord with several notes? With fingers curved you simply cannot open your hand enough to play those. Try it and you'll see. When the idea first arose, with the harpsichord, there simply were no pieces that had the big chords of Chopin, Brahms and Rachmaninoff.

Over-curving the fingers also makes the whole hand tighter and less flexible. We want our hands to be supple and elastic, not muscle-bound and tight. (Once again, another 300-year-old idea says you must build the strength of the fingers, which is not true.)

What we should be doing is playing with the natural curvature of our own hands, which varies between individuals. Turn your hand prone (upside down) on your lap in a relaxed way. Then just turn it over and place your hand on the keys; that is your natural curvature. No one has a completely flat hand, and almost no one has a very curved hand. With a natural curvature, you end up playing on the pads of the finger (where your fingerprint is). 

Generally speaking, you can't play well with very flat fingers. This is because they can't transfer the power of the arm to the keys in this position. However, even though I am a petite woman, I can reach a tenth when I let my hand open up naturally, without stretching, and my hand will be practicially flat. But for someone whose hands are that way naturally, that is how they will play. I recommend you watch some videos of the late great Vladimir Horowitz, who was known for his technical prowess. His hands are practically flat. This obviously was his natural curvature. In fact, you'll see that most professional pianists' fingers are not excessively curved. If your teacher insists you curve your fingers, ask him/her how Horowitz managed to have a huge technigue without curving.

Now that you are playing on the pads of the last joint of the finger, there is no problem for the nails to be longer. Of course, there is a limit. If they are like talons, they are going to bump into the keys and the fallboard, and you will end up with a lot of broken nails.

I keep my nails slightly longer, and I get a manicure regularly. My nails don't "click" nor do they chip or break, and I play many difficult pieces.

Once again, beware of 300-year-old ideas. They don't stand up to scrutiny.

Skim or Dive?

 

In many areas of life, especially when learning something new, you may choose to be a skimmer, or you may choose to be a diver. A skimmer would learn the new skill or subject "well enough," but not at a deep level. You might need to give a talk on the subject, so you study it, but you don't intend to become an expert on it. If you're a diver, you want to go deep into the subject and perhaps attain some level of mastery of it. If you're a skimmer, you can expose yourself to a wide range of material, since you'll spend less time on each skill or topic, but if you're a diver, you'll have to be more selective so you can have the time to acquire the mastery.

Regarding the piano, being a skimmer doesn't necessarily mean you learn superficially. However, many people do just that. They start learning a piece, maybe sight-read through it, but then, when it starts to get difficult to conquer the technical challenges, for example, they lose interest and move on to another piece. There could be some valid reasons to do this: perhaps you want to see if you enjoy the sound of the piece enough to actually work on it. If you don't, you can move on. However, virtually every piece of music affords opportunities to improve your skills; if you don't pursue those, you won't get much out of the time you spent on it. And you'll still have to acquire those skills in another piece in the future. Just "learning the notes" is, by definition, skimming. If you don't imbue the music with expression, nuance, and energy, you are just skating on the surface. No one would want to hear such a rendition, and neither should you.

A concert pianist would have to be a diver. They would need to master every piece they perform, not just in terms of notes, but in order to create as much beauty as possible. However, outside the concert hall, they may enjoy skimming from time to time, to explore new music, perhaps.

Those of you reading this blog are probably neither concert pianists nor aspiring concert pianists. That is fine! Piano is a skill that can be enjoyed at any level, any age, any phase of life. It is my belief that people enjoy it more if they improve and make progress as opposed to repeating the same things over and over. So, for the beginning or intermediate level pianist, let's explore how skimming and diving might apply.

I start my students playing by ear, and add reading later. Whether by ear or reading, the pieces I assign necessitate that the student learn some very basic skills, such as just being able to move your hands around the keyboard (not as easy as it sounds, as any beginner will attest). When they basically have it, we move on. It doesn't need to be "perfect." Trying to get each of these very short beginner pieces perfect would mean you will progress far too slowly. Forget about perfection. You've probably heard the phrase "perfect is the enemy of the good." It definitely is true here. (However, having the correct rhythm is non-negotiable. Once you start cutting corners on rhythm, you may never develop a good sense of rhythm.) So, in a sense, they are skimming, but with a purpose.

Once they are out of the beginner books, I assign pieces that hone primarily one main skill in each piece. For example, Bach's C major prelude from the Well Tempered Clavier, Book I, is a piece where every measure has the same technical skill: broken chords split between hands, which need to be played smoothly connected. Just by working on this piece you would get a lot of practice on this one skill. Of course, it's not just a matter of learning the notes: the teacher needs to show and teach the skill of being able to do this in a way which is legato and well-phrased. This would be a piece which I recommend they "dive" into. We would continue to work on it until it had a "long line" (not be choppy), and had meaningful dynamics, and where the student really engages with it emotionally. It would also be memorized. I have found over the years that my students derive a great deal of satisfaction in playing this staple of piano literature really well.

As the student progresses, we select some pieces to semi-skim, that is, to use as vehicles primarily to attain new skills. Of course I still want them to play with emotional engagement and make it lovely to listen to, but they won't spend long enough on the pieces to really master them. We will choose other pieces that we want to take to a deeper level, to really explore the possibilites for nuance and expression. I feel this approach is best for several reasons. Most students have busy lives and need to practice smart, not long hours. This is the most efficient use of practice time. It is also the most enjoyable. You spend less time on the pieces you like but don't love, yet still get valuable benefits from them. And you spend more time on the pieces you really love.

I once had an adult student who told me that when he was young, his teacher had him work on one piece only for the whole year (yes you read that right!) so that he could play it perfectly at the recital. The teacher wanted "perfection" so it would reflect well on her, of course. Do you think the student played "perfectly?" Of course not; he was so bored and sick of the piece it was probably mechanical and dull. She had him do 100% diving and no skimming. He would have acquired a very limited range of skills from just one piece. And of course he hated the lessons and quit right after the recital. 

It's important for the teacher and student to understand the difference between skimming and diving, and when to employ each.