Teaching musical learning as problem-solving: Applying a theory of musical intelligence to musical instruction

Recognizing the existence of a problem

The learner must first recognize that something is even wrong or in need of improvement. Teachers often try to be helpful by telling students when they make errors. And of course, especially with beginners, such feedback can be helpful. But ultimately, musical learners need to recognize when they make mistakes. During practice, there will be no one to tell them that they are playing, say, too fast or too slow, or out of tune, or with poor phrasing of a bow. They need to be able to say to themselves, without a teacher’s or anyone else’s prompt, “Something sounds wrong,” so that they can learn from their mistake. During music lessons, therefore, we would urge teachers to encourage students to listen for their own mistakes and point out those mistakes only if the students do not recognize them.

For example, often J. (our music teacher coauthor) will ask a student after they have played, “Okay, what did you think?” This practice is an example of what was described above as monitoring of one’s solution process and follows from constructivist and reflective approaches to learning that emphasize the need for students to construct their own learning (Bruner, 1960; Sternberg & Grigorenko, 2007). Some students immediately can assess and answer specifically what they liked or thought needed improvement, such as, “I think my first finger was out of tune,” or “I forgot to do the accents on the second line,” or “I really liked what I did dynamically.” Then there are those students who fall into a self-reflective gray area—they can hear something is not quite right, but they do not know specifically what it is. They almost recognize a problem, but not quite. Rather, they suspect there might be a problem. Their assessment might be something like, “It was okay, I guess? Some parts didn’t seem right. I’m not sure what I did wrong, though.” That’s when J. steps in and offers a little nudge to help them narrow down issues: “Okay, what did you think about the bow stroke? How did the 16ths feel on the second page? Did you like the tempo you chose?” Then, there are students who don’t hear anything amiss and just shrug and say, “I don’t know” or “I thought it was fine.” These students might know something is off but may be apathetic in addressing the problem, or they genuinely may not hear where their playing needs improvement. They may need more specific guidance, such as, “Check your contact point on the string crossings” or “Watch your first finger when you shift.”

Defining the problem

It is one thing to recognize something is wrong with one’s playing. It is another to define specifically what is wrong. For example, a string player may recognize that when they are shifting from first position to fourth position, the fourth position is out of tune. But why is it out of tune? Are they not stretching their fingers far enough? Are they not moving their hand back and forth quickly enough? Are they moving their hand quickly but positioning it wrong on the fingerboard? Or the string player may try to figure out why they are getting squeaks on the highest string. Are they pressing too hard on the bow? Are they positioning the bow incorrectly? Is the string bad?

In lessons, a teacher usually can tell the student what the problem is. But the teacher cannot cover all the problems, and moreover, as the student practices and old problems are solved, new problems emerge. Students need to become self-directed learners who can recognize and then figure out the problems they are facing in learning. As learners, they also become serious problem finders (Csikszentmihalyi, 2013) and problem solvers (Sternberg & Funke, 2019).

Teaching inadvertently can develop a passive mindset that makes it hard for learners to develop self-direction. Short-answer and multiple-choice tests in schools particularly encourage such a mindset. So often, schooling takes the form of the teacher providing the problem and the student then solving it, or the teacher telling the student what to learn and the student then learning it. But to develop expertise in music, students must engage these two prior steps of problem recognition and problem definition without a teacher there to tell them, “Here’s the problem; now you solve it.”

Allocating resources to the solution of the problem

When one is practicing, especially when one is just starting to learn a piece, so many things may be “off” that the learner hardly knows where to begin to make the piece sound good. At all points in learning, the student has to allocate her or his time and effort, deciding which problems are worth dealing with now, which ones will have to be dealt with later, and if the effort is to be made now, how much time and effort to put into the solution of the problem. If, in learning a difficult piece, the intonation needs work, the rhythm is off, the phrasing is inadequate, the dynamics are incorrect, or the playing just fails to create a coherent sense of a musical piece of music, then it just is not possible to address everything at once. (This can also be the case while learning easier pieces, just on a lesser scale.) The student of music needs to set priorities for what to fix when, and how much time and effort to spend in the various fixes. While some problems will need to be addressed later, the student must be careful to avoid practicing mistakes in the meantime, as they can become a learned bad habit. This can slow down the learning process, and may often take a considerable amount of time to undo (Kreitman, 1998).

This is why beginning music students must start with very simple, tangible concepts that will be expanded into more refined practice over time. These are usually foundation-based both in setup (such as proper bow hold or slightly curved left wrist) and in playing (such as correct notes, correct rhythm, and steady tempo). As students become more confident and independent with the basics, they can begin to add broader goals into their practicing. The teacher can be helpful in outlining those goals so that the trajectory remains successful.

For example, J. might ask a beginning student to concentrate solely on holding up their instrument with good posture while plucking open strings. This narrows the focus to instrument setup, placement of the right hand for plucking, and gaining familiarity with the open strings. It also provides an immediate reward for the student, as most beginners are eager simply to play. At this stage, students do not need to worry about much beyond the basics. There is no printed music to look at, so they can easily watch what they are doing. Once their setup is comfortable and confident, the right hand placement is solid, and the notes of the open four strings learned, the student can start adding layers, such as listening for the tone of a well-plucked note while beginning to learn simple plucked scales. If the student is confident in their left hand, the bow is gradually added, and simple rhythms are introduced. No matter the level or learning pace of the student, each layer added is continually reinforced, always going back to the foundation of solid setup, steadiness in tempo, and rhythmic and tonal accuracy. A shaky foundation is like building on quicksand, setting the student up for frustration down the road. When there are many goals to address, priority always should go to the foundation, no matter the difficulty level of the material.

Mentally representing the problem

All problems in playing music somehow have to be mentally represented. Consider, for example, playing a just a few bars of a musical piece. One wants to learn those bars so that they sound great, if not perfect. How does one think about the music? One can represent it visually, seeing the notes in one’s head. One can represent the music aurally, hearing the notes in one’s head. One can represent the music kinesthetically, feeling what it is like to play the music—the breathing and finger movements on the trumpet, the bowings and finger movements on the viola, the positioning of the hands and fingers for both the simultaneous and successive notes on the piano. A successful learner is likely to use more than one mental representation. The mental representation can serve as a model against which to test one’s playing. Sometimes, in our playing of our stringed instruments, we test our own playing against our aural memory of great violinists, violists, or cellists playing the same music. What did they do differently, and especially, what did they do better? They may have achieved technique or levels of musicality we have not achieved. Perhaps they deliberately practiced many more hours than we did, or they may have studied with the best teachers or have extremely strong internal motivation. They also may have also started very young or have come from musical families.

These considerations point to an essential feature of learning to excel in musical performance. We all have strengths and weaknesses, some of which we can help (e.g., developing technique), others of which we are powerless to do anything about (e.g., coming from a musical family). Successful performers figure out their strengths and weaknesses, and then capitalize on their strengths while compensating for or correcting their weaknesses. They succeed in very different ways. One can listen to multiple professional performers play a given difficult piece, such as the Elgar Cello Concerto. They differ in all aspects of performance, from technical skill to interpretive techniques. For example, Heifetz and Kreisler had completely different playing styles, yet both succeeded brilliantly in making the most of their different kinds of virtuosity. Few have matched the incredible precision and technique of Heifetz or the passion of Kreisler.

Music is represented aurally, kinesthetically, and visually. For example, J. hears each note played while visualizing the fingerboard in her head. She can “feel” her fingers contacting the mental fingerboard. When she sees music on a page, she hears the notes in her head, as her mental fingers “remember” what the pitch sounds like when it is placed. Interestingly, when mentally “hearing” very high notes in the treble clef, she has a lot of difficulty, as that part of the fingerboard is not as familiar and therefore not as mentally “imprinted.” In contrast, R., the academic, started on the piano, and often visualizes a piano keyboard when he plays, determining half-steps, full steps, and more on the keyboard and then translating them to the violin, viola, or cello.

We each find a mental representation that works for us. Teachers can help students find representations that work for them. This heuristic applies not just in music. In all expert performance, individuals learn to represent information in ways that help them chunk together in a unified way large strings of information that, for other people, may be just isolated bits of information (Ericsson et al., 1993). For example, a runner may learn long strings of numbers by chunking them as running times.

Formulating a strategy to solve the problem

Once one has figured out that one has a problem, figured out what the problem is, decided how much effort to put into a solution, and mentally represented the problem, one needs to figure out how to solve the problem—how to get from where one is to where one wants to go. How can the learner make the music sound what they want it to sound like?

Strategy formulation opens up an infinite number of possible paths. There are myriad ways one can go about improving one’s performance. But inevitably, one has to decide upon a sequence of steps to effect that improvement. Given that one cannot do everything at once, does one want to start with a small portion of the entire musical piece, or with the piece as a whole: put more initial emphasis on intonation or on simply hitting the notes at all? There is no one formula that works for every piece or for every learner. Students of music have to figure out what works for them. Teachers can suggest to students, especially beginning students, how to structure their practice. But in the end, the students have to find a structure that works for them. Thus, the best the teacher can do is to help the student figure out how he learns best to play music in a way that will optimize on the student’s knowledge and skills (Galamian, 1962).

With beginners, J. usually starts new pieces in small chunks. This makes the music immediately accessible and allows the student to focus on specific techniques that they then later will apply to the rest of the piece. Assigning too much music to a beginner is usually an exercise in frustration for both student and teacher, as there are too many variables to work on. Too much to do at one time dilutes focus, and students who try to do too much inevitably will learn bad habits that will take time to undo. For beginning players, this means helping them structure their practice so that they are practicing in a logical, organized way. As they become more advanced and confident in their abilities, they usually do not need as much guidance from J. in how to organize their practice (though intrinsic motivation, extra-curricular activities, and home environment all can factor into this) (Abeles et al., 1994).

Structuring of practice also is dependent on experience. J. is more involved with helping beginners to structure their practice because beginners have not yet developed a system of organized practice. They often confuse merely playing with practicing. One can tell a student to “go practice,” but what exactly does that involve? At this stage, they are learning not just what to practice, but how to practice (Green & Gallwey, 1986). As students get older and more independent, J. trusts that they will develop their own practice structure that works for them. If their practice is not organized, it will show during lessons, and J. will step in to offer suggestions to help get them back on track. At minimum, deliberate practice always involves, according to Ericsson and Pool (2017), (a) having a specific goal in mind, (b) consistently learning from feedback, which in music would include that generated by hearing the sounds one produces when playing an instrument, (c) learning in one’s zone of proximal development—where one is just a bit uncomfortable in what one is practicing because it is slightly beyond one’s immediate reach (Vygotsky, 1978), (d) building a strong foundation for future work, (e) staying focused on the task at hand, (f) mentally representing information in an expeditious way, and (g) having expert coaching available to help one to improve. As we stated earlier, having a specific goal in mind requires first recognizing that there is a problem that needs to be addressed for which a goal needs to be set.

Monitoring one’s problem-solving during the solution process

A learner needs to monitor their problem-solving in learning while they are in the process of learning: “Is the piece starting to sound better? Am I getting closer to where I want to be? If so, great. If not, what is going wrong?”

Sometimes, the strategy one adopts to improve one’s playing just seems not to be working. Perhaps one is learning the notes but one is tensing up so that the notes actually sound worse than they did previously. Or one is playing rhythmically but the whole piece is too slow or too fast. Or one is learning the piece in a way that will not harmonize with an accompanist or other players in a trio or quartet. If one does not monitor while learning, then one may feel like one is doing all the right things, and then feel at the end that the piece has come out sounding wrong. It is necessary continually to be asking oneself what one can do better.

At the same time, students also must learn how to balance their monitoring so that they don’t get overwhelmed or even become paralyzed in their practice. Students who are perfectionists easily can become bogged down in reflective thought, either focusing too much on one thing at the expense of everything else, or becoming frustrated when faced with multiple variables in their practice. The teacher can help guide students in learning to channel their naturally intensive monitoring in a healthy, productive way that will aid rather than paralyze them. On the flip side, students who don’t have a natural tendency toward reflection may also have difficulty in their practicing. They may need more guidance in practice structure and focus.

Evaluating one’s problem-solving after the problem is solved

After one has learned a piece or whatever one is seeking to learn, one has to look back and ask whether one has indeed gotten to where one hoped to go. It may even help to stand, if possible, in front of a mirror and assess how one looks when playing. Is one sufficiently relaxed? Is one standing or sitting erect or is one hunched? Is the enjoyment there—in the face and in the body? Many times, one finishes “learning” a piece, only to realize that one has merely finished a phase of learning the piece. One has gotten through the basics but now has to pay attention to the details or even to the big picture, which may have been lacking. The final evaluation is the time to take stock of where one is.

Evaluation is a continuous process that becomes more and more refined over time (Suzuki, 1978). There are pieces that are permanently in the musician’s mind and hands that may feel very comfortable, but the musician almost always can find ways to improve on them if the musician goes back to them. This process occurs in lessons, too. Students will finish learning a piece, will move on to other things, and then go back to polish up the piece (usually in preparation for a performance). For performance purposes, this polishing can include working with an accompanist, fine-tuning of intonation, improving muscle memory, building performance stamina (especially if playing a long musical work), and working through performance anxiety. It’s the ironing out of all the little issues that, collectively, can crop up and block the creative flow.

The roles of analytical, creative, practical, and wisdom-based skills in teaching and learning

Musical learning involves memory, of course. Students may memorize pieces or find themselves memorizing patterns of fingering or bow movements. But in their learning as problem-solving, students are applying the metacomponential processes described above analytically, creatively, practically, and perhaps even wisely (Sternberg & Grigorenko, 2007). Teaching using these processes has been shown empirically to improve student achievement (Grigorenko et al., 2002; Sternberg et al., 1998), so long as teachers understand how to teach using these processes and actually use them in their teaching (Sternberg et al., 2014). However, this article is the first to apply these particular metaomponential processes to music instruction, and so empirical evidence specifically for their effectiveness for music instruction awaits future research.

Analytical skills

Analytical learning occurs when students analyze, evaluate, judge, critique, and compare and contrast. For example, the students may analyze the accuracy of their intonation, evaluate the extent to which their performance fulfills the composer’s intentions in composing the piece, critique the musicality of their performance, or compare and contrast their performance to that of expert musicians or perhaps to their performance of a given piece a year earlier.

Analytical skills are probably those that are most emphasized in typical musical instruction. Yet, they are not the only skills that are important in musical learning through problem-solving. Creative skills matter too.

Creative skills

Creative learning is a key to success for learners that goes beyond mere imitation of what past performers have done before them, or mere following of exact instructions from a music teacher as to how to perform a piece. Creative learning occurs when students create, imagine, discover, and invent. For example, students may create a new piece of music. Or they may imagine how the piece would sound if it were played by an expert musician. Or they might discover a new way successfully to achieve a very difficult fingering pattern in a piece that had defied them in the past. Or they even might invent a new musical instrument or a new form of musical composition.

In learning to play a musical composition at an advanced level, the musician is in effect co-creating with the composer. The way two advanced and certainly professional performers play a composition will be different, perhaps quite different. One of our favorite examples is Bach’s Six Suites for Solo Cello, which in the hands of different expert performers, such as Yo-Yo Ma, Pablo Casals, Mstislav Rostropovich, Janos Starker, Mischa Maisky, and others can sound very different. Each performer brings their own creative talents and ambitions to the Suites in a different way. They learned the same music, had to go through the same steps of learning as problem-solving, but in the end used their creativity to perform the Suites in very different ways.

Some teachers believe that creativity in playing music should be reserved for advanced stages of play, once all technique has been mastered. We disagree, as did Bruner (1960). The same argument has been made, of course, in other fields, such as the sciences. The problem is that one not only learns in the early stages of learning but also learns how to learn. And if one learns how to learn in a mechanized rote way, the switch to a more creative way of learning and performing may be at risk, as pointed out in the theory of successful intelligence (Sternberg, 2020a). Many very analytically smart students with excellent memorization skills never develop the kind of creative attitude that will enable them later to challenge existing ways of doing things (Sternberg, 2018) or, in music, of performing or composing. Essentially, schooling wipes out their creative mindset, and they never get it back. Schooling also may remove some students from the practical mindset needed for success.

Practical skills

Practical skills are also paramount in this problem-solving cycle. Practical skills are involved when one applies ideas, implements ideas, puts ideas into practice, and persuades others. For example, a musician might apply what they have learned about making a baroque piece sound “baroque.” Or the musician might implement a difficult phrasing of some measures that previously they were able to imagine but not to perform. Or they might put into practice a routine for deliberate practice to replace what previously had been unreflective playing of pieces without thinking about how to improve one’s performance of them. Or they might try to persuade an audience that their unusual interpretation of how to perform a piece has artistic merit.

Practical skills are the ones that enable musicians not only to reach audiences, but more generally, to succeed in a professional career, including finding and maintaining employment and sometimes “wowing” audiences. Some musicians are technically competent and may even be creative, but they lack the practical skills involved in connecting with an audience. Practical skills are important, but sometimes are utilized only to advance one’s own musicianship or career. Wisdom-based skills go beyond the interests of the individual musician.

Wisdom-based skills

Finally, wisdom-based skills are those that are used when one seeks through music to achieve some kind of common good over a longer term, not just a shorter one. Benefit concerts are a transparent example of how musicians try to do something good for the world. But for professional musicians, wisdom-based skills are also involved in giving lessons at reduced rates to those who cannot afford the full price, in playing music that will uplift the spirits of people whose spirits need uplifting (and whose don’t?), and sometimes in taking a risk and introducing new music to audiences that the audiences may not yet be ready for. Music teachers also try to impart wisdom-based skills as they show students that music is not only an enjoyable experience but also an uplifting one that helps make an often fraught world a better place in which to live.