Piano World Home Page Forums Our Most Popular Forums Piano Teachers Forum "Fundamentals" of piano playing?

I'm an adult beginner, and I have a question for piano teachers. I'm not sure if I can articulate it well enough, but here goes...

What "fundamental" or "foundational" things are you looking for when you watch a student play? By fundamental or foundational I mean core technique or concepts that underpin all of piano playing.

For example, I teach math, and when I'm helping students, I'm looking for fundamental mathematical understandings rather than the particular skills / problems currently being practiced.

For example, when solving simple equations such as 2x + 1 = 7 (does anyone remember these, does anyone care??) some math teachers will concentrate on what I consider to be superficial mechanical steps that aren't mathematical in nature, such as:

• "When you move the 1 to the other side it changes sign"
• "When you move the 2 to the other side, it changes to division"

Of course, the symbols aren't actually moving. We're performing the same operation to both sides of the equation to maintain the equality.

Instead, I try to focus on what I consider to be fundamental mathematical ideas:

• That the "=" means the two sides are equal, rather than the more common "write the answer"
• That the steps to solving an equation involve mathematical operations (e.g. subtract one from both sides of the "=", rather than "moving things to the other side"
• That the solution is a value for the variable that will make the left side equal to the right side

Or perhaps when solving problems in trigonometry, some students and teachers use a flow-chart to decide which equation to use. The flow-chart will include things like "do you know two sides and need to determine one angle". The problem is that this "flow-chart" approach obscures the core fundamental issues, which are quite straight-forward and based in simple logic:

• Pick an equation such that there will only be one unknown quantity
  e.g. If you write a^2 + b^2 = c^2 and you don't know b or c, then you can't use this equation to determine "a"
• Pick an equation that includes the unknown you're looking for
  e.g. If you write cos 15 = 10/9.7, it won't help you determine the length of the side opposite to the 15 degree angle (it doesn't show up in the equation)

Anyway, this wasn't meant to be a treatise on my theories of math education! But perhaps this has helped clarify what I mean by "foundation" ideas. (Or perhaps not :-) )

So I'm curious what you piano teachers think are fundamental, and thus worthy of saying they underpin all of your analysis of student performance.

Looking forward to your responses!

Wow! That's a clever way to arouse interest of piano teachers . Not being a teacher, but an adult beginner, I'm also looking forward to possible responses!

Quick thoughts though:

• playing piano is not algorithmical, unlike solving equations, at least at this level
• if any parallel is to be drawn, I would ask you what fundamental things are you looking for when you watch a mathematician creatively making a discovery in mathematics
• nevertheless, piano playing involves techniques which must be automated, and to this extent in may be compared, at a very abstract level, to solving equations by mechanically applying formal transformations.

And, again with the proviso that I'm not a teacher, it seems to me that piano pedagogy cannot be reduced to a few "core" concepts which might be well described in the forum post format. But I would very much like to be proved wrong.

Hmm, I like this question!

But the part I like is thinking about the ways in which music and maths are similar or dissimilar, and one of the important dissimilarities is the holistic experience that is music as compared to the almost exclusively abstract thinking experience that is maths.

An equation doesn't elicit nostalgia, energy, laughter, or longing, but even if you have had no training as an instrumentalist you will experience these responses when you hear music.

On the other hand there are numerical aspects to the way music works that makes it seem related to maths, and the fact that it is a symbol system outside the paradigms of language creates another instant likeness.

The fundamentals of playing the piano (vis-a-vis maths) are that it is a physical experience, and that until your body understands it your mind hasn't fully grasped it either. There is nothing abstract about using your body to create meaning, and training your body to perform in flow is the purpose of practice.

I'll sleep on this, but again, love this question!

(as student)
I have seen it described by piano teachers are "principles". Here are a few examples that I have gleaned (since I look for them, and consider them like little diamonds hidden in the sand when a teacher drops a gem like that in PW or elsewhere).

- fingering: the shape (3 + 2 black keys, height & size) of the keyboard + the size of fingers + the logic of where your notes are going are what determine fingering. I.e. there is sense behind it rather than sequences of finger numbers to remember. ... from there we might see some principles of certain finger patterns, such as for example of your notes have all black keys.

- fingering: that it is paramount in piano.

- awareness of what area of the keyboard your hand will be on for a length of passage, and which span of hand - preparing your hand for it - anticipation (exists in all instruments) so that you don't vaguely drift in and out of things.

- understanding what a chord actually is. majors & minors as stacked triads where notes can be moved around, where 1 + 5 form a P5 and the middle note determines major or minor. Inversions and what they are, as well as the visual pattern in written music, and tactile & visible pattern in the keyboard. also, that chords have a mood or flavour, and that sequences of chords will make the music move (V7 - I = tension - release (homecoming) )

There is another approach to music which does not stress fundamentals, which might be called utilitarian. "You do this" in order to play a piece. Or an explanation of a chord is dashed off by describing the notes of an inverted 7th chord that has had the 5th note omitted, without ever explaining the whole thing. You memorize the thing and don't worry about it making sense.



I think there is plenty of that in music, as well as approaches that don't go that route.

I have tutored kids at the beginning level of algebra and based on that, I would go one step further, which may give a greater link to music. Typically, the kids don't understand basic division and addition - that is to say - the principle behind it. They have memorized 2 + 3 = 5, and 30 / 6 = 5. 2 + n = 5 stumps them. I take them back to sharing marbles (with actual marbles), dividing pies, moving things around physically. Before even getting to the balance that you are writing about, they have to understand the concept of that balance with concrete terms. What is addition and multiplication? The schools will have done stuff with "counters" and making red symbolize negative, blue symbolize positive - but if the teacher doesn't grasp the principle this should impart, it remained a rote meaningless activity. "When you run out of blue counters you start using red ones."

Somewhere in my musical training I would like these principles to be brought in. I understand that they might be incorporated in some innocent "simple" exercise where I might absorb it through the doing - or through actual explanation. If explanation, I would hope to also experience it through physical exploration (playing) and listening for it, as well as seeing it being part of music. I would NOT want to be given tricks to help me play the piece, for the sake of learning to play the piece - that would be the opposite, and "utilitarian".

Sorry for the length. It is something that I've also thought about a lot as a student.

I think that the 2nd par. is the hardest thing for us to grasp, since we have entered the stage of forming concepts if we begin as adults or teens. If we understand something as a concept intellectually first, then we are close to interpreting it according to what we know and imagine. If we experience it first, and then are given a name to the experience, then the concept gets tied to the experience and comes closer to the real meaning. If we start with the concept, we may actually impose how we first "understood" it onto the experience, and then experience what we imagine we ought to experience - and never get there. It is a poor metaphor to say it is like language learning, where you impose what you already know about language from your mother tongue, and so you speak with an accent and weird syntax.

In this society especially, we are dependent on our intellect, and judged by our intellect. There is something in an educated intelligent adult that balks at the idea that they senses can give a "knowledge" which the mind must grasp second, not first. It would have to be some kind of balance (??) A baseball player does not work out the mathematics and physics of forces and trajectories even though he uses these. But possibly a professional does reach a point where he also studies the abstract principles behind what he does. (?)

The trick seems to involve letting go to the experience as a child does, so that the experience will teach - and hope for a teacher who will be providing those experiences. And not dismiss the "silly really simple part" which might actually be that part that gives those fundamentals. But as adults many of us do actually want to get at principles and are ready for them in a way a child is not (at least not abstractly). More (?)'s.

Hi Glen,

I have tutored young teenagers in mathematics, and I admire your "analytic" troubleshooting approach: identifying basic building block of knowledge and understanding, knowing how these blocks build on each other, and finding out with which ones the student is having trouble.

I think regarding reading and music theory, the same approach is very possible and very useful. I spoke to my sister (teaching music in the classroom) and we talked about how she is restructuring the classroom curriculum, how she wishes to tackle note reading in smaller steps (than the book does) to build a strong foundation.

But that's just music theory. "Piano playing" in general would be harder to analyze, I don't think there would me much consensus on what the fundamentals are. Still, even with such a "holistic" activity as piano playing, a good teacher would try to identify a few specific skills that can be improved, find appropriate repertoire to practice those skills, be able to order the repertoire by difficulty, know how certain skills build on other skills etc.

Actually, one of the fundamentals of math, to me, *is* physical - I have found, when teaching basic math to adults, that many of them got disconnected around fourth or fifth grade, when the concepts started being taught more abstractly and with pencil and paper, rather than with "manipulatives" as they are called - physical objects a student could move around and use to have the concepts in their whole body and from a holistic point of view. Which is a large part, I think, of what Glen R. is addressing when he teaches that you don't "move a symbol to the other side" - that's not at all what's happening. One is making sure that the numbers that are represented by both side of the equation are the same numbers, and why what is remaining makes the numbers in the original equation the same number on both sides. And often what is missing is a sense of what it means to "subtract" from a whole and look at what is remaining, or to "divide" a whole into pieces and look at the pieces - a, quite literally I think, physical number sense, so that the symbols look arbitrary rather than representative.

In music, to me, this might have a parallel to learning to translate notes on the written page without learning to listen to how they sound and how they sound together, whether harmonically or rhythmically. Or, with a student's posture, or finger or arm movements, not understanding how they relate to the piece as a whole and help get them from one phrase to another, or what the difference is in the sound they produce - whether it becomes more detached or more connected, or can be louder or softer, or any number of other basic music-making, not note-reading, effects.

And I think that good teachers of any subject look for those kinds of concepts, and look for ways, as Glen does and as many of the teachers here do, for ways to break it down and address fundamental issues in the context of a larger whole, and that the fundamental issues *are* the larger context in some sense.

If that makes sense

Cathy

Wow, lots of interesting discussion already! Just a clarification regarding my discussion of math-- I wasn't trying to draw parallels between music and math. I was just trying to illustrate what I mean by “foundation” or “fundamental”.

I also wasn't trying to imply that piano playing or pedagogy can be boiled down to a few simple principles. However, I suspected that many piano teachers have their own core principles—whether they've explicitly analyzed and thought about them, or they implicitly know them because they keep commenting on the same things to their students.

Agreed.


Body understanding being primary and mind secondary—I like it.


And that's exactly what I'm hoping to find! And of course there's also the intellectual stimulation of seeing what teachers in a totally different field consider to be important. I really liked the points you listed—that fingering isn't just sequences of numbers to remember, and that understanding what a chord actually is, is important.



I think a big problem here is that they've learned that “=” means “the answer is” as opposed to “the expressions on each side of the = are equivalent”. And going back to concrete terms is exactly what current math pedagogy suggests. There must be concrete understanding prior to abstract symbolic understanding.

As a high school teacher, I see the results of non-math specialists teaching jr. high and elementary all the time. Makes me want to teach grade 2 math!


Ditto! There's definitely a math teaching analogy here—I see many math teachers (of all levels) who concentrate on teaching algorithms to get “the answer”, as opposed to mathematical principles / concepts that promote deep understanding.


Agreed. Many times I have thought about how to provide students with hands-on “play” time to understand things (in my case mathematical concepts). Then once they get an intuitive feel for them, revert to “traditional” teaching where I can help them organize their intuitive understanding into a more formal framework, using formal mathematical notation.

Loved your post. You described the math analogy way better than I did! And of course your thoughts on piano pedagogy.

P.S. I changed my picture just special for you :-) (It's been a while since I posted here...)

Thanks.

As for your picture - ah, yes, now it's syblings And apparently happy ones. You look like you have a happy family - they're beautiful.

Cathy

One of the most fundamental things I've discovered during my
long experience with the piano is that our hands are woefully
underdeveloped for piano playing.

Make a loose fist with a hand, and with the palm facing down
open the hand quickly, then close it again into a fist. What is
underdeveloped in all hands, in my view, is the muscles that open the
fist, since all of our daily actions with our hands are of
the grasping, gripping variety. The opposite action, that of
opening the hand, is never experienced in our daily activities,
thus, this aspect of the muscles is almost non-developed in
the human hand.

You might think, so what? In playing the piano, it seems that
we are using the grasping/gripping muscles of the hand,
since we seem to be "clawing" at the keys when we play. But in
my experience, the opposite is true, that is--in a
seeming paradox--the muscles that open the
hand are actually much more important in playing
than those that close the hand. This is why people who squeeze
a rubber ball or a spring-type grip strengthener, to help
them with piano playing, accomplish nothing that way--they
are exercising the wrong muscles.

Since I've started working the muscles that open the hand, it
has transformed my playing. This is what I do. Close a hand
into a loose fist, then with the other hand hold each of the
five fingers--starting with the thumb and ending with the
little finger--down as you try to open them in the motion as
when you're opening the fist. This exercises the fingers in
a way opposite to when you squeeze a ball, which is exactly
what you need for piano playing.

i kind of agree with you here Gyro.. i find that I have achieved greater control by concentrating on the 'uplifting' muscles of the fingers.

i like to open and close my fingers, one at a time to and away from the thumb.. in an orderly fashion when my hands are at rest.

1) Is the student reading the notes, absorbing the concept that at no time does a finger number indicate the correct note? For this I hammer on the idea that there are 88 keys, and that in advanced music any finger of either hand may, at some time, play any key, that fingering should never be used as clues to find notes.

2) Is rhythm being developed? Can the student play music counting (or mastering rhythm in some other way) so that music sounds right? Music without rhythm is just notes.

3) Is a sense of fingering being developed leading to the student being able to work out fingering for him/herself?

4) Is a sense of balance developing so that one hand can be played louder than the other, and can this be reversed?

5) Is the sustain pedal being used correctly?

6) Is the hand shaping in a natural way, and do the fingers begin to conform to the shapes of the keys that they are playing?

7) Is there a lack of exaggerated movements (economy of movement) combined with natural movement that does not in any way signal unnecessary tension?

8) How is the posture?

This is just the beginning. The overall concept is to develop habits that are useful and sane in a way that leads not to blind following but increasing exploration.

Well, if we compare with math - Romanian curricular practice (after French and Russian models) has been pushing abstract concepts. An algorithmic approach and some intuitive understanding was used mostly at elementary level - afterwards the foundation being abstract logic and endless chains of "For every X there is an Y such that..." proofs. Student understanding and applications were much neglected. But... those who survived this system and migrated to the West found the foundation very useful ;-)

What music has in addition to math is flow in time. The oft suggested ways to practice extremely slowly produce something very unlike the intended musical effect (all the more with instruments like the piano or harpsichord, whose sound decays, and fast). Such time-constrained math is very rare - except, say, trajectory control of missiles, or industrial process control, where formulas are already proven for a computer to execute.

For me personally, this hits a serious limit especially with multitasking, the more steps are involved in decoding the blobs on paper, joining the #/b of key signature, jumping hands and fingers to proper places, timing of pedals (and accurate placing of feet on organs too) etc.

Such that 'easy' pieces like the Minuets for Anna Magdalena Bach are at my upper current level, and Invention #1 beyond the level reachable with practice I can envision myself...

Where the link with math comes again is a principle to solve complex problems: train until each component comes easily and with minimal errors - only then join more components. And so this seems a Sisyphus' task... each tiny progress only requires more work :-(

It's absurd to try to solve a problem of 100 parts if each part has 1/10 chance of getting it wrong ;-)

Students are often able to play many things close to the speed they should go, but the rhythm is very uneven. Concentrating on counting, for example, actually make things sound WORSE, for awhile, because it slows them down to the point that even though they are correct, mathematically, they become unrecognizable to most students.

The solution is to master the *skill* of counting so that it becomes automatic and no longer fights with the finger numbers or other skills already mastered. I work with students on this skill by reviewing their most basic, beginning materials and nailing the skill of counting at tempo, then adding this skill, piece by piece, until it all falls into place.

It's a process. Counting is another tool. It only works when it is used for the right job.

Because as a child I lacked concentration I couldn't do arithmetic. When in grade 7 we got to Mathematics I consistently got in the 90%'s. The difference is that calculation is chalk to equation's cheese. The former takes control over time (concentration), the latter is instantaneous (understanding).

Gyro the extensors are much, much weaker than the flexors but still enormous compared to the intrinsic muscles. (i.e. plenty strong)

Yes to the type of things below. Those are the kinds of things being hoped for, and they are also the kinds of things we as students would not think or know of, and thus not aim for or be able to observe in ourselves. There are parts we can aim for ourselves if we know about, and commonly do - such as learning to sight read - and other we may not. This may often be because we don't even know about it.

Yes! gravity (and arm weight) takes care of the dropping.

No, finger weight is pretty useless while arm weight often too unwieldy.

Thanks! This is the type of thing I was looking for.