Toward Solving the Problem of Problem Solving: An Analysis Framework

602124JMTXXX10.1177/1057083715602124Journal of Music Teacher EducationRoesler research-article2015 Article Toward Solving the Problem of Problem Solving: An Analysis Framework Journal of Music Teacher Education 2016, Vol. 26(1) 28 42 National Association for Music Education 2015 Reprints and permissions: sagepub.com/journalspermissions.nav DOI: 10.1177/1057083715602124 jmte.sagepub.com Rebecca A. Roesler 1 Abstract Teaching is replete with problem solving. Problem solving as a skill, however, is seldom addressed directly within music teacher education curricula, and research in music education has not examined problem solving systematically. A framework detailing problem-solving component skills would provide a needed foundation. I observed problem solving that occurred during 49 video-recorded lessons taught by six renowned artist teachers. When a solution to a problem came about as the result of both teacher and student involvement, I identified the problemsolving behaviors that were differentiable as performed by teacher or student. Five components, synonymous with problem-solving behaviors observed in other fields, emerged as identifiable behaviors that contributed to problem solution: establish goals, evaluate, conceive and consider options, apply principles, and decide and act. To confirm this model, I coded every observable behavior within 18 full-length lessons. Almost every on-task behavior was describable in terms of the proposed problem-solving framework. Keywords instruction, instrumental, modeling, music educators, music teacher preparation, problem solving, reflection, teaching effectiveness, teaching techniques Progress in music performance comprises the realization of numerous intermediate goals, each acquired through the application of a host of behavioral and perceptual skills. In the process of developing technical capacity or preparing repertoire, 1 University of North Texas, Denton, TX, USA Corresponding Author: Rebecca A. Roesler, Professor of Music, Brigham Young University Idaho, 525 South Center St., Rexburg, ID 83460, USA. Email: roeslerr@byui.edu

Roesler 29 teachers and learners make numerous corrections, adjustments, and decisions. Ideally, their ongoing behavior is guided by clearly defined goals that help focus attention and effort advantageously. Each performance goal, each technical goal, each communicative goal, until realized, is a problem to be solved. Thus, the process of musical development is replete with goal pursuit, requiring perpetual problem solving. Problem solving, the process by which teachers and learners achieve goals (see Gerlach, Spreng, Gilmore, & Schacter, 2011; Hambrick & Engle, 2003), has been widely discussed in the literature of many fields, including music composition (Collins & Dunn, 2011), mathematics and science education (e.g., Kotsopoulos & Lee, 2012; Tsai, Hou, Lai, Liu, & Yang, 2012), corporate business (e.g., Buijs, Smulders, & van der Meer, 2009), infant and child development (e.g., Lee, Koh, Cai, & Quek, 2012; McCarty, Clifton, & Collard, 1999), and health care (Hill- Briggs, 2003), to name a few. As illustrated by this great diversity of domains that depend on successful problem solving, it is a nearly ubiquitous human activity. Surprisingly, despite the highly goal-driven nature of music study, problem solving has been largely overlooked in this discipline. It is reasonable to consider that music education could also benefit from investigating the process of solving musical problems. The accomplishment of instructional goals (targets) is one of the fundamental elements that defines progress in music instruction. A productive lesson or rehearsal is the product of the cumulative accomplishment of multiple subgoals that lead to broad aims. It is for this reason that Duke (1999) recommended that systematic research be organized around units of analysis he dubbed rehearsal frames, periods of instructional time in which attention is devoted to accomplishing identifiable proximal goals. The time from the moment attention is first directed toward a goal until attention is directed elsewhere constitutes a rehearsal frame. Prior to Duke s (1999) proposal, research analyses had been typically conducted over entire rehearsals or lesson without regard for learners accomplishment moment to moment (e.g., Francisco, 1998; Menchaca, 1988). Since Duke s call to action, a number of authors have analyzed music learning in relation to instructional targets (Cavitt, 2003; Colprit, 2000; Worthy & Thompson, 2009). Cavitt (2003), for example, found that certain targets elicited different types of teacher behaviors than others, an observation that would have been difficult had she only considered teaching behaviors generally, as they occurred over the course of rehearsals. Although these extant analyses are instructive and important, they do not fully describe the actual process by which targets are accomplished. It seems important to define with some precision the individual components that contribute to the solution of problems in music study. The purpose of this study was to establish a model by which musical problem solving may be researched, analyzed, and evaluated, through observations of problem solving by teachers and students during one-to-one music instruction.

30 Journal of Music Teacher Education 26(1) Table 1. Characteristics of Teachers. Instrument Students educational experience Year videotaped Flute 7 college 2013 Trombone 4 college 2010 Violin 3 adolescents, 10 college 2008 Oboe 7 college 2003 Viola 2 adolescents, 8 college 2003 Piano 8 college 2002 Method Participants Teacher participants were selected from among a pool of distinguished teachers who were honored as guests in a residency series at a major southwestern university. Six teachers were selected based on high-quality video and variety in instrumental expertise. Student participants were those regularly receiving instruction within these teachers studios and with whom teachers had already established an ongoing relationship. These included adolescents (5) and college-aged students (44). See Table 1 for descriptions of teachers and students. The teachers consented to video recording their lessons in their regular teaching environments, on location at their respective schools, and with their own students. 1 Lessons were videotaped by various doctoral students from the hosting university between 2002 and 2013, within the year following these teachers residencies at the university. I analyzed all lessons of which I acquired video footage, a total of 49. All lessons that occurred during a block of 1 to 4 days (depending on the teacher) were videotaped, each with a different student. Videotaped lessons serve as a representative sample of the teaching of these teachers and the students within their studios. Some of the video footage used in this study has been analyzed in previous research (Duke & Chapman, 2011; Duke & Simmons, 2006). The current analysis is independent of these studies. Analysis In accord with the principles of grounded theory (Corbin & Strauss, 2008), I began with unstructured observations of these teachers as they taught individual lessons with their own students. I identified moments in which discernible changes occurred in learners playing and extracted coinciding rehearsal frames according to the time that attention was directed toward accomplishing the change. These changes were usually observable to me and also recognized by the teacher. In a few instances, changes were difficult to observe but acknowledged by the teacher. Using an opencoding approach, I then examined observable behaviors that led to each discernible change in students playing and eventually categorized them according to their function.

Roesler 31 During this analysis, three types of scenarios became apparent through which I could attempt to describe components of the problem-solving process: problem solving by students, problem solving by teachers, and problem solving shared between teacher and student. Problem solving by students proved difficult to observe, as these instances occurred less frequently and students did not usually verbalize their thought processes. Teachers solved problems more frequently and, at times, more explicitly than students, particularly when they made their thinking observable through verbalizations, actions, gestures, and demonstrations, functioning perhaps as natural versions of think-aloud protocols implemented in some studies (e.g., Collins & Dunn, 2011). However, these expert teachers were capable of solving complex problems very quickly, the process appearing deceptively easy. One statement by a teacher could embody several problemsolving skills at once, making it difficult for an observer to parse out the components of the process. One-to-one music instruction, however, provided an additional, more advantageous context through which to observe problem solving: shared involvement in the problem-solving process between teacher and student. These instances occurred far more frequently than when students solved problems independently and, in some lessons, almost as frequently as moments in which teachers solely solved problems. Such scenarios made possible the identification of component behaviors that occurred in relation to the same problem but that were separated between two individuals, indicating that these behaviors could stand alone as components of a larger process. When a solution to a problem came about as the result of both teacher and student involvement, I identified the behaviors that were apparently separable components of the problem-solving process, performed by teacher or student. For example, sometimes learners stopped themselves to solve problems, while other times teachers stopped learners but allowed learners to make decisions to solve problems. In both cases learners were involved in problem solving, but I observed differences in who initially directed attention to problems. Because of this observation, I changed my analysis framework to observe not only whether a teacher or learner solved a problem but also whether teacher or learner first established the pursuit of the goal (labeled establish goal ). I returned several times to the lessons and rehearsal frames I had extracted, coding and categorizing every observable behavior, and adjusted my analysis to reflect more precisely the behaviors I observed, comparing the data I encountered with the category definitions that were forming. As my analysis continued in this way, components of problem solving emerged as differentiable behaviors, subsumed within a complex process, observable as two individuals sought to achieve a shared goal. Results Systematic Description of the Components of Problem Solving After examining the recordings using methods described above, I arrived at the following five components describing the component skills involved in problem solving in music:

32 Journal of Music Teacher Education 26(1) Establish goals Evaluate performance Conceive and consider options Generalize and apply principles Decide and act All these components were observable in the behaviors of teachers and students in every lesson, and in a given rehearsal frame, teachers and students performed them in any combination. Three experienced researchers reviewed these categories and concurred that they accurately describe the behaviors that were observed. Below I define each of these components and their critical and interactive nature during problem solving. I also provide epitomic examples of each of the components as observed in the verbalizations and behaviors of teachers and learners. Establish Goal(s). Direct attention and action to accomplish desired ends. A goal is established when it is verbally identified or intent toward the goal is evident through actions and verbalizations. In situations in which I observed improved performance, teachers and/or learners pursued identifiable goals. Teachers pursued goals in target categories such as tone, intonation, technique, or rhythm. Additionally, teachers usually connected these goals with goals of musical interpretation and communication. Teacher directives and questions that initiated goal pursuit included the following: How are you grouping these chords? Be careful of the quality of the sound. What are you thinking of here in terms of character? Teachers also gave specific feedback that referenced the goal indirectly through evaluations. For example, feedback, such as The tempo is too fast, directed attention to the goal of appropriate tempo. I also observed learners independently seeking goals; for example, they asked questions, verbalized their goals, or stopped to correct themselves without teacher intervention: I want [ed]... no edge to the sound. I didn t take a breath there, did I? Evaluate Performance. Determine the extent to which goals have been met. Evaluations included nonspecific value statements such as good or ouch, or value statements specifically referencing the goal such as these teacher statements: Your tempo is too fast. The C is still sharp.

Roesler 33 That s the tone. That s just fabulous.... That s the control. I also observed learners evaluating themselves, as in the following: I always felt like I accented that last note. My natural slurs aren t smooth at all. Nonverbal behaviors, such as a nod, a moan, or a grimace, often expressed evaluations. Evaluations were also inferred through actions that indicated a learner or teacher was pursuing a goal that was not yet met, for example, a learner stopping and repeating a note several times, differently, or a teacher stopping a student to have him repeat a passage. Conceive and Consider Options. Create and/or consider multiple possibilities that may lead to the accomplishment of a goal, or consider the selection of alternative goals. Teachers or learners may demonstrate possibilities in sound, fingering, position, and so on, or they may verbalize one or more possibilities in sound, fingering, position, and so on. The following are examples: How are you grouping these chords? Are you going [demonstrates]? You could also do [demonstrates a different option]. Those notes sound accented. Right here [demonstrates an exaggeratedly accented sound]. [The teacher demonstrates unaccented, correctly.] Learners also demonstrated various ways of playing passages; they demonstrated possibilities for articulation, interpretation, and technique, sometimes in response to teacher direction, as below: If you try to make it too chirpy, it just doesn t work. Do it once, just chirpy. [The student plays chirpy. ] Now put the bow back on the string. [The student plays the notes slightly longer.] Teachers also called attention to differences between learners performances. They used learners own performances as means of comparison: Now let s get the sound back though. I liked the sound you were doing in the etude, just a second ago. I d like to get that richness back. Generalize and Apply Principles. Formulate and connect knowledge to be applied over many situations, thereby guiding evaluations and decisions. Teachers often explicitly stated principles for students as gleaned from the present situation, and teachers and learners drew from general principles to apply them to the current situation, making it

34 Journal of Music Teacher Education 26(1) possible to diagnose the cause of problems. Principle statements often contained words indicating the generally applicable nature of knowledge within a context, as in The chords in Bach should enhance the beauty or direction of the phrase, rather than get in the way of it. Statements identified as principles often included knowledge as to the consequences of actions, connecting actions with goals: If you [do this], then [this will happen], as in Now sometimes you re pushing the body away, which... takes the weight of the body out of the sound. Or they explained how or why results occur: [This did/didn t happen] because [you did/didn t do this]. These examples demonstrate the relationship between goals and the options (subgoals) leading to goals: Why [does mine sound better]? Because I have much more energy [in the bow], more weight, faster bow speeds, and I don t stop my vibrato. I think there s a very good reason for keeping the staccato that way because it really makes a nice line out of it. Learners rarely verbalized principles that guided their thinking and actions, unless they were invited to do so. For example, a teacher asked a learner, Do you know why the pitch is off? The learner answered, Is it because I m not holding [gestures the slide]? Decide and Act. Select from among possible options those that will be implemented to accomplish desired ends. Teachers may express a decision through modeling or giving specific verbal directives. Learners made decisions when they express intended action or direct their own actions without specific teacher directives, most often seen as changes in their performances. Teachers and students were observed making decisions after they had established goals, evaluated, and considered options. Examples of teacher decisions follow: Change the pedal when you get to [the top]. Get your elbow up at the frog. Don t breathe there.... Try breathing here. [He marks it.] Examples of Problem Solving Rehearsal Frames 1 and 2 (Rehearsal Frames 3-5 provided as supplemental materials at http://jmte.sagepub.com/supplemental) serve as examples of the problem-solving process as demonstrated by these teachers, during which problem-solving components are outwardly observable. These examples illustrate instances in which teachers are the primary directors of the solution to a problem.

Roesler 35 Rehearsal Frame 1. Transcript of action The learner attempts a shift. Teacher: K. Not quite there. You re kind of rounding your finger, and you end up a half step flat. Keep the finger straight until you get there. The learner plays again, as directed. Teacher: Perfect! So that tells you that in motion your finger is going to go from kinda like this to kinda like this [he demonstrates]. Problem-solving behavior EVALUATE GOAL PRINCIPLE EVALUATE OPTIONS DECISION EVALUATE PRINCIPLE OPTIONS Rehearsal Frame 2. Transcript of action The teacher stops the student s playing. Learner: Yeah, those first two notes... Teacher: Yeah, they lack any meat because you re tight with the air stream. So... [the teacher demonstrates]. The student plays, following the teacher s directions. Teacher: Yeah that s the idea. Try to get more of that. If you practice with no tongue, you will get really good at that. Problem-solving behavior EVALUATE EVALUATE GOAL EVALUATE PRINCIPLE OPTIONS DECISION EVALUATE DECISION GOAL PRINCIPLE Frequency of Problem-Solving Behaviors Across Full-Length Lessons and Rehearsals After having established the above framework describing behaviors and skills involved in problem solving, I sought to confirm its representational validity and reliability. To be valid, this framework should describe virtually every behavior leading to the solutions of various problems during music instruction. To examine its validity, I coded problem-solving behaviors within 18 full-length lessons. I also confirmed that these behaviors could be reliably observed. Observation Procedure. I coded every problem-solving behavior within 18 full-length lessons (three lessons with each teacher). Specific behavioral definitions were developed to

36 Journal of Music Teacher Education 26(1) code verbalizations, nonverbal behaviors, and performances. 2 The lessons were selected based on variety in age (four students were adolescents; the others were college-aged, including graduate and undergraduate students) and preliminary impressions that they represented a variety in approach. Scribe Version 4.2 observation software (Duke & Stammen, 2011) was used to collect data. Three reliability observers labeled 370 total problem-solving components within 35 randomly selected rehearsal frames. Total observer responses agreed with mine in 322 of 370 total responses (87.0% agreement). Reliability between each individual observer and myself was as follows: Observer 1, 87.9% (109 agreements in 124 responses), Observer 2, 83.1% (103 agreements in 124 responses), and Observer 3, 90.2% (110 agreements in 122 responses). Results. Table 2 reports the frequency of each of the problem-solving behaviors of teachers and students as I observed in three full-length lessons with each of the six teachers. Because lessons varied in duration (ranging from 40 to 60 minutes), I converted each frequency count so that each data point in the table represents the rate per hour of each component within each lesson. Table 3 (provided as supplemental material at http://jmte.sagepub.com/supplemental) provides each teacher s rate per hour averaged across the three lessons. The data show that all five problem-solving components were explicitly observable in every lesson. Components of problem solving controlled by the teachers occurred frequently, at a rate of approximately 1 to 2 per minute over the course of each lesson. Learners were engaged in all components of problem solving but not as frequently as teachers. Problem-Solving Components in Other Disciplines To further try its validity, I compared components of the present model with problemsolving frameworks that have emerged independently in other disciplines. As problem solving is a fundamental human activity that has been studied in many domains, I expected to find in the literature of various fields models similar to the framework I developed from these observations. This proved to be the case. A post hoc review of problem solving literature in a variety of disciplines yielded several studies that describe the process of problem solving as a whole (Buijs et al., 2009; Camacho & Good, 1989; Hill-Briggs, 2003; Kotsopoulos & Lee, 2012; Lee et al., 2012; McCarty et al., 1999). Although these authors use varied language, nearly all the studies I reviewed identify common components of the process, synonymous with those I observed during musical problem solving. For example, the components of problem solving that I observed in music are strikingly similar to the components involved when infants attempted spoon-feeding (McCarty et al., 1999), children made monetary decisions (Lee et al., 2012), and diabetic patients responded to a glucose monitor (Hill-Briggs, 2003; see Tables 4-5, provided as supplemental material at http://jmte.sagepub.com/supplemental). Within all these situations, participants sought goals (e.g., eat food, save money, or normalize glucose level), evaluated their current status and possibilities (e.g., assess food

Table 2. Rates Per Hour of Teacher and Learner Problem-Solving Behaviors Within 15 Lessons. Problem solving Lesson T1 T2 T3 V1 V2 V3 O1 O2 O3 Va1 Va2 Va3 P1 P2 P3 F1 F2 F3 Teacher Goal 55 65 78 73 72 62 65 77 85 51 42 41 75 71 63 66 29 40 Evaluate 62 75 88 96 41 67 74 104 75 57 42 45 86 27 74 78 37 54 Options 31 45 50 40 65 41 65 55 65 43 30 29 39 39 61 52 36 25 Principle 28 29 50 40 38 33 62 61 42 51 47 30 47 32 54 40 15 31 Decision 23 48 55 46 64 48 54 58 71 43 23 27 18 47 52 38 25 25 Learner Goal 10 8 10 19 13 7 8 2 8 3 6 3 1 1 1 24 26 4 Evaluate 16 23 24 36 31 15 27 14 20 5 17 9 16 8 12 37 33 25 Options 12 16 14 32 22 11 11 12 13 2 9 3 9 4 24 19 17 15 Principle 3 0 5 4 4 2 5 2 1 3 8 2 5 3 3 4 6 4 Decision 37 49 49 46 24 21 35 32 32 9 17 6 58 23 42 44 19 17 Note. Lesson codes indicate the teacher s instrument of expertise: T = trombone; V = violin; O = oboe; Va = viola; P = piano; F = flute. 37

38 Journal of Music Teacher Education 26(1) acquisition, the quality of products, or blood glucose levels), considered options (e.g., ways to grasp the spoon, products to be purchased, strategies that may alter glucose levels), applied knowledge (e.g., which stores have the best prices, or how often to take medication), and made decisions (e.g., turn the spoon, buy a plane, or eat less sugar). Furthermore, the proposed framework contains intimations of some elements of reflective thinking proposed by Dewey (1933): defining problems (establishing goals), proposing solutions (options), selecting solutions (making decisions), and testing consequences (evaluating). The present model of problem solving drawn from these observations of music instruction closely parallels extant models, observations, and analyses of problem solving from a vast range of human experience, thus confirming the validity of the model developed from the current analysis. Discussion Problem solving is a complex cognitive activity. Five components, each complex in its own right, emerged during this analysis of one-to-one music instruction: establish goal, evaluate, conceive and consider options, generalize and apply principles, and decide and act. These components encompass nearly all the on-task instruction time within 18 full-length private lessons and are reliably identifiable within rehearsal frames, regardless of the musical goal sought. The present investigation confirms the importance of these components in music study and further elucidates their interactive nature, best considered in relation to each other rather than as separate, isolated aspects of teaching and learning. The present model, derived from a music performance setting, is consistent with other models of problem solving that have developed within the literature of other fields (Buijs et al., 2009; Camacho & Good, 1989; Collins & Dunn, 2011; Kotsopoulos & Lee, 2012; Lee et al., 2012; McCarty et al., 1999). All the individual components have been studied extensively in various domains, and some have been researched within music instruction (e.g., evaluation: Hewitt, 2011). That music learning a highly goal-driven activity with a high cognitive demand involves the same problem-solving components that are found in other domains of human endeavor demonstrates the ubiquitous nature of problem solving. My description of problem solving corroborates previous studies in music education research that describe teacher error correction behaviors (Cavitt, 2003; Doerksen, 1999; Duke & Simmons, 2006) and learner practice behaviors (Duke, Simmons, & Cash, 2009; Hallam, 1997; McPherson, 2005) and further explicates their findings in terms of a fundamental human process. I propose that teachers and students may become more successful problem solvers through training on each of the problem-solving components that I have outlined, and teacher evaluations may include assessment on these important skills. As Duke (1999) asserted, assessments of teacher effectiveness are most meaningful when they measure teachers abilities to accomplish goals. The components of problem solving provide teacher educators and administrators a more systematic method by which to evaluate this process for achieving short- and long-term performance goals and may elucidate why some teachers are more or less effective in accomplishing these goals.

Roesler 39 My observations indicate that there is a need for training in each of the components of problem solving. I observed that when learners exhibited a deficiency in any one or several of the skills of problem solving, they had difficulty solving problems. Novice teachers may likewise struggle with particular components of the process. One teacher may be excellent at evaluating but lack the knowledge of principles and options that lead to successful decision making; another may struggle to choose appropriate rehearsal targets, and so forth. It is conceivable that teachers could be trained and coached through problem solving by isolating one or more components in the problem-solving process, just as these behaviors were sometimes divided between teacher and student during one-to-one instruction. Teachers may likewise guide learners practicing in terms of problem-solving components. Although not the focus of this particular analysis, Deci and Ryan (2000) provide a rationale for strengthening learners competence and autonomy, and several authors have investigated learner practice behaviors using this self-determination framework (e.g., McPherson, 2005). I propose that learners practice may be most meaningfully evaluated based on their ability to accomplish proximal practice goals, in the same way teachers effectiveness may be evaluated by considering their achievement of rehearsal targets. If applied in a practice setting, the description of problem solving that I developed in this investigation may provide insight as to why learners struggle to progress in their practicing, one possible area of further research. 3 The present model may also be used to investigate problem solving by teachers and learners of varying ages and ability levels during chamber music rehearsals, large group rehearsals, improvisation, composition, and other music settings. The nature of problem solving may be more involved than it at first may seem. It is particularly deceiving when excellent teachers are able to effect change rapidly in their students, as do the six highly experienced teachers I observed. To a naive observer, these teachers may appear to do very little before a change is observed in learners. After more careful scrutiny, however, it becomes clear that these teachers work so efficiently not because of the simplicity of the process but because their skills have been largely automatized. Not unlike world-class musicians who evince an apparent effortlessness while performing, these teachers carry on the act of teaching seemingly effortlessly. Both performing and teaching involve the application of highly complex skills that have become habituated over years of practice. Playing a piece of music involves performing multiple difficult skills simultaneously at a rate faster than the mind is able to consciously process. Likewise, musical problem solving is a complex process in which many behavioral and perceptual skills must be performed simultaneously while also drawing on relevant knowledge in long-term memory. The skills of problem solving require practice for learners to become effective problem solvers, just as performers must practice the skills of performance. Even so, problem solving as a process of behaviors is a tractable phenomenon. The above framework enables the analysis and evaluation of problem solving by teachers and students in music settings, regardless of their level of expertise. Although the present description of problem solving came about specifically to

40 Journal of Music Teacher Education 26(1) describe the extent of teachers and learners problem solving during one-to-one instruction, the potential scope of the application of this framework extends far beyond the original purpose that inspired its inception. As problem solving is a ubiquitous human activity, and the skills in problem solving are critical for success in many fields including music teaching and learning, it is conceivable that this framework may find application within many musical and extramusical domains and pursuits, including music performance, composition, improvisation, music practicing, and music teacher education. Author s Note Rebecca A. Roesler will be affiliated with Brigham Young University Idaho as of the Fall 2015 semester. Supplemental Material The online supplemental materials are available at http://jmte.sagepub.com/supplemental. Declaration of Conflicting Interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) received no financial support for the research, authorship, and/or publication of this article. Notes 1. Observing expert teachers in their natural teaching setting is not new. Gholson (1998), for example, identified several strategies that occurred in the teaching of renowned pedagogue Dorothy DeLay during audio recordings of lessons with DeLay s regular violin students. 2. For the complete list of these behavioral codes and definitions, see Behavior codes in the supplemental materials (available at http://jmte.sagepub.com/supplemental). 3. Roesler (2013) presents one such application of this model. I considered teacher behaviors prior to learners problem-solving behaviors during one-to-one instruction, a possible means of preparing students for self-regulated practice. References Buijs, J., Smulders, F., & van der Meer, H. (2009). Towards a more realistic creative problem solving approach. Creativity and Innovation Management, 18, 286 298. doi:10.1111/ j.1467-8691.2009.00541.x Camacho, M., & Good, R. (1989). Problem solving and chemical equilibrium: Successful versus unsuccessful performance. Journal of Research in Science Teaching, 26, 251 272. Cavitt, M. E. (2003). A descriptive analysis of error correction in instrumental music rehearsals. Journal of Research in Music Education, 51, 218 230. doi:10.2307/3345375 Collins, D., & Dunn, M. (2011). Problem-solving strategies and processes in musical composition: Observations in real time. Journal of Music, Technology & Education, 4, 47 76.

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