Teaching Technique: One: Concerning Beginners Who Have Studied For a Few Months.
April 11, 2017
A teacher may make an unintentional error in judgment when he assumes that the student has learned something simply because 1) “sufficient” time has been spent during previous lessons going over it, or 2) judges solely by the student’s outward behavior (the student ‘seems’ to have learned it).
The role of diagnosis on the teacher’s part:
If you ask the student to read from a score a certain note (E.G. middle C) and then play that note on the keyboard, and as a result of the question the student plays a D. To know where things went wrong we would have to query the student to insure that his visual interpretation of the note on the staff was a C, and, just as important, insure that the key that the student thinks is “C” on the piano keyboard is indeed C on the Keyboard.
Otherwise any of the following things may have happened in the student’s mind:
1) The student thought that the note printed in the score was D, and then played the “correct” note based on his assumption.
2) The student thought that the note printed in the score was C, but did not know where C is located on the keyboard.
3) Or consider that the student knows that the visual notation is for middle-C and knows where middle-C is on the piano keyboard. But he didn’t play the note that he thought he did: he meant to play C but made a careless error and landed on the D next to C on its right.
Such a “careless” error is sometimes the result of nothing more than the fact that a finger is an opaque object. That when it is covering and depressing a certain note on the keyboard, the beginner sometimes make the wrong assumption as to what key on the keyboard is lying under the finger in question. The most invisible part of the key is the point where the student’s finger makes contact with it. This can be made more unclear for the beginning student if it is not only one finger that is poised over a single note but as many as five fingers are covering (and therefore possibly obscuring) as many as five keys on the keyboard. Under these circumstance it might be easy to be unsure of the full geometric shape of the key which lies under one of the fingers in the middle in the middle of the hand.
Sitting at the student’s side the teacher may have a clearer view of what key lies under what finger than the student does, and this leads to a false perception on our part as to what may be going on in the student’s eyes. The student is looking at the keyboard from a point of view over the finger and over the keyboard.
What is the most useful way to provide feedback to the student in each of the three above cases? If we ask the student enough specific questions to diagnose the nature of the confusion in time, then our response, though delayed, can begin with the positive affirmation of the part that the student understood correctly, and then an explanation with how starting with correct judgment can lead to an incorrect conclusion.
Sometimes the student seems to have responded correctly but in fact has not really done so.
An example: the student thought that the note printed in the score was D, but was unsure where D is on the keyboard and thus played C but thinking it was a D. This possibility is intriguing since from the ‘outside’ he appears to have read the note correctly and played the correct key on the piano.
In many of these cases, the student makes assumptions that he thinks are correct, and then makes correctly drawn logical conclusions from the first assumption. The student is then confused about his sense of rightness and wrongness. Beginning piano is far from a clear field of sensory information. It can be a minefield of mental booby traps. So much depends on the order in which things are taught, and the student’s own sense of logic of what ‘follows’ from what. A misunderstanding in one thing can lead to a perfectly correct series of ensuing assumptions or judgments. The younger student then learns from the teacher that he is wrong, the distinction between an incorrect premise and an incorrect conclusion being too sophisticated at his age.
We will look briefly at three other similar situations among many others.
Example 1 . At issue may be something as simple as “Where is middle C”?
As teachers we have decades of experiencing recognizing what about the sound of Middle C makes it different from the sound of any other C. To us if the student answers incorrectly, there is a moment when we are likely to automatically ask ourselves “does the student hear that the answer is incorrect.” However only certain students can make this distinction among C-s by ear in the early months of study.
The student bases his answer on something else than sound.
If the student does not have a piano but rather a 61 key electric keyboard, the lowest C is c2, and then by moving rightwards 2 c-s one finds middle C (c4). This system does not work on the teacher’s piano, where middle C is the fourth C from the left end of the piano. Even if the student can accurately ‘hear’ which C is middle-C on his keyboard, he may not yet have the ability to hear the identity between middle-C-s played on two different instruments, though some of us may consider this ability as given a priori to the human ear.
Even if the student works on a normal piano at home, and also knows that middle C is the fourth C from the left end of the piano keyboard, there is room for confusion. We’ll assume the student is clear about left and right. But has he by now come to perceive clearly the topologically repeating segments of the piano keyboard, for instance not counting correctly because of the similarity of the C and the F keys.
Example 2: The symmetry of the notation of c4 in Bass and Treble clef may lead the student to assume an identity between b3 and d4, or to a3 and e4.
They are mirror images of each other in the written score. Two possibilities for an incorrect assumption on the student’s part are, he cannot distinguish between an image and its mirror image, or he can distinguish between the two images but considers the mirror symmetry between the two notes to be of a higher logical priority than whether the note is high or low on the staff.
Was it the student’s fault that the first note taught him was middle C, in both its visual manifestations, and thus was dutifully applying the same principle to other pairs of mirror image notes. What started as a pleasing symmetry to the eye in the first weeks of study (and a possible conclusion that reading notes was not going to be as difficult as his friend Ellen said it was for her) has instead become the more difficult problem to find a reason or criterion for why b3 and d4 (or a3 and e4) should not the same note.
Groups of Similar or Equivalent Terms:
Consider these types of questions for the student:
-Which direction is a higher pitch on the music staff, up or down?
-Which direction is a higher pitch on the piano keyboard left or right?*
-Which direction on the keyboard is the same as up on the staff, right or left?
-Which direction on the staff is the same as left is on the keyboard, up or down?
These questions have to do with “what goes with what?”. It often comes as a surprise to the teacher that after a month or more at the piano the student has difficulty pairing things together.
We should begin by considering all the possible mismatched pairs and triads. Only then can we give meaningful help to the student about this type of situation.
Here is a table of terms that ‘belong’ with each other, about which the student may be still be confused. Or worse, the student is confident that they have mastered this, but they have not. Only after the teacher uncovers the exact nature of the confusion, will he avoid invalidating the student’s self confidence.
Unless I am absolutely certain that the student is clear about these, I will continue to review these associations at lessons. I always consider that the student may still be in some mid phase of understanding even these most simple things. If I am going to err, I always try to err on the side of not taking too much for granted, and being pleasantly surprised if there was no need to worry.
This chart summarizes these associations among terms.
It was my intention here to include a chart. After several attempts at this I have given up. Instead I describe the chart.
Two lines, one running east-west, the other up-down, intersect at their midpoints.
At the top of the vertical line appears this caption:
up the staff, higher in pitch, forwards in the musical alphabet.
At the bottom of the vertical line appears this caption:
down the staff / lower in pitch / backwards in the alphabet
At the left end of the horizontal line appears this caption:
left on the keyboard / lower in pitch / backwards in the musical alphabet
At the right end of the horizontal line appears this caption:
right on the keyboard / higher in pitch / forwards in the musical alphabet
* after first ruling out a confusion regarding which side is left and which side is right.
There is a group of students, who after several months of lessons, are declared as lacking the necessary talent to learn piano. This conclusion is wrong if we do not first give the student ample time to re-make or re-shape their judgments about things. The problem, easily fixed with patience, lies in fundamental misconceptions. Things so basic that the teacher tacitly assumes the student should know a priori.