'Generalization' in the context of Piano Learning

One of the skills that separates a High Achieving student from an average student is their ability to 'Generalize'.

Generalization can be said to be the ability to conceptualize from a data set by making inferences.

Students who Generalize often teach themselves new materials as they are able to learn faster, deeper and a lot more, which in turn adds and feeds into their already large vocabulary of understanding.

In the context of Piano Learning, Generalization occurs when the student is able to use the following Operations independently:

1) Same and Different: When students can see/hear/feel/perceive the 'Same-ness and/or Difference' in Rhythm or Key/Meter/Tonality/Harmony/Style, etc,.

Example of 'Same and Different' in Piano Learning: Let us say that a student is learning to read a new piece. They figure out that the piece is in 'A-B-A1' form, and they are able to see that the A1-Section is Same as the A-Section but it differs in the Accompaniment Style. Ie, A-Section has Blocked Accompaniment while the A1-Section has Alberti Accompaniment.

2) Extrapolation: Extrapolation involves extending or predicting values or information beyond the known data points or existing range. It means using existing knowledge to make educated guesses about situations that lie outside of what has been directly experienced.

Example of Extrapolation in Piano Learning: Suppose the student has been practicing playing arpeggios in a certain Key. Through extrapolation, they naturally apply the same technique and fingering to play the arpeggio in a higher or lower octave with a Melody in the other hand, even if they have not specifically played something like that before. The student is able to predict its application in a different context in the music.

3) Interpolation: Interpolation involves estimating values or information within the known data points or existing range. It means using existing knowledge to fill in the gaps between known points or to navigate situations that are slightly different from what has been directly experienced.

Example of Interpolation in Piano Learning: Let's say the student has practiced a specific passage in a piece that involves a sequence of chords. Each chord has a designated fingering, and the student has practiced them extensively. However, there is a section in the piece where a new chord appears without any finger numbers given, and student is unsure about the fingering indicated. By using interpolation, they analyze the fingering patterns of the surrounding chords and find a logical and comfortable fingering for the new chord. Here, they are using their knowledge of adjacent chords to estimate the appropriate fingering for the unfamiliar chord.

4) Stipulation: Stipulation involves setting specific conditions or requirements for a particular situation or event. It means establishing rules or constraints that must be followed.

Example of Stipulation in Piano Learning: Let's say the student is studying a piece of music that has a fast and technically challenging passage. The Piano Teacher expects the passage to be in the fingers by following lesson. The student then is able to Stipulate that they must practice this section at a slower tempo first with Metronome and Correct fingering, ensuring accuracy and control, before gradually increasing the speed. They are good at making stipulation to achieve the set goal by establishing a structured approach and routine to master the difficult section.

Concluding Thoughts

Students who have developed the ability to Generalize are usually good candidates to put through the linear track of Piano Exams by doing an Exam a year.

However, for the many students who do not/are not able to Generalize easily, it may be wiser for the student to learn to Generalize first.

This may be done by assigning a lot more pieces than you would for a student that naturally Generalizes.

Each Piece must be similar to a previously learnt Piece with small but with noticeably concrete differences, and the teacher may need to specifically spell them out by leading them with questions.

Note that this would also mean counselling the Parents that the next exam may not happen in the next year as these skills need to be filled which would need more time.

Typically parents start to expect an Exam Grade a year (which may be possible in the early grades even with a low Aptitude Student where the teacher can teach pieces by Rote), however this progress hits a wall come the middle grades.

Teachers hopefully are able to educate the parents on the different aspects of Piano Learning as there are a lot of mis-expectations when it comes to Piano Learning. They (the parents) begin to compare Piano Learning with other Academic Subject that the kid learns in school.

A common expectation is for the kids to finish Grade 8 by the time they finish High School because another friend did so.

However what they are not able to perceive is that the other kid is good at Generalization and their own child is not yet there, and ego comes in the way of accepting that reality.

I feel many Piano teachers struggle with being able to articulate about 'Generalization' as a concept other than just say that so-and-so student is 'musical'... What they're actually trying to say is that, a particular student is able to generalize naturally apart from being high aptitude.

Piano Teaching as a Profession is fairly in its nascent stages in India, so teachers may also be figuring their way around different kinds of challenges they could be facing.

My hope is to be able to share my experiences by shedding light on different areas of Piano Teaching and Learning to make this journey smoother for all parties involved, setting Expectations being a primary one.