I’m proud to announce my most recent music publication: a four-piano arrangement of the opening chorus (“Herr, unser Herrscher”) of St. John’s Passion, available at Orange Note. A high-quality computer rendering of the full work can be heard there. The work was commissioned in 2025 by Piano 4te, the same group who commissioned my four-piano original work, Cosmosis. Piano 4te will be performing the world premiere of the work in December 2026 in Pittsburgh, PA.

This chorus is my favorite of all of Bach’s choral works, and it has been a decades-long desire of mine to produce a piano ensemble version of this music. It is a monstrous, 10-minute long piece of intensely passionate music. The piece quickly dispels of any notion that Bach writes his music in a purely cerebral way, void of any emotion or passion – a notion that I can’t entirely blame intermediate piano students for having when their primary exposure to Bach consists of inventions and sinfonias. In fact, I can’t think of any other piece of music that has more emotion packed into it.

When I was asked to write another work for Piano 4te, for some reason, I decided to revisit this issue, and try out a solution that I had dismissed a thousand times before: simulating the sustaining quality of the woodwinds via measured tremolos and repeated notes. I had previously thought this would be an obnoxious effect not even worthy of pursuing, but once I gave the technique a fair chance, I was more than pleasantly surprised at how quickly the listener “normalizes” the effect throughout the piece, even when these notes are played fairly prominently. “Solving” the problem by always playing those notes softer than everything else doesn’t solve the problem, because sometimes these voices are the only thing going on in the music – fortunately, it turns out it’s OK for this effect to be prominently present.

The work follows an A-B-A structure, but when section A returns, I give it a fuller texture (more notes/octaves), and I take some liberty to give it a different dynamic plan.

In the end, this four-piano arrangement represents not just a transcription, but a heartfelt dialogue with Bach’s masterpiece—one that honors his unparalleled emotional intensity while embracing the piano’s unique voice. By expanding to four instruments, I’ve aimed to preserve nearly every layer of his rich contrapuntal tapestry, allowing those profound suspensions and majestic proclamations to resonate fully in a new medium. I’m deeply grateful to Piano 4te for inspiring this revival of a long-dormant dream, and I can’t wait for audiences to experience the dramatic power of this music when they bring it to life in the world premiere next December. If Bach’s “Herr, unser Herrscher” has ever moved you, I hope this version will capture that same grandeur amid degradation, restlessness amid lamentation, in a way that feels both faithful and freshly alive.

“I often wish I could see my students every day, the way public school teachers do. But, this is a practical world, so we have to find ways to follow through at home, to be with them in every practice period, even without being there personally.”

Louise Goss

Most students lack metacognition, or they don’t demonstrate metacognitive skill by putting their metacognitive knowledge to use. Articles 2-8 attempt to remedy this as much as possible through tangible, practical strategies for both teacher and student. But there is still an upper limit to what we can do when we only see students once each week. This and numerous other limitations of metacognition-oriented teaching are addressed effectively by MetaPractice. MetaPractice is an app (for both web and also iPhone) into which I’ve poured my life blood (literally countless hours) over the course of almost a decade, based on all of my obsessive research into metacognition. I designed it, but I didn’t code it – I paid 85 bajillion dollars (give or take a kajillion) to have it coded, and it is released through Orange Note. It is actually two apps: MetaPractice Teacher, for assigning and evaluating goals, and MetaPractice Student, for practicing goals. The introduction video is here.

Article #1, Defining the Problem, outlines a number of metacognitive issues in musical study. Perhaps the most serious of these issues is the tendency for students to play all the way through a piece / pleasure seek / practice while in stage 3 “autonomous” mode. Even when students cognitively know how they should be practicing, they still tend to practice like musical snow plows since we are not there with them. MetaPractice significantly helps to address this issue by allowing the teacher to set each student to Beginner, Skilled or Advanced mode, and these modes affect how many goals the student is shown at a time (one goal at a time, one piece at a time, or their entire goalbook at a time). This powerful tool is demonstrated in this video (1:47). Also relevant is the tendency of students to practice certain things more than others or to skip over some things entirely, and this is addressed in a video students see about pausing and postponing practice (4:41).

Article #2, Quantifying Practice Quality, discusses the benefits of giving tangible feedback to students in the form of Trouble Goals and scores, which also encourages teachers to assign goals that are specific and measurable each week. MetaPractice gives teachers the option to use trouble goals and scores to make their feedback to students and parents more effective. This video (4:59) demonstrates how Trouble goals work in MetaPractice.

Article #3, PIT Practicing, outlines a simple framework that students can use in practicing and that teachers can use in helping students reflect on their practicing (see article #6, Reflection). This framework is especially useful for spot goals and spread goals, both of which are discussed in article #4, Goal Types. Not only does MetaPractice allow goals to be assigned with these goal types, it also adjusts students’ practice routine based on how the goals are assigned. MetaPractice also offers “goal guidance,” giving students a way to engage in a drilling game for individual goals analogous to the “jelly bean game” discussed in Article #3. PIT Practicing and goal types are even explained to students in videos that are available in Help areas of MetaPractice. See the following videos for both teachers and for students:

A critically important aspect of Article #8, The 1-3 Rule, is backward practicing, and MetaPractice offers this option via its Goal Sorting feature shown in this video (4:06). Note that Article #5 (Goal Interactions) discusses the importance of recognizing strategy in how goals are ordered. The teacher’s Universal goals video above touches on this, showing that teachers can specify whether Universal goals are listed first or last when shown alongside other goals.

MetaPractice also offers a lot of what might be called “convenience” features, such as its core ability to organize the goalbook with categories, subcategories and goals (2:11), a media library (2:55), templates (3:04) that allow teachers to save and load commonly used lesson plans, an audio scratchpad (1:42) that makes quick temporary recording for review easy, badges (2:39) that help teachers identify what was neglected in the previous lesson, an interface for completing pieces and a powerful repertoire list (4:42), and goal memory (2:14) to help teachers know when a previously completed goal reverts to a bad habit.

Other relevant links:

Official MetaPractice website
OrangeNote Facebook group
YouTube playlists for OrangeNote products

(c) 2022 Cerebroom

The most obvious metacognitive guidance to give to accompany these open-ended goals is to first analyze the piece: identify key, look for difficult spots to start practicing now, find patterns, etc. This is great advice, and also commonly advocated by many teachers. But this advice just isn’t enough. What is less obvious is how to get students to use metacognitive skill in planning, executing and evaluating the practicing of new material when the teacher did not necessarily offer any specific strategies. These skills include:

1. Prioritize: practice material that is in the worst shape first each day;
2. Chunk size: work on manageable chunks of music each day rather than being a musical snow plow, playing through way too much material mindlessly without much repetition;
3. Daily progress: work on chunks with enough repetition so that daily progress is significant rather than barely noticeable;
4. Practicing backward: work from the end of the piece to the beginning.

Of course, a teacher can explicitly tell students to do all of these things, and maybe some students will be successful. But most won’t be successful with even half of these things just because they are told to do so. To accomplish all of this at once, there is one single rule which acts as an algorithm that is simple to follow, killing all four metacognitive birds with one stone.

Before introducing this stone, let’s clarify the idea of “practicing backward,” which means different things to different teachers. Most teachers define this to be always starting at the end of a piece, and working toward the beginning. Even when beginning a new piece of music (the first day the student ever practices the piece), the student works on the last couple lines or last page. The common argument in favor of this strategy is that the student experiences more and more comfort/security while performing the piece as the piece progresses, because the closer to the end the student approaches, the more total practice time has been spent on the material. There may be some truth to this, but unfortunately, this is a zero-sum gain: it also means the student will be less secure in the beginning of the piece. Students tend to be more nervous when they first start playing than they are after a minute or two and they start to approach the end of a piece, so it would seem that more security would be needed for the first 10-30 seconds than at any other point in the piece. This assumes the piece is well-prepared; if the piece is not well-prepared, then the likelihood of heart rate and nervousness increasing as the performance progresses goes up as the student inevitably accumulates mistakes throughout the performance.

But no matter, because the idea of “practicing backward” used in this article has nothing to do with gaining psychological comfort as a student performs; it has to do with minimizing temptation to pleasure-seek (i.e., play all the way through) as the student practices. If one practices measures 8-12, then 24-34, then 56-60, etc., every single repetition of those chunks carries a huge temptation to go on and continue playing prematurely, before enough repetition has occurred. Sometimes students willfully give into this temptation, or perhaps they accidentally get distracted and forget they are drilling. But if these spots are drilled in reverse order (108-112, then 88-98, then 56-62, etc.), the student’s temptation to “keep going” is greatly reduced or eliminated. To keep going would mean to quickly approach material they just finished drilling five seconds ago. A student would be mentally and emotionally tired of that spot they just practiced, so the student doesn’t goes on. Finally, when the student reaches the beginning of the piece, they perform all the way through as “dessert” for the discipline of drilling, reaping the benefits of all the drilling they just finished (but still stopping to drill more if additional problems are encountered).

The benefits of careful prioritization, intelligent choice of chunk size, daily progress from sufficient repetition, and practicing backward are produced with the 1-3 Rule.

The 1-to-3 Rule

Suppose we define a “security scale” from 1 to 10 for how well a piece (or section of a piece) is prepared:

1. Unknown: Not started yet (resembles sight-reading)
2. Very Uncomfortable: Frequent stops/stumbles at any tempo
3. Uncomfortable: Still frequent stops/stumbles, comfortable to play only at an extremely slow tempo

4. Barely Comfortable: stops/stumbles infrequent or nonexistent at a slow tempo
5. Comfortable: stops/stumbles infrequent or nonexistent at a somewhat slow tempo
6. Very Comfortable: stops/stumbles infrequent or nonexistent at a moderate tempo, often partially memorized
7. Extremely Comfortable: stops/stumbles infrequent or nonexistent at a faster tempo, almost all memorized

8. Secure: Memorized, ready for an informal performance such as a group class
9. Very Secure: Ready for a recital or festival
10. Owned: Ready for a competition

The 1-to-3 Rule is as follows.

EVERY DAY:

• Bring some part of the music that is in the 1-3 category into the 4-7 category that same day
• Improve previous 4-7 material
• Improve previous 8-10 material
• Play entire piece

One could write this more concisely and just explain it to students in words:

• 1-3 –> 4-7
• 4-7
• 8-10
• Play

Here is what is accomplished by this seemingly simple, almost juvenile rule/algorithm. Suppose a student has already been applying it on a new piece for a couple weeks:

• First, the student is forced to evaluate and quantify exactly how well they think they know various parts of the music. They are forced to prioritize each day, which in turn helps to avoid stagnation. They know they can’t begin with what is familiar (pleasure-seek) because the algorithm says to work on 1-3 material first.
• Once the student identifies the first place in the music that falls in the 1-3 category, the student must strategize about how large of a chunk to work on. The student might think, “I know my teacher won’t be happy if I just bring one single measure into the 4-7 category today, and I know I could never do 8 measures. Maybe I’ll try 4 measures today.”
• In order to bring the selected material up into a 4-7 range the same day, the student is forced to engage in more repetition than most students normally would, deriving great benefit from small amounts of time. Because the student is constantly trying to optimize chunk size and repetition, the student makes daily progress that is sometimes magnitudes beyond what was previously experienced with the non-strategic “play from the beginning until I get tired” strategy.
• Supposing the “1-3” material one or two days ago was measures 36-40, today’s “1-3” material might be 41-45. The next newest (more secure) material today would be 36-40 (yesterday’s “1-3” material). After that it would be 46-50, and so on. While learning or securing a learned piece, even though a student is progressing “forward” through the piece from one week to the next, this automatically causes a student to practice backward from one minute to the next. When a piece is fairly strong (i.e. when everything is “8” or above), the practice routine will continue evolving to the point where a student jumps straight into all the weakest parts of the piece (whether it is backward or forward), practicing those spots first, then performing the piece, which is an ideal general strategy in preparing for performances.

Very often, a chunk that is raised from the 1-3 category into the 4-7 category drops back down a little the next day. For example, “1” material might be brought up to “4” on Tuesday, but then on Wednesday when first starting to practice, it feels more like “3.” It’s fine for a student to begin with this “3” material again that day since it is still part of the 1-3 category (but by the end of practicing that day, it should be at a “5” so it doesn’t fall down to a “3” the next day). Even if students take a couple days to solidify each chunk, this still avoids stagnation.

Over the course of weeks and months of doing this, the student builds extensive metacognitive knowledge about themselves. Having to continually quantify (assign numeric values to) previously practiced material causes students to continually adjust their idea about what it feels like for material to be “learned” or “secure.” Practicing weak material first produces progress that is more rapid, not to mention higher quality as mistakes are more likely to be caught. This in turn helps students to learn just what they are capable of doing in a day’s practice, not to mention rapid progress experienced over the course of many weeks will often become addictive and “fun.” Students learn through experience the difference between playing and practicing – they learn to stop lying to themselves when they say “I practiced” when they really just played.

Most of all, one could almost call this routine the “Delay of Gratification Algorithm.” The 1-3 Rule trains students to seek out weakness first rather than sitting down and immediately pleasure-seeking at the piano.

Article #9 (the final article) in this series will discuss MetaPractice.

(c) 2022 Cerebroom

References

Son, Lisa K., and Nate Kornell. “Simultaneous decisions at study: Time allocation, ordering, and spacing.” Metacognition and Learning 4.3 (2009): 237-248.

“A man cannot search either for what he knows or for what he does not know. He cannot search for what he knows: since he knows it, there is no need to search; nor can he search for what he does not know, for he does not know what to look for.“

Plato

Part of the reason reflection (discussed in the previous article) is so important is because it makes the student part of the goal-assigning process, which is far more effective than being corrected directly by the teacher. While reflection with the teacher may not be 100% pure, unguided self-correction, it is certainly closer than if the teacher just plainly describes the problem and prescribes the solution. In a way, it turns the teacher into a diplomat according to Daniele Varè’s definition: “Diplomacy is the art of letting other people have your way.” Robert Duke (2012) succinctly points out that “Learning is error correction,” so of course whether the error correction is self-imposed or comes from a teacher doesn’t matter as much as simply making sure the correction (i.e. learning) takes place. But keeping this “diplomacy” in mind, the most elegant, artful teaching would cause students to feel as if assigned goals every week were their own idea. Even more effective is when pride comes before the fall:

“A person pays more attention to the correction of an error he makes when he committed the error under high confidence, and this added attention leads to better memory of the correction.”

Butterfield & Metcalfe, 2006

Self-error-correction, especially in its purest form (independent, unguided by a teacher) motivates a brain to commit an experience to memory far better than when errors are corrected by teachers. Duke elaborates that memory resulting from self-directed error correction will always be more persistent, understandable, and generalizable than memory from a correction directly from the teacher. But not every teacher capitalizes on this. Duke writes that well-meaning teachers:

“…correct their [students’] errors efficiently, consistently, and ultimately, unfortunately, in ways that limited their [students’] own cognitive involvement (and cognitive effort). Not good. Not enough (self-directed) error correction.

Aiello (2003) agrees, saying that the model of teaching that involves a lot of teacher modeling and student imitation:

“…does not foster a dialogue between the teacher and the student. It does not encourage the student to ask questions. … Such an imitation model does not necessarily foster metacognitive abilities.”

“Teachers should explicitly help their students develop their metacognitive capacities…”

All of this points back to the Pedagogy 101 fundamental that the primary goal of a teacher should be to teach themselves out of their job, or in the words of Jain (2014), when reflecting on Louise Goss’s legacy (emphasis added):

“Goss’s primary goal as a teacher was to develop students’ minds so they grow to be independent learners, making the teacher expendable.”

Holland (2014) also remembers Louise Goss in a similar way:

“After reviewing their teaching during the past year and listing what they should do differently based on what they learned from Louise Goss, one graduate student wrote, ‘I will begin to judge my success as a teacher by what my students can do on their own without any help from me.’”

This principle is not new, nor is it owned by western culture. As the Chinese proverb says, “Give a man a fish, and you feed him for a day. Teach a man to fish, and you feed him for a lifetime.” I believe most or all teachers have seen various examples of “fish handouts” in the world of music teaching. The most common example I’ve witnessed is nearly every year when various college faculty colleagues (in multiple states – I believe this happens everywhere) talk about one or two freshman students with dazzling technique who “don’t understand anything they’re doing.” This is the result of the kind of teaching that uses modeling so much that it hampers music literacy and leaves little room for students to develop independence from the teacher. One faculty member describes this as “Try-it-this-way-dear” teaching.

But before we get too righteous about this, we must stop and remember that modeling holds a critically important place in music instruction. Knowing the precise place it should have in teaching from student to student, piece to piece, and goal to goal can be one of the most difficult balancing jobs a music instructor has. It presents an always-present independence vs. modeling dilemma since self-error-correction is impossible without intention. In other words, before practicing a spot in the music, the student must have in their mind some kind of analytical/audio/visual/kinesthetic “answer key.” Without this answer key (or “intention”) in mind before they practice the spot, the student’s ability to detect an error, no matter how slow they go, is limited or impossible, depending on the student and the goal.

Meno’s Paradox (Plato) outlines this dilemma perfectly:

“A man cannot search either for what he knows or for what he does not know. He cannot search for what he knows: since he knows it, there is no need to search; nor can he search for what he does not know, for he does not know what to look for.“

We should note that Plato’s idea of “not knowing” here is quite rigid, because it is certainly possible to “know that we don’t know something.” But Plato is not talking about this kind of ignorance; he is talking about the cold absence of information or any clues that would point to it. Interestingly, Schwartz (2006) argues that the feeling of not knowing something is a metacognitive state, not a cognitive one (i.e., the feeling of not knowing something, rather than the cold absence of information), although I would argue it is both.

But regardless of such philosophical distinctions, Plato’s point is well-taken by music teachers who know all too well that there are some goals and skills that a student cannot complete / acquire without modeling from the teacher, while there are also some metacognitive skills a student cannot develop if modeling robs them of the opportunity. Teachers must achieve a very careful balance between developing independence and modeling. How specifically is this done?

Five Stages of Metacognitive Development

First, it is helpful to think of five theoretical stages of metacognitive development in musical study. Some disclaimers first:

• These stages assume the student is given sufficient guidance over the years by their teacher to develop metacognitively, or the student is exceptional in their ability to develop their own metacognition. What follows does not represent the typical student if left to their own.  As you might recall from the first article of this series, there are metacognitive stagnation and dipping effects as students progress in their studies (Hallam, 2012).
• All of the following skills develop in parallel to each other, but for the most part, they are mastered in the order of the stages.
• It is unimportant whether these stages are defined in this exact way or that we memorize which stage implies which skill. What is important is the general concept conveyed by this table, which will be highly useful later on.

A stage 1 student can only be relied upon to follow their teacher’s instructions on their own, and even this can be unreliable, depending on the student’s age/development (a 5-year-old needs the help of parents just to even follow directions). In stage 2, a student gets better at detecting errors on their own. Fixing of errors also improves, although smart strategies in fixing errors are not necessarily employed. Smart error-fixing strategies are more often employed in stage 3. In stage 4, a student draws on years of experience of “being burned” by careless strategies in learning new material, so the student exercises more metacognitive caution to avoid making errors in the first place. Stage 5 represents a large jump from stage 4. Not only are errors avoided (all marks in the music are observed), the student even tries to fully interpret what is not written in the music. (Said differently, while the stage 4 student tries to avoid receiving error correction goals from their teacher, the stage 5 student tries to avoid receiving any goals from their teacher.)

How these stages actually map to levels of advancement might be more accurately estimated by this table:

To elaborate a bit on the “Artist” level, metacognitive skills are now intuitive, and lesson plans at this level may be controlled more by the student than by the teacher (i.e., “What do you need me to help you with today?”). I like to think of #5 as the point where the teacher is no longer instructing the student. At this point, the teacher is coaching their colleague, and the “student” might as well be called an “artist.” That is why a world-renowned pianist could coach any piano professor, and likewise, any piano professor could coach a world-renowned pianist. (Whether or not egos would allow each of them to follow the other’s advice is another story!)

But again, these are only estimates. It would be fascinating to see how these skills really do map out in reality in a study of a couple hundred students, but no matter. The principle is established, and this is where everything comes together. What does it really mean in practical terms for an effective teacher to find the balance between developing independence vs. modeling?

Uncovering the Flowchart

Every word that we write down in students’ notebooks each week must be guided by a sense of how much capability the student has to follow directions, detect errors, prevent errors, and interpret music. This brings to the surface a decision flowchart that effective teachers have working in the back of their minds:

1. If I say nothing about this error, will the student still fix it? If so, do nothing (end here). If not, go on to step 2.
2. Will the student be able to fix the error just by mentioning it? If so, mention the error during the lesson (end here). If not, go on to step 3.
3. Will the student be able to fix the error just by notating it? If so, notate the error in the student’s notebook and/or in the music (end here). If not, go on to step 4.
4. Will the student be able to fix the error if I tell the student how to fix the error? If so, write down the instructions in the notebook or music (end here). If not, go on to step 5.
5. Have the student practice the passage in the lesson with your guidance (including your own modeling if necessary) until it is clear that the student is ready to practice it effectively at home. Write the goal down in the notebook or music with practice instructions included, and possibly have the parent or other practice partner at home guiding the student’s practice. Maybe even send the student home with a recording and/or video.

One could say that great teachers always try to maximize a student’s metacognitive development, turning goals into “puzzles” that the teacher knows with 100% certainty the student can solve, but never giving the student such an excess of information that it deprives the student of the chance to experience an “ah-ha!” moment. When the student lacks experience to solve the puzzle even when all the pieces are in front of them, only then does it become necessary to supplement the puzzle with additional instruction, in-lesson drilling, notated practice tips, and/or modeling.

Notice that the first step in this flowchart appears invisible to the student. This scenario happens a lot more frequently when coaching students at the artist level than when teaching other students. For the teacher, this is truly a “luxury” in the full sense of the word, much like how a billionaire doesn’t need to concern themselves with cleaning their house or going grocery shopping.

To make this “puzzle making” as practical as possible, here are four examples of errors a student might make, and how a teacher always seeks to maximize metacognitive development, supplementing it only when necessary. For each example, five different ways of conveying this goal to the student are listed, depending on the student’s ability:

Example 1: A fourth beat in m.4 in 3/4 time

• Artist: m.4 – fix rhythm
• Advanced: m.4 – you added a 4th beat
• Late Intermediate: m.4 – last note is quarter note, not half note
• Early Intermediate: m.4 – last note is quarter note, not half note; play m.4-5 counting out loud
• Beginner: m.4 – last note is quarter note, not half note – play m.3-5 counting out loud with metronome (possibly have student do this during lesson, possibly model if they have trouble).

Example 2: Legato interrupted in m.4 because of bad “thumb-thumb” fingering

• Artist: m.4 – seriously?
• Advanced: m.4 – some legato missing
• Late Intermediate: m.4 – bad fingering prevented legato
• Early Intermediate: m.4 beat 3 – bad fingering prevented legato
• Beginner: m.4 beat 3 – cross thumb over so you don’t run out of fingers! (Possibly have student do 2 or 3 repetitions in the lesson.)

Note that in the artist level, the teacher’s “puzzle making” can be quite fun, meaning the teacher can reduce their communication skills to that of a caveman and still trust the student will easily figure out what is meant at home: “Yeah, I kind of knew my fingering was messed-up there, never got around to fixing it.” If it were possible for a level beyond “Artist” to exist (perhaps “Jedi Artist?”), maybe a teacher could literally write down Tarzan’s “Oongawa” for every goal, and all of the goals would be completed as the teacher wished.

Also note that for the late intermediate student and below, remembering article #5, the notated goal consists of two monogamous complementary goals (fix fingering / play legato), combined (“married”) into one.

Example 3: Mushy pedal in m.4

• Artist: m.4 – clear pedaling
• Advanced: notes from m.3 bled into m.4
• Late Intermediate: m.4 beat 1 – pedal went down too soon
• Early Intermediate: m.4 beat 1 – pedal goes down after the beat, when the sound from m.3 is all gone
• Beginner: m.4 beat 1 – pedal goes down after the beat, when the sound from m.3 is all gone (have student play m.3-4 extremely slowly to coordinate overlapping pedal technique)

Example 4: Phrase is cut off too abruptly in m.4

• Artist: m.4 – don’t slap your audience in the face at the end of the phrase
• Advanced: m.4 – taper phrase
• Late Intermediate: m.4 – taper phrase with arm lift
• Early Intermediate: m.4 – last note of phrase softer and not so short – use arm lift
• Beginner: m.4 – last note of phrase softer and not so short – use arm lift. Demonstrate, possibly physically manipulate student’s arm/hand if they have trouble copying the motion. Explain why the lift is done with the arm (wrist/forearm) instead of the fingers alone.

Article 8, The 1-to-3 Rule, will give students an extremely powerful tool to use when starting a new piece or when continuing to learn a piece, specifically when their teacher didn’t assign any specific goals or when the assigned goals are already completed.

(c) 2022 Cerebroom

References

Aiello, Rita. “The importance of metacognition research in music.” Proceedings of the 5th Triennial Conference of European Society for the Cognitive Sciences of Music. Hanover, Germany: Hanover University of Music and Drama, Institute for Research in Music Education, 2003.

Butterfield, Brady, and Janet Metcalfe. “The correction of errors committed with high confidence.” Metacognition and Learning 1.1 (2006): 69-84.

Duke, Robert A. “Their own best teachers: How we help and hinder the development of learners’ independence.” Music Educators Journal 99.2 (2012): 36-41.

Hallam, Susan, et al. “The development of practising strategies in young people.” Psychology of Music 40.5 (2012): 652-680.

Holland, Sam. “Teaching tips from Louise Goss.” Clavier Companion 6:5 (Sep/Oct 2015), 28-30.

Jain, Judith. “The professional contributions of Louise Goss.” Clavier Companion 6:5 (Sep/Oct 2015), 14-17.

Schwartz, Bennett L. “Tip-of-the-tongue states as metacognition.” Metacognition and Learning 1.2 (2006): 149-158.

First, it’s informative to consider a meta-view of how goal difficulty intersects with a student’s skill level. Depending on the student, a result-oriented goal will already be in one of the following three stages of goal completion when assigned:

1. Acquisition goal: a goal that requires the student to acquire an entirely new skill. [Highly challenging]
2. Application goal: a goal that requires the student to apply a recently acquired skill to a new piece. [Moderately challenging]
3. Habituation goal: a goal that requires the student to apply an already mastered skill to a new piece. [Not challenging]

Let’s consider goals such as, “Play RH louder than LH” or “Smooth ritardando.” This table shows what a typical student at various skill levels will need to go through to complete these goals:

Students tend to work hardest and smartest on acquisition goals. Students exercise more humility and what might be called “healthy self-doubt” when trying to acquire a brand new skill, and sometimes students will even perceive a skill they haven’t yet acquired as being more difficult than it really is. And while many articles could be written about various specific practice tips to help a student acquire this or that skill, it is also impossible to generalize about acquisition goals. Every new skill that must be learned has its own set of unique problems and unique solutions, often relating to the various unpredictable quirks of physical coordination and perception. What’s more, even when an acquisition goal isn’t completed, it is almost always improved upon, and most teachers (myself included) do not consider this to be a “failure” to the point of reassigning it as a trouble goal (as defined in article #2). In other words, failure to complete an acquisition goal in 1 or 2 weeks is often not a metacognitive failure. These are the reasons why this article will focus on the more common and less acceptable failure to complete application goals and habituation goals. When faced with these goals, students don’t naturally work as hard or as efficiently. (This is a more general version of the Midvale Effect discussed in article #3, as this overconfidence applies to everyone, not just those with high IQ). Metacognitive failures in completing application and habituation goals are more easily generalized.

Before entering “Detective Mode” (below) to have students reflect on a metacognitive failure to apply/habituate a goal, I like to first ask students the biggest metacognitive question of them all:

• Are you surprised that this goal isn’t done, or did you already know it wasn’t done before today’s lesson started?

If there is no surprise, then often the student already knows the nature of their metacognitive failure, and discussion can progress naturally from there. If the student was surprised, that’s where Detective Mode comes in.

Detective Mode

When a failure occurs on even the simplest application or habituation goal such as fixing a wrong note, I like to tell students that we are entering Detective Mode to figure out what went wrong during practice so that students are more open to self-critique. Making them my “Watson” helps them to shed a lot of potential defensiveness in the self-critiquing process. With the little ones, one could even have fun with this and utilize props such as a detective hat, pipe, spectacles and magnifying glass. This is where I might remind a student that this detective work is the most valuable part of the piano lesson; not only are they learning about music like with any other goal, they’re also learning about practicing. And make no mistake, failing to get application and habituation goals done is, without exception, always due a metacognitive failure of some kind. A teacher simply cannot let this reflective opportunity go to waste. When reassigning a goal after the student fails to complete it, the teacher should always make sure the student understands where their practicing went wrong.

Sometimes students are able to quickly state what went wrong, especially if the answer is painfully obvious, such as, “I didn’t get to this piece this week.” When the answer isn’t so obvious to the student, PIT Practicing serves as an excellent framework on which reflection can be based. When a student just can’t seem to figure out what exactly caused the failure (a more common occurrence than we’d like, as it is no surprise that a student who doesn’t have the metacognitive skill to put a staccato on some particular note after a week of practice would also lack the metacognitive skill to figure out why they failed), a series of questions for the student might go something like this, with the specific PIT Practicing failure indicated in parenthesis:

• Did you read the goal every day? (Prepare)

This is another one that is usually “obvious” to students, but sometimes not. Sometimes students are more careful their first day of practice, then they let their guard down on the second or third day, thinking it’s not necessary to prepare their goals carefully.

• Did you fully understand the goal or misunderstand the goal in any way? (Prepare)

These “detective mode” questions are only asked after some discussion of the goal has already taken place and the student now understands the goal, so if misunderstanding the goal is the nature of the metacognitive failure, this is usually revealed while initially discussing the goal, before entering detective mode. Sometimes the failure is even the teacher’s fault for not writing the goal down clearly enough. Still, this question is included here for the sake of keeping the logical progression together.

• Did you read too many goals at once and practice them all at the same time? (Prepare)

This metacognitive failure involves underestimating the difficulty of getting any single goal done and/or overestimating one’s own ability to concentrate on multiple things while practicing. Just because a goal seems easy and simple, again such as fixing a wrong note, wrong fingering, lift between slurs, etc., doesn’t mean it can be “studied in groups” like we do with vocabulary words when we study for a vocabulary test… at least not on the first day or two of practice. Since music involves timing and coordination (two dimensions that don’t exist in the realm of academics), even the simplest goals still take a decent amount of focused work to apply and habituate.

• What size practice chunk did you take while drilling this goal? (Isolate/Drill)

This question could also be asked, “Did you lose concentration on the goal while practicing it?” In almost every case when concentration is the issue, it’s because the practice chunk was too large and allowed for distraction to occur before actually reaching the goal in the score. But I prefer asking more directly about the practice chunk, as it’s an easier question for students to answer with clarity.

• How slow did you go when you isolated and drilled it?

All experienced teachers know that a teacher’s definition of “slow” is often very different (much, much slower) than a student’s definition. What’s important to emphasize here is that the fastest way to get any goal done is to do it correctly on the first try, second try, third try, and every try after that, no matter how slow 100% correctness requires.

• Did you practice it correctly all week long, but maybe you didn’t drill it enough times? (Isolate/Drill)

Merely telling the student to “drill more,” while good advice, doesn’t necessarily get to the metacognitive cause of this failure. This goes back to the “listen to your feelings” wisdom that students must follow while engaging in step 2 of PIT Practicing. The definition of “enough times” will change with every goal, but what shouldn’t change is the feeling of security that a student has before concluding the goal has been practiced enough. When this particular failure occurs (and it does for every student at some point), this is where we tell students to modify their definition of what it means for a goal to “feel secure.” There are many creative ways to convey this, such as, “You stopped practicing this goal just because you thought it was ready for this piano lesson. But you need to keep practicing a goal until you feel like you could play it on live television in front of a billion people.”

• Did you practice the goal correctly all week long, then it fell apart in the lesson? (Test Yourself)

This is a common failure. For many, the process of testing oneself (simulating the next lesson / putting the goal under pressure) doesn’t come naturally. Students are often content to read the goal, drill the goal, and move on without ever playing the goal in a larger context. These are the students who express the most surprise in the lesson that the goal isn’t done, even on rare occasions resulting in great frustration. This is certainly understandable, as there is nothing more disheartening in a music lesson than the feeling of doing everything right and still getting it wrong “on the test.” That is why this metacognitive reflection is so important. When a student learns that there is a very sensible, rational, and even predictable reason why the goal didn’t hold up to the pressure of the lesson, the frustration evaporates and turns into renewed focus for the upcoming practice week.

I certainly do not have these questions memorized or documented as a flowchart that progresses exactly the same way every time. I improvise these questions in each lesson in a manner that comes naturally in conversation, although I do have the steps of PIT Practicing in mind as I ask the questions, so they usually come out in a fairly logical fashion. Every unique student, unique piece, and unique failure will lead me to ask questions a bit differently each time. The point isn’t to turn these questions into a formal flowchart; the point is to empower the student to avoid making the same practicing mistake again in the future.

ESP Self-Evaluation

Nielsen (2001) offers a simplified model for self-evaluation, which can also be applied to in-lesson reflection:

• Successful performance –> New problem
• Unsuccessful performance –>
  • More effort
  • More effort and revise strategy
  • More effort, revise strategy and revise problem belief

To make this useful, when practicing fails, use ESP:

• Effort
• Strategy
• Problem

There are three caveats I would issue about ESP evaluation. First, there is overlap between Effort and Strategy. While the intensity of concentration is certainly 100% effort, how many times one drills a correction is part of both effort and strategy. Second, I think it’s critical that the idea of Testing Yourself is considered a distinctly separate step from Strategy, which ESP Evaluation fails to do. Instead, Test Yourself is implicitly (silently) included in the Strategy category. It is more difficult to identify a “Test Yourself” failure in one’s strategy when the idea isn’t made explicit. Finally, while the order “Effort, Strategy, Problem” does make sense when a student is in the middle of practicing, it makes more sense to approach it in reverse order when reflecting on it during a lesson (i.e. while the student is not in the middle of practicing): “Problem, Strategy, Effort,” which lines up more closely with PIT Practicing.

Our Traitorous Senses

There is one more general principle that I’ve found to be extremely useful in helping students to understand the failure to habituate certain kinds of goals (correcting rhythm, memorizing/looking at the score, and creating/correcting muscle memory), a principle relating to our three non-analytical memories (audio, visual, kinesthetic). This principle comes in the form of a quotation from yours truly that I repeat to my students frequently:

To clarify:

1. Evil ears make it difficult to correct wrong rhythms. Audio memory can be like the devil on a student’s shoulder: “Come on, just play it the way you ‘know’ it should sound. Don’t count the rhythm out loud, just play what comes naturally! You’ll love how it sounds, and if you love it, how can it be wrong?” This devil leads music students astray. The angel on the student’s other shoulder, dressed like a nerdy math teacher, says, “Forget what it sounds like – in fact, forget that you’re even playing music! This is math! Count the numbers with the steadiness of an extremely slow clock, and match the notes up with the counts!” Practicing a wrong rhythm locks students into what I tell them is an “audio prison,” and until they become very skilled in rhythmic and metric awareness, the only “key” to get out of that prison is to latch onto outside realities such as the metronome, counting out loud, tapping while counting out loud, etc.
2. Lazy eyes get in the way of looking at the unfamiliar. When memorizing music, or when needing to refer to the score after something is comfortably memorized, it requires less mental effort to just look at what is most familiar, so out of laziness, a student resists looking at their hands / score, respectively.
3. Stupid muscles make just about everything take longer than we think, especially correcting fingerings. Students may know this cognitively, but as far as their metacognitive skill demonstrates at home, many students clearly believe their muscles are “smarter” than they actually are, especially when body map goals are involved, requiring thousands of repetitions to habituate.

Reflection is the beginning of the more general process of error correction, leading directly into the next article on Independence vs. Modeling.

(c) 2022 Cerebroom

References

Nielsen, Siw. “Self-regulating Learning Strategies in Instrumental Music Practice.” Music Education Research 3.2 (2001): 155-167.

It’s important to recognize the temporal relationship that any two goals have with each other:

• Overlapping goals: goals that occur simultaneously in the music.
• Separated goals: goals that occur in different places in the music.

…and to recognize their functional relationship as well:

• Complementary goal: a goal that facilitates completion of another goal.
• Clashing goal: a goal that undermines completion of another goal.
• Independent goal: a goal that neither facilitates nor undermines the completion of another goal.

Overlapping & Separated Goals

Examples of overlapping goals would be:

• m.8 – bigger crescendo
• m.8 – RH don’t ignore key signature

Examples of separated goals would be these same two goals in different measures:

• m.4 – bigger crescendo
• m.12 – RH don’t ignore key signature

Students will often practice overlapping goals simultaneously since they occur in the same place. Most students will combine overlapping goals even when given no instruction whatsoever about this kind of strategy, and even those who don’t combine on the first day of practice will almost always combine them on the second or third day of practice, again, even without any instruction about this strategy. So why is the overlapping nature of some goals still so important to notice?

It’s important for the teacher, because it affects the order in which goals should be written in the notebook, which in turn impacts how students practice. Overlapping goals should be grouped together so that students can more easily recognize the option of grouping these goals together during practice. I already noted that universal goals should be notated first. Now we can see why: without exception, universal goals overlap with all other goals. The overlapping nature of any two goals should be made clear to students as soon as possible when they practice, and notating a universal goal last prevents the student from recognizing this relationship until the last possible moment during practicing. While there is a danger that the student might see the universal goal and then proceed to play the entire piece while observing the universal goal and nothing else, this scenario is still better than the inverse scenario of fixing wrong notes, rhythms and articulations while neglecting the universal goal, since universal goals are already the most challenging to habituate as it is.

Complementary, Clashing and Independent Goals

Examples of complementary goals would be:

• m.8 – RH correct fingering
• m.8 – RH play legato

…or:

• “Adagio” means slow!
• (pretty much any other goal)

In the first example, fixing fingering in measure 8 happens to also enable the RH in measure 8 to play legato. Thus, while the second goal does not complement the first goal, the first goal complements the second goal, making this complementary relationship unidirectional. But whether complementary goals are unidirectional or bidirectional is not as important as whether they are monogamous or polygamous. Monogamous complementary goals complement only each other; they leave other goals alone, and they are more effective when “married” as one goal:

• m.8 – RH correct fingering so you can play legato

Without combining the goals together, the student may not even recognize the complementary relationship.

The second example, playing Adagio, is an example of a polygamous complementary goal, because it complements all other goals. All other goals will be helped by playing more slowly. Therefore, it shouldn’t be combined with any other goals (in our monogamous society, the polygamous goal avoids marriage), and it should be listed first, before all goals it complements. In fact, this goal even complements any universal goal. Thus, this is a special case of a spread goal taking chronological priority over the universal goal in a written list of goals. This may seem at first like an exception to the rule that the universal goal always goes first, but actually, this presents us with a more robust logic to the notation of goals, which I will get to later.

Examples of clashing goals would be:

• Loud f
• Play with fingers, not with arms

…or:

• (almost any goal)
• speed up to q = 144

In the first example, I’m imagining a beginner. Nearly every beginner, even adults, can’t play very loud [by the way, this isn’t because of the myth that the inability to play loud is due to lack of finger strength – it’s because of not having enough finger coordination]. When beginners try to play louder, they tend to bounce their arm, even while playing legato. But when they are told to get rid of their bouncing arm, they fall back to a softer mp or mf sound. Progress with one goal causes trouble with the other. Since these two goals only clash with each other and no other goals, it is better to write these monogamous clashing goals (two goals that clash only with each other) as one goal, again to convey this clashing relationship to the student:

• Loud f with fingers, not arms

And as you might expect, just like “play slower” complements other goals, “Speed up to quarter note = 144” clashes with them. A polygamous clashing goal (a goal that clashes with many other goals) should not be written as one goal and should be listed following all goals it clashes with. Not only do I write “speed up” goals last among the list of goals for a piece, I might even add to it something like, “speed up to q = 144 when comfortable with other goals,” or “speed up to q = 144 on practice day 3.” Or maybe I don’t write it at all this week, saving it for next week’s lesson.

The same example I used above for separated goals also works for independent goals:

• m.4 – bigger crescendo
• m.12 – RH don’t ignore key signature

Not only are these two goals located in different places in the music (temporally, they are separated), working on one has no effect on the other (functionally, they are independent).

Goal Notation Framework

Bringing all of this together so far, this brings us to an effective framework to use when writing goals to better arm students for strategic practicing:

• Universal goals should precede all other goals.
• Complementary goals should precede any goals they complement, including universal goals.
• Clashing goals should follow any goals they clash with.
• Monogamous goals should be married; Polygamous goals should stay single.
• Overlapping goals should be grouped together in case the student wants to combine them.
• Process-oriented goals should be primarily assigned to support result-oriented goals unless there is no intention to evaluate (score) them.

Doing this on paper can be difficult at first as it requires that the teacher have a kind of “meta-view” of all the goals in their head before notation of the goals begins, but with practice, it becomes a skill like any other skill.

Article #5 will discuss perhaps the most fertile ground for nurturing metacognition in students: reflection.

(c) 2022 Cerebroom

“We classify things for the purpose of doing something to them. Any classification which does not assist manipulation is worse than useless.”

Randolph Bourne

In the quest to help students practice more effectively through the use of metacognitive skill, we must empower students to select and implement various practicing strategies based on the nature of goals they encounter, and we must also have our own strategy for notating these goals in a way that facilitates practicing the most. All teachers to some degree (some more than others) give students “practice this way for this goal, practice that way for that goal” instruction, which of course works in service of these endeavors. But it is hugely helpful for both students and teachers to understand goals in more generalized ways. Parts 4 and 5 of this series will outline a generalized framework for understanding, assigning and practicing goals.

It makes the most sense to classify goals according to how drastically practice routine is affected. Musical duration of the goal (i.e. number of measures) is the best way to accomplish this:

• Spot goal: occurs in a small spot in the music.
• Spread goal: occurs over the course of a few lines of music, a section, or even a whole piece.
• Universal goal: occurs all the time, in all pieces.
  • Body map goal: involves changing one’s body map.

We should also be aware of the orientation of any given goal:

• Process-oriented goal: a goal that explicitly tells a student how to practice.
• Result-oriented goal: a goal that explicitly tells a student what to achieve.

The Spot Goal

Examples of the spot goal would be:

• m.6 – fix wrong note
• m.12-13 – play LH detached
• m.15 – gradual crescendo
• no stop/stumble on repeat

Applying PIT Practicing to the spot goal is straight-forward for students. We can advise a student to employ something like a 2-to-7 jelly bean game each day for the typical spot goal. But something like 2-to-15 might be necessary if it’s a more difficult spot goal, such as changing fingering in rapid passagework when it’s already up to (or near) full speed.

Also, when doing step 1 of PIT Practicing (Prepare), spot goals will often take a little more careful attention than other goals since there is more locational information to decode in a tiny little spot goal (which measure number, which beat, which hand) as well as sometimes the goal itself being nit-picky (“don’t chop phrase off abruptly” or “play the staccato note more staccato”), as opposed to spread goals or universal goals (below), which require less decoding on the part of the student. It is for this reason that I always put the locational information of a goal first, followed by the goal. For example (deliberately making up as complicated a goal as I can), instead of writing this jumbled nightmare:

• RH more gentle lift m.4 at the end of the phrase on beat 3

I write:

• 4R3 – more gentle lift at the end of the phrase

This “code” explodes out to “measure 4, right hand, beat 3.” I don’t have to use beat numbers very often, so most goals in measure 4 would just start with something like “4R” or even just “4,” which students learn pretty much immediately (the first time I explain it to them).

The Spread Goal

Examples of the spread goal would be:

• m.1-16 – keep LH soft
• middle section – no rushing or dragging
• whole piece – faster tempo
• remember to take repeat

I often tell students that spread goals are usually a whole bunch of identical spot goals, one after another. For example, in the case of the first goal above (keep LH soft), supposing there are 4 LH bass notes / chords in each measure, this is like having 64 spot goals in a row [4 beats x 16 measures]. Thus, it wouldn’t make sense for the student to engage in as much repetition as with a spot goal; each repetition of the musical chunk yields greater benefit to the student than a single repetition of a spot goal (in this case, one repetition yields 64 opportunities to practice the goal), and it also takes longer to complete each repetition. While a typical spot goal might call for the jelly bean game to end at 7 points, a spread goal would end at anywhere between 2 and 5, depending on the length of the section. A goal that spans an entire piece might only require a single correct repetition each day, or essentially a silly “0-to-1” jelly bean game.

Because of this and the fact that spread goals tend to involve more generalized concepts that are hard to ignore instead of nit-picky details that are hard to notice, students tend to be more successful habituating spread goals than spot goals. This can seem counterintuitive at first since, psychologically, “smaller” goals seem “easier.”

The threshold that distinguishes between a spot and spread goal (5 measures? 8 measures?) will of course depend on the density of material in each measure. What’s important is that the student understand that larger musical chunks require less repetition because of (a) the time it takes to complete a single repetition and (b) the benefit derived from each repetition.

There is one exception to this. Note that I define “remember to take repeat” as a spread goal, while I define “no stop/stumble on repeat” to be a spot goal. This is because remembering to take a repeat is a very different goal than merely being able to take it. Being able to take a repeat smoothly (without stops or stumbles) might be as easy as drilling two measures 5-10 times. But remembering to take the repeat in the first place relies on what we might call structural audio memory. Part of our audio memory includes the structural length of certain sections of music, so when we have a problem of simply forgetting to take a repeat, unfortunately there is no shortcut to fixing this. We must start at the beginning of the repeated section and practice hearing all of it twice before going on to the next section (and be sure to go on for a measure or two after that before stopping). Once we have this structural audio memory in place, this effectively sets an “alarm” in our mind so that when we perform the section, it sounds incomplete after only playing it once, while it sounds complete after playing it twice. Unfortunately, depending on the length of the repeated material, it can take a long time to achieve just one repetition of this goal, so true habituation of this goal can take a long time.

The Universal Goal

Examples of the universal goal would be:

• louder f‘s
• be able to count out loud

To clarify these examples, a beginning student who has had only a few lessons will commonly have trouble playing loud enough when their music indicates forte, so the goal of playing “louder f‘s” wouldn’t just apply to one single piece – it would apply to all pieces. As for the goal, “be able to count out loud,” perhaps a transfer student plays with incorrect rhythm in all of their pieces, so when they start two or three new ones, their primary goal that week is to be able to count out loud in all of their pieces. Neither of these examples are inherently universal goals. These examples show that many goals can become universal goals as long as the failure that produced the goal is present in all of the student’s playing.

A subcategory of the universal goal would be the body map goal. First, the term body map refers to the brain’s knowledge of the body and how it moves in 3D space (often automatically, without deliberate thought). To demonstrate the idea of the body map to my students, I will position myself just within reach of grabbing a pen on my piano. “I’m not reaching for the pen yet, but somehow I just ‘know’ that my arm is now within reach of it. That’s because my brain is reading a kind of ‘map’ of my body, telling me how close I need to be to this pen before I reach for it because my body map already knows how long my arm is.” I then grab the pen and explain all of the amazing things my brain did “in the background” to accomplish this seemingly simple task, lifting from the shoulder joint, arm rotation, and moving a couple fingers to grab the pen, all without any deliberate thought. Then I might say, “Contrast this with what a 6-month-old baby would do with his or her incomplete body map…”, and I proceed to grab the pen again, this time accidentally grabbing 4 or 5 other objects along with it (2 or 3 of them fall onto my keyboard) because all 5 fingers of my hand are acting in clumsy unison, with the imprecision of a tractor claw.

A body map goal is a goal that requires changing the body map – the way the body generally moves – every time a certain action is performed at the piano, no matter what piece is performed. Here are a couple examples of body map goals:

• no collapsing fingers [i.e. 2nd knuckle in each finger should maintain its curve rather than bending backward when depressing a key]
• sit up straight

Sitting up straight might not seem like a body map goal at first, but a student has to think about sitting up straight during the entire performance of all of their pieces, not just when they first sit down at the piano. As it turns out, the example of sitting up straight is always a universal goal. The other goal, no collapsing fingers, is also always a body map goal. If a student is bending their index finger backward in one piece whenever the finger depresses a key, then they’re bending that finger backward in all pieces, because that’s just how their finger naturally moves to depress a key in any context.

Remember that the 16-measure “keep LH soft” spread goal could be considered 64 instances of the same spot goal. Universal goals and body map goals can be viewed this way as well. In fact, this phenomenon is greatly compounded with universal goals. If a student plays 950 notes during their entire practice routine, this is 950 opportunities to habituate the goal. Assuming a 5-day practice week, that would be 4,750 goal-habituating opportunities. In light of this, shouldn’t universal goals be the easiest kinds of goals to complete in a week’s time?

Unfortunately, no – not even close. While universal goals are typically very easy to cognitively understand (step 1 of PIT Practicing is often trivial), the universal goal is the most challenging type of goal to actually practice effectively, because it requires constant, obsessive, mind-numbing concentration throughout the entire practice routine. This can easily become tedious and produce boredom long before enough successful repetitions have been achieved. In my experience, in the rare best case scenario, a student gets a universal goal completely habituated in two weeks.

Above and beyond the general universal goal, the body map goal is additionally difficult to habituate. While it might take 50, 100 or even 200 repetitions of other universal goals to habituate, changing one’s body map takes thousands of repetitions, because the body map is so slow to change. In fact, despite the high metacognitive skill that correlates with those who have high IQ, overconfidence can easily get in the way of progress on body map goals due to underestimating the amount of repetition necessary to reprogram the body map. Many students with high IQs are accustomed to being able to get high grades in school with minimal work compared to other students, but this academic talent means nothing in the realm of retraining one’s body map. Ironically, despite the fact that high IQ students tend to have the highest levels of metacognitive skill, in my experience, the students who seem to have the most trouble with body map goals are disproportionately academically gifted students. I call this the Midvale Effect, after Gary Larson’s famous “Midvale School for the Gifted” cartoon, which unfortunately I can’t get permission to display in this article. (Spoiler of the cartoon: an academically gifted child is attempting to enter the school by pushing as hard as he can on a door labeled “pull.”)

Generally, if possible, we should try to notate goals in either chronological order, or even better, reverse chronological order. (More on that in article #7.) Either way, the universal goal should always be notated first in a goal list. Unlike spot goals and spread goals, we know that all universal goals begin on the first note of measure 1 and end on the last note of the last measure. There is no goal in the entire piece that is unaffected by the universal goal. If we are serious about helping students to practice as efficiently as possible, we should present students with the possibility that their first day practicing will be error-free. Just because this probably won’t happen doesn’t mean we still shouldn’t aim for it. If we put a universal goal at the bottom of the goal list, it is practically guaranteed that the student will continue reinforcing the bad universal goal habit until they finally encounter it in their list of goals.

Ideally, we would love to be able to write a universal goal over and over again as the first goal listed for all of the student’s pieces and exercises that week. My “workaround” for this when writing goals on paper is to write the universal goal at the top of the paper with a “cloud” drawn around it. If I want to notate it with even greater urgency, I draw rain and lightning bolts coming out of the cloud, figuratively drenching and electrocuting all the other goals that week.

Process-Oriented and Result-Oriented Goals

Examples of process-oriented goals (goals that tell a student how to practice) would be:

• Drill m.5-6 10x each day
• Ghost the LH

To clarify the second goal, “ghosting” a hand means to play hands together, except with one hand playing so softly that the notes literally don’t make any sound. Keys still move, but they don’t touch the bottom of the keybed, so no sound comes out. This is a useful technique to use when helping students to play one hand louder than the other hand for the first time.

Process-oriented goals like this are wonderful tips, but they are also difficult or impossible to evaluate. After ghosting the LH for a week, the student may still have just as much trouble playing the LH softer, so the teacher has no way to verify whether any ghosting was actually done. Conversely, the student might not have ghosted the LH at all that week, but they still managed to achieve playing the LH softer than the RH. There’s nothing wrong with that as long as these goals were not assigned with any intention to “evaluate” them; the only way a teacher can evaluate process-oriented goals is to take the student’s word for it. If the aim is to assign goals that can be objectively evaluated the next week (to help quantify a student’s practice quality as described in part 2), the teacher should make sure that a process-oriented goal should be assigned underneath the result-oriented goal it supports.

Result-oriented goals such as “play LH softer than RH” or “fix wrong note” are easy to evaluate. They are either done or they aren’t, as evidenced by what the student habituated that week. To reiterate, process-oriented goals should be assigned in support of result-oriented goals. When writing goals in a paper notebook, I precede result-oriented goals with a hyphen, as with a bullet list. When writing supporting process-oriented goals, I use indented L-shaped arrows underneath result-oriented goals that visually show the supportive nature of the goals.

In part 5, Goal Interactions, I will continue developing a framework for both students and teachers to understand goals, helping them to strategize in practicing and teaching, respectively.

(c) 2022 Cerebroom

“For every minute spent in organizing, an hour is earned.”

Benjamin Franklin

Those who practice effectively utilize strategy (planning) when practicing. Some do it naturally and may not even realize there is strategy in their routine, while others might do it deliberately in one way or another. Regardless of how deliberate a student’s strategic effort is during practice, the results of planning / strategizing (or as Hallam describes it, “practice organisation”) are undeniable:

“…those musicians who were well organised also exhibited high levels of concentration, those who reported low levels of organisation had either low or moderate levels of concentration, while the moderate planners tended to have high levels of concentration. It seems that there is some relationship between level of organisation in practice and level of concentration.”

Susan Hallam (2001)

It makes no difference whether a student is naturally organized or the student imposes organization onto themselves to compensate for a perceived disorganization. Organization will greatly help any practice routine, whether it is achieved naturally or artificially.

Around 2013, I realized that the best way to get students to approach the practicing of a single goal metacognitively is to model a system of organized practice modeled directly after the three parts of the metacognitive skill cycle discussed in the first article (planning, monitoring, evaluating), which I call PIT Practicing:

1. Prepare
2. Isolate & Drill
3. Test Yourself

I have found “PIT” practicing to be a profoundly powerful tool in helping students to display far greater levels of metacognitive skill in their practicing of a single goal. Steps 1 and 2 might even seem trivial to many. But as you will soon see, none of these steps are trivial – there is a lot more to each step than it seems, and plenty of room for error in every step. In fact, in my experience over the years, when I ask students questions to determine what went wrong in practicing a goal, there is no practice step failure above that dominates other failures. Practicing failures seem to be spread quite evenly throughout all three steps/categories.

1. Prepare

Preparing a goal essentially consists of fully understanding and experiencing the kinesthetic, audio and visual differences between playing the goal correctly and incorrectly. A good tip for students to follow for this practice step is, “When you prepare a goal, if it doesn’t sound, feel and look strange or at least very different, you’re probably still doing it wrong.” If a student practices the goal incorrectly on their first try, chances are, the student will practice the goal incorrectly all week long and show up to the lesson falsely believing the goal to be done. It is vitally important that students perceive the “first time they practice a goal” as a distinctly different step than the second step of isolating and drilling.

When preparing a goal, the student should isolate to the most extreme degree possible. In other words:

• Take the smallest chunk that makes sense, possibly as few as 2 or 3 notes.
• Go extremely slow to ensure 110% certainty of correctness – it should be so slow that it “doesn’t sound like music.”
• If the error involves only one hand (most errors do), only play that one hand by itself.
• Be able to play the goal both correctly and incorrectly on purpose.

I like to tell students that this step is kind of like putting up a target before starting to shoot at it. It would make no sense at all to execute the command, “Ready, Fire, Aim!”, and yet that’s exactly what students so often do when they go straight to steps 2 and/or 3, skipping over step 1 completely. In reality, it’s often more like “Fire!” since there is no readying or aiming involved; many students are content to fire the gun while it’s still in the holster.

Self-error-correction motivates a brain to commit an experience to memory far better than when errors are corrected by teachers, and that is why playing the goal both correctly and incorrectly on purpose is a hugely helpful step in the preparation process, as it simulates self-error correction. In fact, in the words of Robert Duke (2012), “Learning is error correction.” Memory that results from self-directed error correction is more persistent, understandable and generalizable than memory from a correction directly from the teacher. This carries the additional benefit of drawing more significant distinction between “right” and “wrong” in the student’s mind, making future successful error detection more likely.

For maximum retention of goals, a student can also spend just 5 minutes carefully going through just the “prepare” step of practicing, once for each goal, immediately after getting home from the lesson. Students who do this retain more of their goals than students whose first practice session is 24 hours after the lesson.

The importance and difficulty of this preparation step is magnitudes more difficult for goals involving the correction of rhythm. It’s possible a student may have to spend more time preparing rhythmic goals than they spend drilling them. As an extra preliminary step, sometimes I will tell a student to put their music down on a desk or on their lap and tap the correct rhythm while counting out loud. They must tap loudly with a single finger, always tapping below the note that is being tapped, so that the correct rhythm can be heard and the visual tracking of the music is shown by the finger.

While rhythmic difficulty can obviously be caused by rhythmic complexity, it can also ironically be caused by simplicity. A good example would be when students play dotted rhythms and 8th notes in a method book’s “Jingle Bells” arrangement that doesn’t have any dotted rhythms or eighth notes, because that’s how the student is used to hearing the song. In either case, the ideal solution is still the same: the student must be taught to break themselves out of the auditory prison they’re trapped in, either because of practicing a wrong rhythm for a week or because of hearing it a different way their whole lives. (A full discussion of teaching rhythm is too far outside the scope of this article series. The point here is to recognize that while the “Prepare” step of PIT Practicing is always important, it is magnitudes more important for temporal goals involving meter, rhythm, accelerando, ritardando, rubato, etc.)

Isolate & Drill

If “Prepare” is analogous to setting up a target before shooting at it, “Isolate & Drill” would be the part where you back up and practice carefully shooting at the target. Unlike goal preparation, which takes a goal out of context, isolating and drilling puts the goal back into context – enough to perceive whatever challenges are built into the goal, but still isolated enough to be able to accumulate a decent number of repetitions over a short amount of time and ensure the goal is still easy to concentrate on. When a student isolates and drills, they practice:

• A larger chunk (i.e. 2-4 measures), starting a little before the goal and ending one or two notes after
• Faster, but slow enough to have confidence in detecting errors
• Hands together

This is where I become like Darth Sidious as I tell my students to “listen to your feelings.” “Do you feel that you will easily remember how to play this goal correctly tomorrow even if you are not reminded of this goal? If not, keep drilling.” “Do you feel that you are barely able to play this goal correctly with 100% of your concentration / by the skin of your teeth? If so, keep drilling.” Sometimes students are overconfident, and their feelings betray them as the goal cracks under pressure in their next lesson. This is a learning experience for the student: I tell them that they need to aim for a higher feeling of security in the practice room than the feeling they thought was good enough.

The “jelly bean / M&M / pencil / whatever objects are nearby” game can come into play to make the process of drilling more fun. In this classic drilling game, a student might start with two jelly beans (let’s just call them “points”), and each time the student completes a correct repetition, the student gets one point. When they drill incorrectly, they lose a point. The game isn’t over until they have 5, 7, 10, or 15 points, depending on the difficulty of the goal. A teacher should specify starting and ending points for this game if the student is to play it all week, because if, for example, a student always starts with 2 points and goes to 7 points no matter what the goal, this may not be enough for some goals and might be too much for others. Ultimately, jelly bean game or not, a student must still learn how it feels for a goal to be done.

Test Yourself

After studying 20 vocabulary words, students intuitively know to cover up the words, quizzing themselves at the end of each day in order to simulate how a vocabulary test at the end of the week will go. This gives a good sense of whether or not to conclude studying. This natural intuition is a rare commodity in the context of music lessons – most students must be taught to do this. Just because a student can play a goal correctly when drilled in a 2- or 4-measure chunk doesn’t mean they will remember to do it correctly after being distracted by the 39 measures that comes before the goal, let alone after spending 24 hours away from the piano. Repetition will lead to ease, but this ease doesn’t become permanent until several days of practicing correctly, and it’s easy for students to mistake temporary ease (ability) for permanent ease (habit). It is rare for a student to naturally possess the healthy amount of self-doubt necessary to see past this illusion.

Concluding our analogy, once a student has placed the target and has spent some time shooting at it, it’s time for the student to run through the entire biathlon race to see if they can still hit the target even after doing some cross-country skiing. When testing a goal, the student takes:

• Much bigger chunks (i.e. 8+ measures)
• Up to speed (or whatever current performance tempo is)

If a piece has many goals to work on (wrong notes, rhythms, articulations, etc.), the student could possibly wait until isolating/drilling is done on all of the goals before testing themselves. The student could play the whole piece, stopping to isolate/drill some more on various goals that need more work.

But whether the student tests themselves after each goal or after all goals have been practiced, playing the entire piece should always wait until the end anyway, for many reasons. When students engage in what is sometimes called “whole to parts” practicing (play the whole piece before working on spots), as opposed to “parts to whole” practicing, it means:

1. Reinforced mistakes: Mistakes that haven’t been habituated yet are reinforced at the beginning of every practice routine, every day.
2. Fatigue: Boredom or frustration happens sooner during the practice routine since a good amount of mental energy was already spent playing the entire piece.
3. Dopamine effect: The student goes into “play” mode (go fast, ignore even the biggest mistakes, pleasure-inducing, dopamine-releasing), making it harder to switch into “practice” mode (go slow, correct even the smallest mistakes, not pleasurable). It is the opposite of “delay of gratification,” like eating a candy bar before every meal or like playing video games before doing homework. The act of practicing with discipline causes a student to “hunger” more for the “dessert” of performing the piece and causes the performance itself to be more focused and discipline-oriented, while performing first lends itself to less disciplined performance and spoils the student’s “appetite” for practice.

The main exceptions to practicing “parts to whole” would be when:

• a student has completed all of a teacher’s assigned goals and doesn’t know what to work on. The student could perform the piece first, searching for weaknesses, stopping to work on weaknesses as they are encountered.
• a student is quite experienced/advanced and already possesses (and chooses to use!) decent metacognitive skill. (In this case, practicing “whole to parts” is not an advantage, it’s just that with enough metacognitive skill and discipline, it’s no longer a huge disadvantage.)

Special Cases of PIT Practicing

There are at least a couple types of goals that require modifying PIT Practicing to “TPIT” Practicing. In other words, Test Yourself first, then use the test results to inform PIT practicing. These two goals are:

• Adjusting starting tempo: The student should begin performing without the metronome, stopping after a few measures to see if the starting tempo was accurate. Otherwise, there is no way for the student to truly know if they can conjure the tempo out of thin air, which is exactly the point of the goal and what the student will be expected to do in the next piano lesson.
• Memorizing: One doesn’t know what is in need of further memorizing until one attempts to play from memory. This is one goal that should never (not even in the beginning of the week) begin with “practicing with the music,” unless of course the piece is brand new and the student literally has nothing memorized. Some students of course memorize very naturally, but for other students, I tell them to make three “attempts” each day, where an “attempt” is defined as (1) performing with the music closed until your memory completely fails (unable to fight/think your way through), and (2) opening up the music and correcting/drilling the failure. This would essentially boil down to “TPI-TPI-TPI” practicing. (With an extra “T” at the end if the student so desires.)

It is helpful to remind students in the context of these two goals that part of the reason we practice is to simulate what will happen in the next lesson so that the results of the next lesson are not surprising to the student. If a student doesn’t test themselves first before practicing these two goals, the process of isolating/drilling runs the risk of “tainting the test” at the end, delivering a false positive to the student when the goal really isn’t secure. With this in mind, the third step of PIT Practicing could be thought of as “practicing performing” or “simulation training.”

Finally, there is one more exception. In this case, we use PIT Practicing, except that the last two steps (Isolate/Drill and Test Yourself) are combined:

• Securing tempo: While adjusting starting tempo is a problem of initially conjuring a tempo, securing tempo is a problem of maintaining a tempo that is correctly established in the beginning of the piece. Because a performer always believes their self-directed tempo is steady when performing without a metronome, even when it isn’t steady, it is not possible to drill tempo steadiness without the metronome, nor is it possible to test oneself without the metronome. Thus, steps 2 and 3 of PIT Practicing cannot be distinguished from each other. While the student drills with the metronome on, they are also continuously and simultaneously testing to determine if more work with the metronome is needed. This testing/evaluation must take the form of continuous microscopically-sensitive detection of the slightest urge to deviate from the metronome. Even if the smallest urge still exists, the metronome must still be used. As soon as the metronome is removed, neither drilling nor testing oneself can occur. The metronome can only be removed when the student is 100% certain the goal has been habituated by finally feeling continuously and perfectly “at one” with the metronome.

To summarize these exceptions:

• Adjusting starting tempo: TPI Practicing
• Memorizing: TPI TPI TPI with an optional additional T.
• Securing tempo: I and T are the same step (metronome can’t be removed until the goal is completed)

This simple, general framework for organizing the practicing of a typical goal is extremely beneficial to students. The next article on Goal Types will give teachers and students more detailed tools to use in service of strategizing both the assigning and practicing of goals.

(c) 2022 Cerebroom

References

Duke, Robert A. “Their own best teachers: How we help and hinder the development of learners’ independence.” Music Educators Journal 99.2 (2012): 36-41.

Hallam, Susan. “The development of metacognition in musicians: Implications for education.” British Journal Of Music Education 18.01 (2001): 27-39.

“Problem-solving skills mean little if a person is not motivated to use them.”

Zimmerman & Campillo (2003)

When I moved across the United States in 2012, I went from a studio of 45 intermediate and advanced students to zero students. As I waited for my first students to trickle in, I had a lot of time to reflect upon what I feel should be the highest priority in teaching piano: how to get students to practice efficiently. I knew that teachers should all be aiming to turn students into independent learners. In fact, I had known for a long time that practice efficiency has a 1-to-1 relationship with independent learning; you simply can’t have one without the other. This led me to do extensive research into metacognition, reading every study, article and chapter I could get my hands on.

Before I detail the changes that resulted from this research in parts 3-9, I will first describe the way I had already quantified practice quality (and still do), starting probably around 2003. I don’t remember a time in my teaching career when I wasn’t focused on aiming to “teach myself out of the job.” Getting students to be independent learners was always my primary aim, and even before my formal research began, this naturally led me to focus obsessively in each lesson on trying to make sure the student knew how to practice efficiently.

It didn’t take me very long after I started teaching in 1997 to realize that I needed a way to deliver feedback to students and parents that would be both accurate and useful, just like the valuable feedback we get in school from good teachers on homework assignments, or for that matter, like the instant feedback we get from video games when we get squashed by a boulder because we jumped too late or ran too slowly. This led me to a system of scoring goals in the notebook.

Before continuing, it’s helpful to coin a couple simple terms dealing with goal evaluation that I will use in this article and in future articles:

• Trouble goal: a goal that is “unacceptably incomplete” – a goal that should have been completed that week, but wasn’t.
• Reassigned goal: a goal that is “acceptably incomplete” – a goal that was expected to take longer than a week to complete when it was assigned.

A Simple Quantifying Scenario

The following would be a common example of one piece of music with its goals notated in the notebook. The typical student would have 3-4 pieces like this in addition to theory and technique assigned, but for the sake of simplicity in discussion, suppose this is all a student is working on:

Beethoven

– m.5 – fix counting
– m.13 – diminuendo
– m.24 – remember repeat
– LH always softer than RH
– speed up to q = 112

Suppose the next week the student gets everything done except the first and last goals. The student’s notebook will then look like this:

Beethoven

1 – m.5 – fix counting

1 – speed up to q = 112

Since it was fair of me to expect the student to achieve the first goal in one week, the student received a 1-point penalty for not fixing counting in measure 5 (a red-colored Trouble Goal). However, the goal to speed up to 112 (or similarly, a goal to “memorize”) might take more than one week to complete, so it is a neutrally Reassigned Goal with no point penalty (thus still written in black). The black number just acts as a counter showing how many weeks it has been reassigned. The student’s total score this week is the total of the Trouble goals (1), with a perfect score being 0.

Suppose next week the student speeds up successfully, but again fails to fix the counting. Their notebook would then read:

Beethoven

2 – m. 5 – fix counting

The student’s total Trouble goal score would be 2, signifying two weeks the student failed to get the goal done (and in this case, forming a “double Trouble goal”).

When a student completed a piece after performing it in a recital/group class (or simply after the student plays it at performance quality from memory), I would write “Done!” next to that piece in their notebook with a red-colored -1 (negative one) in the margin. This acts as a bonus point to cancel out a Trouble goal penalty point.

I also used a different color to assign Bonus goals once in a while, such as “m. 17 – add rubato.” If the student completed that goal, I’d score it as a -1 (negative one), but if the student never completed the goal, it was fine with me. Finally, if a student received an overall negative score one week, the negative points carried into future weeks until they cancel out Trouble goals.

When using this system, it is also critical to give students a clear definition of what it actually means for a goal to be considered “done” or “completed.” A goal is only done when it is habituated. This carries a few implications:

• If a student plays the goal wrong in the lesson and immediately corrects it, the goal is still considered incomplete and is marked as a Trouble goal. Demonstrating mere intellectual awareness of the goal by saying “darn it” immediately after failing to do it right isn’t enough.
• If a student already completed a goal last week, but the goal reappears this week, this is proof that the goal was not habituated last week but was instead learned only well enough to barely scrape by with deliberate concentration in the previous lesson. The Trouble goal score continues from where it left off. If the goal already had a penalty of 2 attached to it before, it now has a penalty of 3.

The Benefits

This simple system quantifies practice quality. Not only does this give students feedback they need so they can make immediate adjustments to ineffective practice strategies, the score itself makes it easy for parents to know at any time exactly how well a student is doing. In terms of metacognition, I always make it clear to students that while black (Assigned / Reassigned) goals teach students about music, Trouble goals teach students about music and about practicing. Thus, in terms of getting value out of each piano lesson, Trouble goals are students’ most valuable goals. They are the metacognitive goals, the goals that offer the student the most potential to grow.

Without this quantification system, when all goals are notated neutrally in the notebook, teachers will sometimes forget that certain notated goals were already reassigned from previous weeks, and more importantly, students will almost always normalize the reassignment of goals, thinking it’s no big deal for a goal to repeat from one week to the next, which is not conducive to students making adjustments to their inadequate practice strategies.

This system forced me to become a much better teacher since I had to rethink the way I delivered goals to students. Every goal I assigned needed to be both specific and measurable in one week, meaning there was no more writing down things like “more secure” or “louder forte.” These goals may sound good on the surface, but they present a huge problem to both the teacher and the student. Suppose the student received both of these goals for a piece last week, and after just hearing it this week, you notice the forte is indeed a little louder, and maybe the piece has less stumbles than last week, but still both unsatisfying (i.e. you were looking for 100% improvement, but you only got 25%). Unfortunately, you are now backed into a corner, facing two bad choices. You must now either (1) tell the student “good job” for making miniscule improvement (which most likely resulted from inefficient practicing) since, technically, the student did exactly what you asked them to do, or (2) opt for the more cold-hearted, “Sorry, that wasn’t good enough” to make sure the student learns your standards of improvement even though doing so is clearly unfair.

Of course, there is an option (3) here, which is the option I would take: “Sorry Jake, my bad. I was apparently out of my mind last week when I assigned these two goals to you, so even though you did exactly what I asked, I have to reassign them, this time written differently.” And of course they would be written in black so as not to penalize the student.

Not only does this force a teacher to become more precise in defining goals, it also forces teachers to ensure that goals are achievable in one week. There are exceptions. For example, very often when I tell a student to memorize or speed up to a certain tempo, I will precede the goal with the word “eventually.” This signals to the student that I won’t be penalizing them the next week if the goal isn’t complete. It is a goal that must be completed, but not necessarily this week.

The other big teaching benefit of using this system is that it is freed me from having to get the student to care about incomplete goals. To illustrate exactly what I mean by this, bear with me as I describe an interesting poster presentation at the 2009 MTNA National Convention titled “Tell The Truth Or Not” (presented by Yuking Mühlböck-Chou). Yuking detailed two talent scenarios that educators encounter and shows two possible choices for each scenario: if a student is talented, do we tell the student or not? If a student is not talented, do we tell the student or not? In correspondence with Yuking, she noted that the U.S. and east Asia seem to be polar opposites of each other: in the U.S., untalented kids are often told they’re talented (emphasis on self-esteem), while in east Asia, talented kids are often told they’re untalented (emphasis on pushing to work harder). Europe would be more of a middle ground, with educators always delivering the truth no matter how flattering or devastating it may be (emphasis on professional duty to the student).

Which is the best way? Whether we teachers are consciously aware of it or not, this dilemma is always present. Every student is different. Do I walk on egg shells and give my suggestion as gently as possible? Do I light a figurative fire under the student’s britches and motivate them to work harder? Or do I deliver the neutral truth? If only all of our students were little Spocks who only cared about improving and didn’t ever attach any part of their ego to their practicing each week, we could always do the latter.

The bondage of this constant, annoying feedback dilemma was broken when I implemented this system of scoring. Students already instinctively cared enough about Trouble goals they received, so I no longer had to try to “get them to care.” My feedback system acted as an unbiased mirror that made illusion impossible and forced students to see themselves as they actually are, and this was liberating. I felt free to teach with more gentle honesty than I ever had before (“gentle honesty” is one of the core philosophies I live by in my teaching), because my students didn’t like seeing that red pen no matter how nice I was about using it. No school teacher feels good marking a homework assignment or test question wrong, and the best teachers empathize with you when you mess up. But the best teachers are also the ones you can always trust to deliver to you the absolute truth about your playing. Students need to be able to count on honest, reliable, accurate feedback every minute of every lesson.

In retrospect, it seems so obvious: students earn grades in their academic pursuits. Without grades, school teachers would have a nightmare job of constantly trying to get students not only to understand their progress clearly each week but to also care about it, and since almost every child is afflicted with a disease I call “workophobia,” this would be a hopeless battle. Contrary to some fringe opinions about education, I believe that grades do far more good than harm to student motivation, whether in school or in private lessons.

Although there is a benefit of convenience in making marks directly in sheet music (as opposed to notating goals in the notebook), I’ve always had a minimalist philosophy in marking music. I don’t want to inadvertently train students to ignore composer/editor marks in the music when those marks aren’t circled by their teachers (notebook-notated goals train students to notice the marks in the music without the help of other visual prompts), and equally as important, I also want the notebook to serve as an ongoing dated record or log of goals. It takes a bit more time to notate goals this way as opposed to writing and circling things in the music, but in the long run, it benefits both the student and the teacher. (As an accidental side benefit, it is excellent practice for adjudication, in which the multitasking of listening while writing comments on a separate sheet of paper is essential.)

Some teachers may have a philosophical objection to writing scores down, such as “Students are already graded in school; I want music lessons to be a recreational escape for them.” Students are motivated by grades, and research supports this – although, frankly, I don’t think we needed research to reach this conclusion. All we need to do is imagine what kids would do in school if the notion of “grades” were abolished in school. I’ve been assigning grades for years now with nothing but positive results, for all the reasons discussed above. But for those who are not swayed, consider this: even if you don’t write a final “score” on the page each week, you can still write week counters next to reassigned goals and even use a red pen for trouble goals. Whether you officially tally up the total grade each week or not to produce an actual “score,” you’re still giving students and parents specific, useful feedback. But I think writing down the score is even better.

Part 3 on PIT Practicing will outline a general and practical metacognition-based strategy of practice routine organization.

(c) 2022 Cerebroom

References

Zimmerman, Barry J., and Magda Campillo. “Motivating self-regulated problem solvers.” The psychology of problem solving (2003): 233-262.

“I am absolutely convinced that there is, overall, far too little rather than enough or too much cognitive monitoring in this world. This is true for adults as well as for children, but it is especially true for children.”

Flavell, 1979

This nine-part series of articles is the result of more than 10 years of on-and-off research and an unquantifiable amount of obsession, experimentation and invention within the realm of metacognition and its application to private piano instruction. Each article will publish 1 week apart.

The parts will consist of:

1. Defining the Problem (this article)
2. Quantifying Practice Quality
3. PIT Practicing
4. Goal Types
5. Goal Interactions
6. Reflection
7. Independence vs. Modeling
8. The One-to-Three Rule
9. MetaPractice

Metacognition (“thinking about thinking”) can be understood in terms of both skill and knowledge. Metacognitive skill can be thought of as a never-ending three-part cycle consisting of planning, monitoring and evaluation:

In the self-translated words of Jurgen Baumert, self-regulated learning is “a dynamic interaction of ‘skill and will.'”

Metacognitive knowledge consists of knowledge that informs metacognitive skill. All of the following examples could be considered cognitive knowledge, just like any other knowledge, but when they are used in service of informing practice strategy, they become metacognitive:

• Self: “I struggle with memorizing.”
• Environment: “The keys on my piano at home are really easy to push down compared to most other pianos.”
• Subject matter: “It’s generally harder to fix a wrong rhythm than it is to fix a wrong note.”

Metacognition has been found to play a greater role in learning than mere cognition alone (Veenman, et al, 2006). In the context of musical study, practice strategy has been found to make a bigger difference in performance quality than how much or how long one practices (Duke, Simmons & Cash, 2009). As Louise Goss aptly put it, “Practice is not a matter of time spent, but a matter of mind spent.”

Flavell, the scholar who ignited interest in metacognition in the ’80s by coining the term and offering an insightful breakdown of it, spoke of a concern that still rings true today:

“I am absolutely convinced that there is, overall, far too little rather than enough or too much cognitive monitoring in this world. This is true for adults as well as for children, but it is especially true for children.”

(Flavell, 1979)

Pitts, et al (2000) echo this concern through observation, applied more specifically to music practicing:

“…the majority [of children practicing] display few self-correction techniques, and play through their pieces or exercises with little discernable self-evaluation.”

“…we witnessed [in students’ practice routines] a great deal of time-wasting and avoidance…”

Pitts & Davidson (2000)

While teachers universally acknowledge the great need for students to develop metacognitive skill, very few teachers know how to specifically go about accomplishing this goal (Wilson & Bai, 2010). Veenman and others reach the same conclusion:

“When we interviewed teachers about metacognition, their incidental responses did not go beyond ‘independent learning…,’ while a further query about how they applied metacognition in their lessons only resulted in blanks (Veenman, Kok & Kuilenburg, 2001; but see also Zohar, 1999). Teachers are absolutely willing to invest effort in the instruction of metacognition within their lessons, but they need the tools for implementing metacognition as an integral part of their lessons, and for making students aware of their metacognitive activities and the utility of those activities.”

Veenman, et al (2006)

Teachers are universally interested in doing more to develop their students’ metacognitive skills. Which students stand to benefit the most? Cheng found that metacognition and giftedness come as a pair:

“Several psychologists take a strong position on the relationship between metacognition and giftedness. Central to this position is the view that the gifted individual is an active and efficient information-processor and problem-solver.”

Cheng (1993)

Similarly, Alexander (2006) finds that metacognition is unsurprisingly correlated positively with high IQ (cognition), and that improving metacognition makes the biggest difference in helping students with lower IQs. Zohar, et al. (2008) similarly found that “meta-strategic knowledge” has a strong effect on low-achieving students. This is compounded by self-efficacy, as Nielsen (2004) found that students with high self-efficacy in musical practice are more likely to be cognitively and metacognitively involved in trying to learn the music compared to those who doubt their abilities.

What all this means is that students with average or below average musical predisposition (who very often correlate with students with average or below average self-efficacy) stand to benefit the most from deliberate effort to develop metacognitive skill.

Complexity of Music

While there is a substantial amount of research into metacognition in the classroom environment, comparatively little research has been carried out exploring metacognition in the environment of private instruction, especially in musical instruction. And yet the need for research seems inverted: while students’ scholastic pursuits are purely academic in nature, musical pursuits involve developing not only academic knowledge of music, but also physical coordination and synchronization of sound in time, both of which introduce magnitudes more possibility of error during practice than when engaged in purely academic pursuits.

Additionally, even the mere academic element of developing musical competency is a considerably complex human endeavor, especially with regard to learning to play piano, because those learning to read sheet music must read both horizontally for the passage of time, as well as vertically for the movement of both hands, with organists covering even more vertical space on the page to read instructions for their left foot. The fact that there is so much more room for error to occur during musical practice would suggest that there is an even greater need to develop metacognitive skill in the context of private music lessons than there is in the classroom environment.

This great need is reinforced on a personal level by private music teachers on a daily basis when their students show up to lessons each week with so few of their assigned goals completed. For a majority of teachers (with possible exception to teachers in renowned institutes, music professors, and other teachers with access to select, competitive students), many students will show up to lessons with half or less of their goals done, and this seems acceptable to most of the students and their parents even though similar effort in their academic pursuits would be considered mediocre at best and failure at worst.

Love Of Music: The Double-Edged Sword

Love of music causes a student to beg for music lessons and sit down each day and joyfully play their instrument. Unfortunately, it is this same love of music that also causes students to play music (pleasure-seek) even when they should be practicing (working) instead. Most students will take a fast tempo while trying to fix a mistake, even when the fast tempo prevents the mistake from being detected, simply because it is more enjoyable to take a fast tempo.

Brundage (2016) describes this problem as a problem of being in “stage 3” mode while attempting to practice goals when one should be in stage 1 or 2, according to a three-stage learning model of motor skill:

1. Cognitive stage – more cognitive engagement than physical effort (“more thinking than doing”)
2. Associative stage – less concepts/procedures, more concentration on physical movement
3. Autonomous stage – little or no cognitive engagement (“more doing than thinking”)

Practicing while in “stage 3” mode creates a fluency illusion in which familiarity is mistaken for correctness. As a student often thinks, “If it’s easy, it must be correct.”

Many students will also fail to isolate mistakes, starting in the beginning of the piece, playing all the way through the piece, even when told to fix a wrong note in one small spot. At best, this results in more elapsed time between repetitions when trying to fix the goal, and at worst, it results in no repetition.

Both of these common examples (playing too fast, and playing from the beginning/not isolating) demonstrate monumental metacognitive failure while practicing: there is no planning/strategizing, there is little (if any) monitoring for error (and the monitoring is marginally effective because of the fast tempo and/or failure to isolate problems), and later evaluating the success of the practicing is difficult or impossible for the same reason. The end result is the ignoring of mistakes. This would be analogous to trying to study for a biology test by speed reading 15 pages of notes from beginning to end over and over again. The biology notes would eventually be learned by this method, but at an abysmally slower pace and with more errors than if small sections of the biology notes are carefully studied one section at a time, including drilling and self-quizzing.

If this “speed read all the way through from the beginning” technique of study is lunacy, then the vast majority of music students (young and old) would be, by that definition, lunatics. Even the best private teacher has difficulty helping the average student develop metacognitive skill in the daily practice routine without actually being at the student’s side every day during practice, which is why:

“…the teaching of practise skills and strategies is an important part of the instrumental teacher’s role, allowing learning to become independent and therefore sustainable beyond the confines of the weekly lesson.”

Pitts & Davidson (2000)

Even despite our great diligence, so many students pleasure-seek at home even when shown how to properly practice during the lesson:

“…children’s awareness of desirable practise strategies is not always carried through into their own work.”

Pitts & Davidson (2000)

In fact, counterintuitively, as the average student’s musical skill increases, there is no improvement on organization of practice, analytic approach, or level of concentration (Hallam, et al., 2012). Additionally, even though the most advanced students tend to practice more efficiently, there is a dip in the use of effective practice strategies in the middle years of study, starting at around grade 3. I believe these metacognitive stagnation and dipping effects are enabled or compounded by two factors: piece level and at-home accountability.

First, pieces at the beginning level are shorter than more advanced pieces, so even when a beginning student pleasure-seeks and plays their entire 12- or 16-measure piece over and over again, the student may still derive great benefit from practicing since the music is short enough to produce relatively short time intervals between repetitions. The habits of this kind of practicing continue into the next levels as intermediate students underestimate the need to isolate and drill when it is so critical that they transition into more effective practice strategies. And unlike intermediate students, advanced students (if they make it that far) simply cannot progress at all without finding more ways to practice efficiently, so only out of dire necessity, they finally practice small sections of music, practice more slowly, monitor more closely for errors, etc.

Second, since so many students practice unsupervised, they are denied the environment they need to develop metacognitive skill:

“…for many learning activities, particularly academic tasks, teachers are usually present to give feedback on the accuracy or success of a child’s performance.”

Pitts & Davidson (2000)

A student may very well know that the best way to fix a wrong fingering is to isolate a small spot in the music and “drill” it until it is habituated (i.e. the teacher has given the student the correct metacognitive knowledge), but the student continues to pleasure-seek anyway instead of practicing (i.e. the student does not exercise metacognitive skill). Stephanie E. Christensen found in a case study (2010) that a gap exists between the students’ metacognitive knowledge and their application of effective practice strategies. As a student gains musical skill over the course of years of lessons, the gap between musical and metacognitive skill can even widen due to musical skill increasing at a more rapid pace than metacognitive skill, even sometimes despite the most skilled teacher’s best efforts in providing in-lesson hands-on instruction on efficient practice strategies.

The blessing and curse of loving music doesn’t end there. This metacognitive gap is not helped by a false assumption among students and some parents that since music is so enjoyable to listen to or sing along with, it must also be enjoyable to study at all times. This makes some parents more reluctant to “make” their child practice out of fear that it will strip their child of the joy of music making. Some parents seek traditional musical instruction for their child with the expectation that their children quickly gain musical skill and become competent musicians while simultaneously expecting music to be a recreational escape from the disciplines of the day. In reality, it takes as much or more work to develop musical skill as it takes to develop skill in any other discipline. In that regard, some parents sign their children up for failure from the first day of lessons because they hold unreasonable expectations for the music practicing experience, unless they specifically seek lessons from an RMM teacher. [“Recreational Music Making,” much like in the field of music therapy, focuses on the enjoyment of the musical experience rather than pace of musical progress.] In truth, when done right, traditional musical study may very well be the most mentally vigorous of all the day’s activities. Ironically, it is typically the students who approach their musical study with vigor and discipline who enjoy musical study the most, because the highest musical joy and excitement comes from making rapid and consistent musical progress.

That said, optics matter. While it’s important for parents and teachers to be mentally prepared for the fact that music is a vigorous study that cannot experience genuine success without disciplined study, there is no reason to advertise it that way to the new, excited student who is first starting lessons:

“Treating practise as something that is ‘good for you’ … is an attitude unwittingly perpetuated by teachers and parents, and one which fails to connect with children’s intrinsic motivation…

…

…Hallam cites achievement, reward and social motivation as being powerful forces in supporting a child’s interest and developing sustainable intrinsic motivation.”

Pitts & Davidson (2000)

Additionally, it is more difficult to receive negative feedback from a teacher when the instruction is one-on-one, which is by far the most common setting for music lessons (rightfully so, since there is so much that can go wrong with practicing). The previously-mentioned love so many students have for music, which typically exceeds the love students have for any academic subjects they study in school, can cause a greater attachment of ego to the musical pursuit, which increases the need for delicacy when giving criticism to certain students.

Giving negative feedback to students in a way that does not damage students’ self-efficacy is further complicated by the fact that so much time elapses between each lesson. This effectively raises the stakes. Unlike school work, which is evaluated on a daily basis, every music lesson (and therefore every word of negative feedback) is judging an entire week of work. Certain students of all ages and genders, especially adults, have a difficult time hearing various types and degrees of negative feedback, no matter how warranted it is or how diplomatically it is delivered. Consequently, many teachers will water down the truth or downplay its importance so that the student is not disheartened, because sometimes disheartened students quit.

It is also interesting to note that as far as metacognition is concerned, age and wisdom are not correlated. Krätzig & Arbuthnott (2009) found that while both kids and adults tended to gain metacognitive skill as they gained item-specific experience (e.g., gaining experience studying piano naturally leads to the development of some metacognitive skill in piano with time), a more general “lifetime experience” had no effect on metacognitive skill. This implies a beginning adult student is in equally dire need of metacognitive instruction as young students. Unfortunately, while younger adults showed significant improvement in metacognitive skill with item-specific experience, older adults did not, reinforcing the cliché that one cannot teach old dogs new tricks.

Truth vs. Self-Efficacy

Because of the bad habits this pleasure-seeking creates and the pressure teachers feel to “walk on egg shells” to avoid harming student self-efficacy and motivation, music instructors face the difficult choice of (a) being honest about the gravity of a student’s practicing failures week after week, which may deflate and therefore demotivate the student and/or parent, or (b) downplaying the failed practicing routine, which can give the student a false sense of accomplishment and reinforce bad practicing habits.

In light of false perceptions that parents have for musical study and identities entangled with musical pursuits, only the most confident teachers are willing to lean toward option (a), risking student and/or parent demotivation by conveying failure to the student and/or parent whenever it is truly needed. That is, while a typical music student may very well be told to fix the same problem week after week, the student is never given any sort of score, grade, or any other tangible form of critical feedback that allows the student to discern the difference between great success, average progress, or utter failure in their overall weekly practice routine. And yet:

…feedback is more strongly and consistently related to achievement than any other teaching behaviour…this relationship is consistent regardless of grade, socioeconomic status, race, or school setting.

(Bellon, et al, 1992)

This presents an issue that should be of the very biggest concern within the field of private music pedagogy: despite the fact that musical study places greater demands on a student than most or all other pursuits, students are typically given insufficiently concrete feedback on the quality of their practicing and are therefore at a disadvantage in developing metacognitive skill. While general musical feedback (e.g., pointing out a student’s mistakes during a lesson) enables a mindful student to alter failed practice strategies, unfortunately, the average student will not be as mindful as needed if the feedback received is not delivered in a way that makes it matter. As Zimmerman and Campillo (2003) state, “Problem-solving skills mean little if a person is not motivated to use them.”

The issue of feedback (making it clear and making it matter) will lead directly into part 2 of this article series, Quantifying Practice Quality. But after detailing all of this metacognitive doom and gloom, I’d like to end with perhaps the single most effective thing we can do to address all of these problems: be direct with students and parents. Let them know when the issue at hand doesn’t just involve learning music, but learning how to learn music:

“Metacognitive strategy instruction that combines instruction on how to use particular strategies with an emphasis on the conditional knowledge of when and why to employ such strategies has long been considered the key to regulating one’s learning (Baker and Brown, 1984).”

(Huff & Nietfeld, 2009)

“Seminars on metacognitive strategies and the integration of music knowledge should become part of the music school curriculum.”

(Aiello, 2014)

Group performance classes would be the perfect place to start with a quick 5-minute discussion on metacognition. For example, “On the whiteboard is a goal. Take two minutes to think about the most effective way to practice that goal, and why. After the two minutes is up, we’ll share answers and discuss.” This is extremely engaging for students in any group setting, regardless of the mix of age or level.

Now that the various metacognitive problems that students have are documented, the remaining eight articles will focus on solutions to these problems, most of which will be extremely useful to share with students, and some of which are more for internal decision-making on the part of the teacher.

(c) 2022 Cerebroom

References

Aiello, Rita. “The Importance of Metacognition Research in Music.” Proceedings of the 5th Triennial ESCOM Conference (2003): 656-658. Electronic Publishing Osnabruck Music. Web, 13 Oct. 2014.

Alexander, Joyce M., Kathy E. Johnson, Jennifer Albano, Thea Freygang, and Brianna Scott. “Relations between intelligence and the development of metaconceptual knowledge.” Metacognition and Learning 1.1 (2006): 51-67.

Baumert, Jürgen. “lernstrategien, motivationale orientierung und selbstwirksamkeitsüberzeugungen im kontext schulischen lernens.” Unterrichtswissenschaft 21.4 (1993): 327-354.

Bellon, Jerry J., Elner C. Bellon, and Mary Ann Blank. “Teaching from a research knowledge base.” NASSP Bulletin 76.547 (1992): 121-122.

Brundage, Steven. “Fooled by Fluency: Understanding Illusions and Misjudgments in Music Learning.” American Music Teacher (Oct/Nov 2016): 10-13.

Cheng, Pui-wan. “Metacognition and giftedness: The state of the relationship.” Gifted Child Quarterly 37.3 (1993): 105-112.

Christensen, Stephanie E. “Practicing strategically: The difference between knowledge and action in two eighth-grade students’ independent instrumental practice.” Update: Applications of Research in Music Education 29.1 (2010): 22-32.

Duke, Robert A., Amy L. Simmons, and Carla Davis Cash. “It’s not how much; it’s how: Characteristics of practice behavior and retention of performance skills.” Journal of Research in Music Education 56.4 (2009): 310-321.

Fitts, Paul M., and Michael I. Posner. “Human performance.” (1967).

Hallam, Susan, et al. “The development of practising strategies in young people.” Psychology of Music 40.5 (2012): 652-680.

Krätzig, Gregory P., and Katherine D. Arbuthnott. “Metacognitive learning: the effect of item-specific experience and age on metamemory calibration and planning.” Metacognition and Learning 4.2 (2009): 125-144.

Nielsen, Siw. “Strategies and self-efficacy beliefs in instrumental and vocal individual practice: a study of students in higher music education.” Psychology of Music 32.4 (2004): 418-431.

Pitts, Stephanie, and Jane Davidson. “Developing effective practise strategies: case studies of three young instrumentalists.” Music Education Research 2.1 (2000): 45-56.

Veenman, Marcel VJ, Bernadette HAM Van Hout-Wolters, and Peter Afflerbach. “Metacognition and learning: Conceptual and methodological considerations.” Metacognition and learning 1.1 (2006): 3-14.

Wilson, Nance S., and Haiyan Bai. “The relationships and impact of teachers’ metacognitive knowledge and pedagogical understandings of metacognition.” Metacognition and learning 5.3 (2010): 269-288.

Zimmerman, Barry J., and Magda Campillo. “Motivating self-regulated problem solvers.” The psychology of problem solving (2003): 233-262.

Zohar, Anat, and Adi Ben David. “Explicit teaching of meta-strategic knowledge in authentic classroom situations.” Metacognition and Learning 3.1 (2008): 59-82.