like teacher, like student? conceptions of children from traditional and constructive teachers...

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Like Teacher, Like Student? Conceptionsof Children From Traditional andConstructive Teachers Regardingthe Teaching and Learning of StringInstrumentsGuadalupe López-Íñigueza & Juan Ignacio Pozoa

a Universidad Autónoma de MadridPublished online: 07 Jul 2014.

To cite this article: Guadalupe López-Íñiguez & Juan Ignacio Pozo (2014) Like Teacher, LikeStudent? Conceptions of Children From Traditional and Constructive Teachers Regarding theTeaching and Learning of String Instruments, Cognition and Instruction, 32:3, 219-252, DOI:10.1080/07370008.2014.918132

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COGNITION AND INSTRUCTION, 32(3), 219–252, 2014Copyright C© Taylor & Francis Group, LLCISSN: 0737-0008 print / 1532-690X onlineDOI: 10.1080/07370008.2014.918132

Like Teacher, Like Student? Conceptions of ChildrenFrom Traditional and Constructive Teachers Regarding

the Teaching and Learning of String Instruments

Guadalupe Lopez-Iniguez and Juan Ignacio PozoUniversidad Autonoma de Madrid

While many studies have considered the association between teachers’ and students’ conceptions ofteaching and learning and classroom practices, few studies have researched the influence of teach-ers’ conceptions on students’ conceptions. Our objective was to analyze the influence of musicteachers’ conceptions on student ideas regarding teaching and learning. We interviewed 30 childrenwith teachers with traditional conceptions of teaching and learning and 30 with teachers with con-structive conceptions. Interviews were conducted after children viewed videos of instrument lessonsdemonstrating direct, interpretative or constructive teaching and learning. A first quantitative analysis(ANOVA) considered the video choice. A second qualitative analysis (lexicometric analysis) wasbased on video choice explanations. Results showed that students’ conceptions corresponded to theirteachers’ profiles. Student explanations in the constructive group were longer and more elaborate,focusing on learning processes and conditions and student autonomy, whereas the traditional groupfocused on outcomes and responding to teacher instructions.

Some of the most relevant factors in the change in teaching and learning practices are the concep-tions held by teachers and students about teaching and learning, especially when those conceptionssupport constructivist models, which transfer much of the control of learning to the student. Asnoted by Olson and Bruner (1996) with reference to internalization of the learning focus, themost sophisticated approaches or internalist theories focus on student-centered learning, wherethe student has his or her own view of thinking, learning, and knowing. Thus, implementingteaching strategies that focus on the students taking on more control of learning requires not onlya change in teaching methodology but also that teachers and learners should conceive of learningas an internalized process that depends on the constructive activity of the learners.

In this regard, there has been increasing interest over recent years in studying the concep-tions held by teachers and students about teaching and learning. These studies tend to focus onthe beliefs about which processes make learning possible and which teaching activities, tasks,or social influences can promote learning. Specific conceptions of teaching and learning held

Correspondence should be addressed to Guadalupe Lopez-Iniguez, Universidad Autonoma de Madrid, Facultad dePsicologıa, Despacho-Aula PIF, C/ Ivan P. Pavlov, 6, 28049- Madrid, Spain. E-mail: [email protected]

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220 LOPEZ-INIGUEZ AND POZO

by teachers and students have been studied in different fields of learning. These include chil-dren’s conceptions of the writing process (Scheuer, de la Cruz, Pozo, Echenique, & Marquez,2009; Scheuer, de la Cruz, Pozo, Huarte, & Sola, 2006a; Scheuer, de la Cruz, Pozo, & Neira,2006b), teachers’ conceptions of children’s learning (Strauss & Shilony, 1994), and teachers’and students’ conceptions across different educational domains, such as mathematics, music, orscience, and at different educational levels, from primary school to university (Martın, Pozo,Mateos, Martın, & Perez Echeverrıa, in press; Pozo et al., 2006). The way in which these con-ceptions may influence classroom practices of preservice teachers (de la Cruz, Pozo, Huarte, &Scheuer, 2006) and children’s ideas about teachers’ practices (Bar Tikva, 2010) have also beenstudied.

Most of these studies assume that these conceptions are acquired implicitly as a result ofeveryday teaching and learning practices. However, few studies have attempted to show therelationship between the conceptions of teachers and those of their learners. In this study,using a privileged setting for testing these relationships, namely, learning to play a musi-cal instrument at conservatories where stable, long-lasting dyadic teacher-–learner relation-ships are established, we propose to test the influence of teachers’ conceptions on those oflearners.

CONCEPTIONS OF LEARNING AND TEACHING

Just as children develop intuitive physics very early in the world of objects (Carey & Xu, 2001;Hespos & vanMarle, 2012; Pozo & Gomez Crespo, 2005), they also develop and build specificrepresentations to interact with highly complex “social objects,” which are human beings. Atabout 3 to 4 years of age, the attribution of intentions and goals to people’s actions leads to thedevelopment of a theory of the mind, which implies that people’s actions should be understood inthe field of the representations that those people create and acquire toward the world. However,as shown by the false belief task, children who develop a theory of the mind seem to initiallybelieve that those representations acquired or incorporated by the representational mind are adirect copy of the objects in the observed world (e.g., where was the candy seen last time?). Butas children interact with new learning contexts, this representational theory of the direct copy(Wellman, 1990) gives rise to new, more complex conceptions about learning and the learningactivities that can promote learning.

Thirty years ago, Pramling (1983) proposed that as children learn, they not only acquirespecific knowledge but also generate and develop conceptions regarding how they learn and whatthey learn. In a phenomenographic study, she asked 3- to 8-year-old children to think about howthey learn specific tasks and found that their conceptions of learning progressed from conceivingof learning as doing to conceiving of it as knowing and, in a further level, as understanding.These children would move from holding an externalist conception of learning as the result ofknowledge transmission from an external influence (teacher) toward an internalist conception, inwhich, at a more basic stage, learning would take place through experience and would later beachieved through personal reflection.

When children take on the role of teacher with their peers, they seem to show those sameconceptions. In a study of children aged 3 to 5 years, Strauss, Ziv, and Stein (2002) found

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LIKE TEACHER, LIKE STUDENT? 221

important associations between the theory of the mind and conceptions of teaching, as well asa clear evolutionary development pattern in those children. Although the children in both agegroups used teaching strategies combining demonstration by action with verbal explanation,demonstration prevailed among the younger children, while verbal explanation prevailed amongthe older ones. In addition, only the older children said they took into account actions performedby the learner and asked explicitly about his or her understanding and remembering of the rulesof the game. These differences were maintained in the children’s’ explanations of how theyhad taught: For younger children, the core of teaching was demonstration, while for the olderchildren it was explanation, indicating developmental change from focusing on behavioral aspectsto attention to the mental states involved, specifically knowledge and understanding. Together,the results of this study support the idea that both the understanding of teaching and effectiveteaching strategies change during preschool years and that these changes correspond to changesin the theory of the mind.

Similarly, a series of studies on the conceptions of learning held by children in different settings,such as the acquisition of writing or drawing (Scheuer, de la Cruz, & Pozo, 2002; Scheuer et al.,2006a, 2006b, 2009), found that in younger children, from 4 years of age, prevailing conceptionsconsisted of a kind of naıve behaviorism, a direct conception of learning centered only onoutcomes, without taking into account the psychological process that enable this learning. Olderchildren, as from 5 or 6 years of age, identified the mediation of some psychological processesneeded for learning (such as attention or motivation) but always under adult supervision, whilethe eldest, aged 9 or 10 years old, seemed to hold more complex conceptions with increasinglycognitive learner autonomy. Thus, children’s conceptions of learning and perhaps instructionseem to change with age in three dimensions (Scheuer et al., 2006b): They become increasinglycomplex (by considering a larger number of factors and conditions), more dynamic (by increasingthe associations among those factors), and more internalized (endowing the learner with greaterautonomy).

Within the theoretical framework proposed by Scheuer, Pozo, and colleagues (Pozo et al.,2006; Scheuer et al., 2002, 2006a, 2006b, 2009), we assume, in contrast to the aforementionedphenomenographic approach, that those conceptions of teaching and learning are articulated ac-cording to the main characteristics required for a set of mental representations to constitute actualtheories. Abstraction, causality, coherence, and ontological commitment (Gopnik & Meltzoff,1997) form consistent personal theories (Claxton, 1990), or in Vosniadou’s (2007) terms “theory-like structures of knowledge,” which enable individuals to formulate relatively consistent predic-tions and explanations about educational issues and to infer—more or less explicitly—differentsorts of generalizations, categories, and rules from learning and teaching settings. However, weconsider them to be implicit theories, to the extent that most of their psychological assumptions,as we describe below, often cannot be made explicitly, but rather, underlie the actions, predictionsand beliefs that people hold. This means that access to those theories must be based not onlyon the analysis of explicit discourse, but also on other kinds of tasks, such as the selection oftasks used in this study (see Tasks section), which allow us convergent access to more implicitrepresentations based on judgments and to the explicit justifications for those judgments. Butwhat are the characteristics of these conceptions? To answer this question, we will describe eachconception of teaching and learning, based on both the psychological-educational literature andon research focusing specifically on the domain of music.

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TABLE 1Assumptions of the Different Conceptions About Learning and Instruction

Assumptions Direct Conception Interpretative Conception Constructive Conception

Epistemological Ingenuous realism:Knowledge reflects

reality in an evidentand objective way.

Interpretative realism:Knowledge reflects reality

in an evident andobjective way. However,subject has an importantand active role in theknowing process.

Constructivism:Knowledge is a

construction elaboratedby the subject, whobuilds own and personalmodels to interpret thereality (which can bemore or lessappropriate).

Ontological States-products:Learning is conceived in

terms of states or staticproducts (e.g.,academic contents).

Actions and processes:Learning is conceived in

terms of actions andprocesses (e.g.,cognitive, motivational),which are externallymanaged.

Complex systems:Learning is conceived in

terms of complexsystems (e.g., self-regulation processes),internally managed bythe learner in order tobuild and developabilities or strategies.

Conceptual Simple causality:A direct and lineal

relation is establishedbetween learningconditions andlearning outcomes.

Lineal multiple causality:A direct and lineal relation

is established betweenlearning conditions,learning processes,and learning outcomes.

Interactive causality:A complex and interactive

relation is establishedbetween learningconditions, learningprocesses andlearning outcomes.

Note. Adapted from Bautista, Perez Echeverrıa, and Pozo (2010).

CONCEPTIONS AT MUSIC CONSERVATORIES

Various recent studies on learners of musical instruments have dealt with conceptions of teachingand learning held both by music teachers (Bautista, Perez Echeverrıa, & Pozo, 2010; Lopez-Iniguez, Pozo, & de Dios, 2014) and intermediate––advanced students (Bautista, Perez Echev-errıa, Pozo, & Brizuela, 2012; Casas-Mas, Pozo, & Montero, 2014; Marın, Perez Echeverrıa,& Hallam, 2012; Marın, Scheuer, & Perez Echeverrıa, 2013). However, with the exception of afew exploratory studies on young children learning arts (e.g., see from the theoretical frameworkof developmental pedagogy, the work of Pramling Samuelsson, Carlsson, Olsson, Pramling,& Wallerstedt, 2009), there is very little in the literature about children’s conceptions in theinstrumental-musical setting. Therefore, as this article proposes to study how teachers influencetheir students’ conceptions in a one-to-one lesson setting, we need to know what the concep-tions of young students are regarding how a string instrument is taught and learned, and morespecifically, for children encountering the instrument for the first time at music conservatories.

Based on some of these prior papers as well as on our own research, Table 1 summarizesthe main features of the three conceptions that have been identified: direct, interpretative, and

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FIGURE 1 Direct conception of instrument teaching and learning.

constructive, in terms of their ontological, epistemological and conceptual assumptions. In thefollowing sections, we describe the main characteristics of the assumptions of the model, such asrepresentational plurarity (every individual holds more than one conception, they are not “pure”),clearly different profiles (which are assigned to individuals but not randomly), transition from thesimplest conceptions to the more constructive, or even the way conceptions predict how young(and not so young) children interpret or understand music scores (even within different cultures).

Direct Conception

The direct conception, which is simpler and closer to naıve behaviorism and similar to Wellman’s(1990) direct copy theory, claims that there is a direct causal relationship between teachingconditions and the desired outcome. It therefore teaches the final product sought (in our case, themusic score) in a direct manner. The role of the teacher is to expose the student to external learningcontents as clearly as possible, although without explicit instruction, so that the student willincorporate or accumulate them through adequate practice (Scheuer et al., 2002, 2006a, 2006b),or in the terms of Pramling (1996), “traditionally.” Teaching is a one-directional monologue,which seeks the performance of the tunes very precisely, works, studies and/or exercises, whichare conceived from a radical epistemological realism. Figure 11 illustrates the most traditional

1Please note that while Figures 1, 2, and 3 represent a cello lesson, this research was conducted on students whoplay different stringed instruments: violin, viola, cello, and double bass. In addition to being practical and not showing12 drawings (three per instrument), the reason why we used the cello as an example is that it is the instrument that was

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FIGURE 2 Interpretative conception of instrument teaching and learning.

or direct version of teaching–learning cello at music conservatories, showing that both teacherand student focus exclusively on playing the score, with the teacher following it to check that thestudent is playing the notes correctly, regardless of the mental processes of the student.

Interpretative Conception

Following Scheuer et al. (2006b), the interpretative conception considers the existence of complex,dynamic mental processes in the learner (e.g., deliberate observation, memory or evaluation),which mediate learning, although it is believed that the teacher should control these processes.It is a more complex version of the direct conception (Lopez-Iniguez et al., 2014). The teacher’srole is to regulate externally the mental and motor procedures involved in the student’s instrumentplaying, with the aim of getting the student to play the score faithfully. is also interpreted from acertain epistemological realism. The role of the student is active, though reproductive; the studentaccepts himself or herself as the agent of his or her own learning (Scheuer & Pozo, 2006). Theteaching objective is that the student should achieve technical and conceptual mastery of the musicbeing played, as a means to play the piece in the most academically correct way. This is shownin Figure 2, in which both the teacher and the student focus on the technical execution neededin order to play the graphic symbols on the score precisely, as occurs in the direct conception.The illustration shows the student looking carefully at the music stand, similarly to Figure 1, but

available for developing the materials in this article, and the artist was drawing a real classroom situation, where theteacher shown in the video and one of her students were acting. Although the position of the four different instrumentschanges depending on size and technique, the gestures and ideas of each conception are well represented in these drawings,so that the reader who is not familiar with conservatoire settings may have a better idea of what a one-to-one instrumentlesson looks like.

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FIGURE 3 Constructive conception of instrument teaching and learning.

here with verbal explicitation from the teacher, who points out the technical requirements thatthe student must perform actively in order to be able to play the piece.

Constructive Conception

The constructive conception would be close in its assumptions to the constructivist approachas it is defended in instructional science, despite their obvious representational differences, asthese three conceptions are more implicit in their nature. But constructive conceptions faithfullyrepresent Olson and Bruner’s (1996) “meeting of minds” in that in contrast to the other twoconceptions, the student would learn “experientially” (Pramling, 1996). The principles involvedin the constructive conception—a product of the knowledge generated during recent decades bypsychological, philosophical, pedagogical, and educational research—contrast radically with theclaims of previous learning cultures. Teaching according to this conception involves activating,stimulating, and developing the student’s mental processes through reflection. The goal is that thestudent should learn to regulate and manage his or her own cognitive and motor processes and toconstruct a personal representation of the music he or she plays. The student’s role is active andconstructive (based on epistemological constructivism) in such a way that the role of the teacheris to guide and supervise the start-up of the student’s reflective, metacognitive, emotional, andaffective processes as the primary way to foster his or her understanding and autonomy. Teachingfocuses on the interactive relationship among the student, the teacher and the learning material orinstrument, as shown in Figure 3, where teacher and student actively converse about what aspectsmight help the student to learn and play not only the score on the music stand (at its symbolic,stylistic, analytic, and referential levels) but also other scores in which the learning material is

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similar, so that he or she can transfer the knowledge acquired consciously and constructively inthis piece to other pieces.

We interpret the transition from one conception to another as a process of hierarchical inte-gration involving increasing complexity, dynamization and internalization of the agent (Scheueret al., 2002), similar to the trend proposed by Dienes and Perner (1999) in their theory of knowl-edge as a progressive process and hierarchical explicitation of the three knowledge components:content, attitude, and self. Therefore, the changes in the conceptions of learning and teaching,regardless of their differences with the conceptual changes that take place in the acquisition ofscientific knowledge (Vosniadou, 2008), could also partly be the product of some kind of con-ceptual change. That kind of conceptual change may occur whether in terms of weak or strongrestructuring (Carey, 1985; White & Gunstone, 2008), if we accept that conceptual change doesnot usually involve the replacement of some theory by another but is the hierarchical integrationof the old ideas in a more complex theoretical framework (Pozo & Gomez Crespo, 2005). Infact, it seems that while the direct and interpretative conceptions are conceptually compatible andshare some of the essential assumptions, as we can see in Table 1, the acceptance of a constructiveconception is in many ways incompatible with the other two.

In this regard, among music teachers, the selection of constructive positions in a multiple choicequestionnaire tended to covariate negatively with the acceptance of direct and interpretativeresponses (Lopez-Iniguez et al., 2014). In addition, several studies have shown resistance toassuming those constructive positions, not only among students of music (Hallam, 1998; Lopez-Iniguez & Pozo, 2014a), but also among students of mathematics (Bar Tikva, 2010) or readingand writing (Mateos, Martın, Villalon, & Luna, 2008). The same tendencies are found amongteachers in the field of mathematics (Tirosh & Even 2002) again in the domain of music (Bautistaet al., 2010; Torrado & Pozo, 2008). Resistance to assuming constructive positions is found evenamong teachers exposed to specific training with the aim of achieving those conceptions (e.g.,see Rivero, Azcarate, Porlan, Martın del Pozo, & Harres, 2011 for the methodology of teaching;see Porlan & Martın del Pozo, 2004 for science teaching and learning).

Factors That Influence Development and Change in Students’ Conceptions

From the theoretical framework that views conceptions as implicit theories (Pozo et al., 2006;Strauss & Shilony, 1994; Strauss et al., 2002), it is assumed that the conceptions are acquiredimplicitly, that students take them in during their own practice of learning and teaching, andthat they change over time. We therefore ask: What are the factors that promote this conceptualchange?

In a study of piano students using a multiple choice questionnaire of typical learning–teachingscenarios at music conservatories, Bautista et al. (2012) found that the three conceptions describedabove characterized the way those students thought about teaching, learning and evaluation,and that those conceptions became more complex, progressing from direct to interpretative toconstructive, with increasing age and level, two variables that are difficult to separate in musiclearning settings. In a later study, Marın, Scheuer, et al. (2013) found similar results, with studentconceptions growing more complex according to the same age or instructional level variable.

However, along with this possible effect of age and/or years’ of instruction, it may be assumedthat there should also be an effect not only of quantity of practice during instrument learning butalso of the quality of this practice and the kind of instruction imparted to the students. Indeed,

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most studies on music teachers show that most of them do not hold a constructive conception (inthe field of piano teaching see Bautista et al., 2010; among string instruments, see Lopez-Iniguez& Pozo, 2014a), and the results found for students are very similar (again in piano lessons, seeBautista et al., 2012; with strings, see Lopez-Iniguez & Pozo, 2013; with wind players, see Marın,Perez Echeverrıa et al., 2012; Marın, Scheuer, et al., 2013; and in different guitar cultures such asflamenco, jazz and classical, see Casas et al., 2014). In fact, the different approaches that examineconceptions have for years supported the hypothesis that conceptions are somehow transferredfrom teachers to students, as a result of daily contact with instruction in specific domains ofknowledge. It is understood that the representations held by teachers regarding teaching andlearning their subject are somehow transferred to the students, who gradually take them in untilthey consider them as natural and their own.

However, with a few exceptions, there is very little empirical research on the issue. One ofthose studies is by Bar Tikva (2010), where 36 children from 13 to 15 years of age watched threevideos with different visions of teaching mathematics: one with a direct-transmissive vision,another one with a Socratic view of teaching, and a third version where there was no intention ofteaching. All children agreed that teaching was happening only in the direct-transmissive video,and they did not change their opinions even after the teaching intention held by the teacher in eachvideo was explained to them. The author explained that this result might be related to the direct-transmissive teaching models to which we are generally exposed, and also that small childrenusually hold direct conceptions of teaching and learning (in the line of Hallam, 2001). Anotherexception is Pramling’s (1996) study (adopting the phenomenographic perspective), in whichshe observed that when 5- and 6-year-olds were trained using a metacognitive approach (whichshe called experiential), they adopted more sophisticated conceptions of learning, although to alimited extent. Most of these children understood learning as “learning to know,” and very fewunderstood it as “learning to understand.” However, it is worth noting that children trained usinga traditional approach in the same experiment held the belief that learning is, in fact, “learning todo.”

Our study attempts to test by means of a quasiexperimental method whether the conceptionsheld by teachers really influence those held by learners at music conservatories during child-hood, adding the teaching conception that they come from, specifically the most extreme: fromtraditional to constructive. In Pramling’s (1996) terms, we aim to analyze whether the studentslearn traditionally versus experientially according to the teaching profile of their instructors. Inaddition, this study seeks to continue the work of authors in different educational settings regard-ing the conceptions of children at earlier ages. It seeks to test whether, as has been shown to date,children hold simpler conceptions during the first years and whether these conceptions evolve afew years later toward more interpretative conceptions (in line with the findings of Scheuer et al.,2006a), with constructive conceptions being very scarce, as predicted by these previous studies(Pozo et al., 2006; Strauss & Shilony, 1994; Strauss et al., 2002). The study also attempts toanalyze if more complex conceptions can be found in students exposed to more complex teach-ing models. As claimed by Entwhistle, Skinner, Entwhistle, and Orr (2000), the most complexteaching models conceive of teaching as an epistemic student-centered form focused on learningprocesses, or more specifically, metacognitive processes, which articulate and lend meaning tothe different pedagogical stages upon which lessons are structured.

With regard to the above and following Scheuer et al. (2006b), who structured the analysesin their study of children on four key moments of writing (anticipating, writing, revising, andrereading), we thought it would be interesting to structure the classes on different pedagogical

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stages, namely the three essential stages of individual music lessons proposed by Torrado andPozo (2008): planning (when the student selects and organizes the points to work on in class orat home), supervision (when points to be improved are worked on during the lesson or after thestudent has studied at home), and evaluation (usually when the degree to which the student haslearned and achieved the teaching objectives is analyzed at any point during the class).

OBJECTIVES

The main objective was to analyze the influence of the teaching conception held by the teacher(traditional vs. constructive2) and level of musical instruction (First Elementary Level [EL] andFourth EL) on students’ conceptions of learning and teaching music (direct, interpretative, orconstructive) to determine whether, according to these variables, elementary students at musicconservatories differ in their conception of teaching and learning string instruments. Students’conceptions were determined according to the analysis of choices and rejections in the video taskdescribed in Materials. Specifically, we want to find out whether the differences in conceptionsare related to age or instructional level, or rather, to the teaching conception they are included in.

The second objective was to examine whether there are differences in children’s conceptions ofthe three stages of dyadic teacher–student interaction in instrument lessons: planning, supervision,and evaluation, according to the independent variables mentioned above. In addition to analyzingthe conceptions preferred by students, which might only reflect acceptance of the teachingsituations or contexts most familiar to them, we are also interested in how they explain theirbeliefs or preferences. Therefore, in order to gain in-depth understanding and describe the natureof the results of the above objectives, and to find points in common through quantitative andqualitative research methods, we sought to analyze whether participants’ lexicon could be groupedaccording to the same variables—teaching conception and instruction level. By grouping theparticipants according to those variables, it would be possible to produce a qualitative descriptionof children’s verbal explanations for their choices and rejections by using the features of theirmost characteristic or prototypical explanations during the video viewing tasks.

METHOD

Participants

Based on a preliminary study (Lopez-Iniguez et al., 2014) in which teaching profiles were assignedto music teachers according to their conceptions of teaching and learning string instruments, weconsidered students of the teachers who were selected as the most representative and “extreme”

2Please note that we did not select the interpretative teaching conception as an independent variable because we wantedto analyze whether by selecting the most extreme positions, we would be able to identify in students only those extremepositions or also the interpretative position, which could mean that children’s conceptions would be a “contamination”or mixture of at least two positions, regardless of the teaching conception they come from. On the contrary, if we onlyfound the extreme conceptions, we could consider the children to hold pure conceptions, following that of their teacher.This issue is explained further in the limitations of the study in the section Conclusions and Discussion.

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TABLE 2Number of Participants per Instructional Level, Teaching Conception, and Gender

Instructional Level Teaching Conception Gender Total

First elementary level Traditional 10 female, 5 male 15Constructive 11 female, 4 male 15

Fourth elementary level Traditional 11 female, 4 male 15Constructive 10 female, 5 male 15

of the two most opposite conceptions—direct and constructive. In that preliminary study, amultiple choice questionnaire, originally prepared and validated by Bautista et al. to be usedwith piano students (Bautista, 2009; Bautista et al., 2012), was adapted for use with 53 stringteachers. The questionnaire contained 16 questions related to situations of teaching, learning, andevaluation at the elementary levels in music conservatoires, followed by three different answersrepresenting the assumptions of the three conceptions described in the theoretical framework(direct, interpretative, and constructive). After the teachers selected the option they most agreedwith and rejected the option they least agreed with, the authors were able to identify (afterapplying cluster analysis, ANOVA, and post hoc tests) three different consistent teaching profilesor conceptions (direct, interpretative and constructive), and test how those teachers were affectedby the variable teaching experience (in three groups: (a) less than 7 years, (b) 7–14 years, and (c)more than 14 years).

We selected 12 teachers at 10 music conservatories in four different regions of Spain —six foreach conception, and 60 students who had studied only with those 12 teachers and were enrolledin the EL3, so that their ages were 8 to 9 years for First EL, and 11 to 12 years for Fourth EL (M =9 years, 10 months; SD = 1 year 8 months; Gender = 18 male, 42 female). Thirty of these studentsstudied with teachers who used a direct or traditional teaching conception (the six representativesof the direct teaching–learning conception) while the other 30 studied with teachers who useda constructive teaching conception. None of them were previously selected by their teacher butallocated by the institution to the teachers who had space for them in their lessons. For analysis,the students were distributed according to their instructors’ teaching conception (traditional v.constructive) and their instructional level (first EL or fourth EL), as shown in Table 2.

Tasks

The data were collected at individual structured, video-recorded interviews lasting approximatelyone hour. The participants viewed nine short videos, lasting 2–3 minutes each, in which a teacherand a student attempt to resolve a tuning problem on a cello, during three stages of a typicalconservatory lesson: planning, supervision, and evaluation. There were three videos for each

3Spanish specialized musical education system is organized into three levels (Ley Organica de Educacion, 2006):Elementary Level (EL, four levels), Professional Level (six levels), and Tertiary Level (four levels, corresponding to theBachelor of Music). Music students usually start EL at the age of 8, attending lessons at the conservatory after school orintegrated into the general school system in few cases. In addition to one-to-one instrument lessons, students might haveother classes such as musical theory, analysis, music history, choir, chamber music, orchestra, and so on.

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TABLE 3Summary of the Video Dialogues

Stages Direct Video Interpretative Video Constructive Video

Planning Student’s playing is evaluatedpositively by the teacher, whosets the homework for nextlesson in relation to a exam ofscales.

Student’s playing is evaluatedpositively by the teacher, whosets the homework for nextlesson in relation to a exam ofscales, and explains whichtechnical aspects shall beimproved in order to play thescales in tune.

Student and teacher, aftermaking a negative attributionon the student’s playing,discuss about which possiblestrategies might help toimprove playing the scales inrelation to a concert of scales.

Supervision After playing the scale, thestudent is evaluated negativelyby the teacher, who orders toplay the scale together again,explaining what the studentshould do in order to play itcorrectly.

While the student is playing thescale, the teacher givesinstructions about how to keepthe hand in the same place toplay it in tune, and correctsthe student’s left handposition with her own hands.

Student and teacher discussabout what strategies andlearning processes might helpthe student to play the scale intune during the lesson.

Evaluation Student’s playing is evaluatednegatively by the teacher, whostops her inmediately afterplaying wrong, and usesmodeling as tool for teachingthe child to learn to play thescale correctly.

Student’s playing is evaluatednegatively by the teacher, whostops her inmediately afterplaying wrong, and usesmodeling together with verbalexplanations about thetechnical aspects to beimproved, as tools forteaching the child to learn toplay the scale correctly.

Teacher asks the student abouthow is the scale going, andafter agreeing that it stillneeds some improvement,they decide to exchange theirteacher-learner roles as a goodstrategy for the child tobecome aware of what toimprove when playing thescale, while helping theteacher to play in tune.

stage depicting direct, interpretative and constructive conceptions (see Table 3 for a summaryof the videos, and the Appendices A, B, and C at the end of this article for the transcriptionof the complete dialogues between teacher and student in the original videos, which may beviewed as supplementary material online at http://vimeo.com/channels/psycellogy). After a fewintroductory questions to break the ice (asking their names, music preferences, etc.), three videosfor each stage (planning, supervision, and evaluation) were viewed in random order. From eachgroup of three videos at each stage, the children were asked to select which one showed howthey believed they learned best (Which of the three ways of teaching would you learn best with?Why?) and worst (And which way would you learn worst with? Why?) and to explain theirresponses verbally.

The videos took two 8-hour days to prepare. The actors were a cello teacher with about10 years’ teaching experience who is also an expert in the field of music teaching and learningconceptions, and one of her students, aged 12. The scripts were developed at various discussionsessions over three years with expert researchers in the field of music teaching and learning. Fullinterjudge agreement was achieved for the identification of each situation and its correspondingconception, after being tested in two pilot studies with small children, in order to polish thedialogues to ensure they would be understood.

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Procedure

We contacted the teachers selected to let them know that we wanted to continue to researchtheir students. Parents of the students (as described in the Participants section) were contactedto request cooperation. They were asked for authorization after being informed in writing thata 1-hour interview would be video-recorded with only the researcher and the student present.Participation was voluntary and unpaid, and 83% accepted to take part. Fifty-four students wereinterviewed individually in their music conservatoires, and only six were interviewed at theirhomes, because the parents so preferred.

Design

This was a simple prospective ex post facto cross-sectional study. The dependent variable videopreference (direct, interpretative, and constructive) was contrasted to the independent variablesteaching conception (traditional or constructive), instructional level (first course and fourthcourse), and stage (planning, supervision, and evaluation).

Analysis

A score was assigned to each participant according to his or her preference in each block ofvideos in general and for each video in each stage separately. Each block consists of the threevideo stages for each conception, so that there are three blocks: (a) a block of three videos for thedirect conception, (b) a block of three videos for the interpretative conception, and (c) a blockof three videos for the constructive conception. By adding one point for each video selected andsubtracting one point for each rejection, the scores were 3 to −3 in the block video preference ingeneral (first objective) and 1 to −1 in the block video preference by stages (second objective).

Once the scores were assigned, the data were analyzed in five phases. The first two phasescorresponded to the first two objectives, while the last three phases corresponded to the thirdobjective. First, two analyses of variance were performed for the first objective, 2 (TeachingConception) × 3 (Video Preference in General) and 2 (Instructional Level) × 3 (Video Preferencein General). Another analysis of variance was performed for the second objective, 2 (TeachingConception) × 3 (Video Preference by Stages), using the repeated measures model to test theextent to which the video preference would be affected by the variable teaching conception andto examine the details for each stage of the significant resulting variable. The first two stages,which are quantitative, were performed using SPSS version 19.0 statistical analysis software.

Given that preferences and rejections in the first two stages of the analysis could be interpretedin terms of simple emulation of the teaching actions or contexts that children are most familiarwith according to the teaching conception they have been exposed to, we believe that a deeperanalysis is needed of the explanations for the choices. This would help to determine whether theyreflect true understanding and assimilation and are not simply learned by imitation.

For the third objective, we performed a qualitative analysis on the content of those explanationsusing lexicometrical analysis, which, according to Baccala, de la Cruz, and Scheuer (2002),provides a substantially different way of analyzing and interpreting, in a reasonably fast procedure,

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large amounts of people’s verbal discourse compared to the traditional methods in our setting(categorical analyses). The lexicometrical procedure determines the most representative answersfrom participants according to statistical criteria and inductive access to the children’s very owndiscourse, and not to categories established a priori, which being sustained in the theoreticalframework of researchers, would mean circular reasoning. This prevents the most implicit partof discourse—the emotional and sentimental charge (Becue-Bertaut, 2008; Becue-Bertaut &Lebart, 2000)—from being missed. In our opinion, this “progressive spiraling” analysis (the termused by Baccala et al., 2002) helps to keep us within our theoretical starting assumptions andempirical evidence, helps to access the lexical transitions in developmental studies, and can showtendencies in order to create well-defined categories of analysis or patterns of interaction orindividual behaviors a posteriori. We were interested in ascertaining whether students’ selectionsor rejections corresponded to different ways of thinking and talking about teaching and learningmusic.

On the other hand, some people might think that the results obtained after the computationalprocess of this method are somehow trivial and could easily be seen already by the naked eye,because it is carried out with the most apparent elements of verbal production, which are closestto the conscience. However, when the production of textual data as large as what we presentherein, we cannot but disagree with such a claim, since it would be impossible to see these resultsin-depth as easily. If anything, one of the weaknesses we find in the use of the lexicometricalanalysis is that it does not assign each individual to a distinct category or lexical group, but onlyidentifies which variables would be predictive of those different ways of talking. This is whywe believe that the first part of the analysis, based on central tendency measures, reduces thatdeficiency, above all when the results from both analyses are converging.

Because lexicometry has not often been used in educational psychology research, we shall de-scribe each stage in detail. (For an in-depth description, see Becue-Bertaut, 2008; Becue-Bertaut& Lebart, 2000, Lebart & Salem, 1988, 1998.) First, we performed two factorial correspondenceanalyses (FCAs) on the lexical tables. As a brief explanation in order to understand this phasein lexicometric analysis, it should be mentioned that the basic component of FCA analysis isa lexical table or contingency table in which the rows correspond to all participants (in ourcase, the 60 children) and the columns correspond to the different words in the corpus whichmeet certain criteria or filters. In this case we decided to apply a single frequency threshold tothe whole corpus, to eliminate words that are rare in the corpus, retaining only those with arelatively high frequency (in this case, 11 or more), so that out of the 1,012 original differentwords, our corpus was reduced to 97. Then, a simple correspondence factorial analysis (CORBIprocedure) was used to test the lexical differentiation hypothesis considering the modalities ofthe active variable (teaching conception, traditional vs. constructive), of the illustrative vari-able (instructional level, first EL vs. fourth EL), and of grouping of individuals. After that, weapplied the binary correspondence factorial analysis (CORBIT procedure) to show the lexicalgroups of the modalities whose contribution was greater than average and that considered thesame modalities for the active and illustrative variable as well as the modalities of the wordvariable.

After the two FCAs, we continued with the typical lexicon detection (VOSPEC procedure)to put the explanations into hierarchical order according to their degree of prototypicality. Forthe VOSPEC procedure we used automatic selection of modal or typical responses (ASMR)and their qualitative description. Once the FCAs in the two previous stages distinguish between

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the modalities of the active variable (traditional teaching conception and constructive teachingconception), the ASMR procedure is applied according to the criterion χ2 (which is suitablefor fairly extensive explanations). It was important and useful to apply this procedure because,as mentioned above, it allowed us to place all the explanations provided by participants in hi-erarchical order according to their prototypicality, (i.e., the explanation at the top of the listwould be the nearest to the center of gravity of this part of the corpus). Considering several ofthe most typical modal explanations for each text (since one alone does not suffice to summa-rize the information provided by the text), it was possible to infer the meanings of the lexicalgroups in the context they were originally produced in and to make a qualitative descriptionof the most typical features of each group formed. The third stage was conducted using theWinSPAD data analysis software version 5.5 (manufactured by Decisia) because of its qualitativecharacteristics.

RESULTS

To present the results, we will begin with a brief description of student choices and rejectionsin each age group and teaching conception group, regarding each of the conceptions representedin the videos, in order to show the probability of each conception appearing. Then we willdescribe the quantitative part of the study, with the analysis of variance stage, in order to testthe effect of the teaching conception and instructional level on the students’ preferred videos,for all three videos representing each conception as well as for each individual stage (planning,supervision and evaluation). Lastly, we will focus on the more qualitative part of the analysis anddescribe the factorial correspondence analyses for lexical differentiation and grouping individualsin two stages (CORBI and CORBIT procedures) and conclude with the qualitative description ofparticipants’ most typical explanations according to the VOSPEC procedure.

For a global approach to the data, Table 4 shows the results of video choices and rejectionsaccording to teaching conception and instructional level.

Based on these rates of acceptance and rejection of each conception and according to our firsttwo objectives, we shall describe which variables influence student conceptions. After analyzingthe three variables, we shall continue with the analysis of possible differences or similaritiesamong the three pedagogical stages in our study.

Which Variables Influence the Students’ Conceptions?

As mentioned above, we are interested in analyzing the effect that teaching conception andinstructional level might have on students’ conceptions. The scores were 3 to −3 in this block (asa result of adding one point for each video selected and subtracting one point for each rejection,in each of the stages, planning, supervision and evaluation). To determine what significant effectsthe teaching conception has on general video preference, an analysis of variance was performed,which was significant F(2, 116) = 59.43, p < .001, η2 = .506, direct videos M = −1.02(traditional M = 0.4; constructive M = −2.43), interpretative videos M = 0.27 (traditionalM = –0.57; constructive M = −0.03), constructive videos M = .75 (traditional M = −0.97;constructive M = 2.47), as shown in Figure 4.

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TABLE 4Number and Proportion of Selections and Rejections in Each Group for the Videos for Each Conception,

Organized According to Instructional Level and Teaching Conception

Student Preferences

Group Direct Video Interpretative Video Constructive Video

Traditional TC S = 24(53.4%) S = 14(31.1%) S = 7(15.5%)First EL R = 10(22.2%) R = 7(15.5%) R = 28(62.3%)Traditional TC S = 18(40%) S = 16(35.5%) S = 11(24.4%)Fourth EL R = 18(40%) R = 8(17.8%) R = 19(42.2%)Constructive TC S = 3(6.7%) S = 5(11.1%) S = 37(82.2%)First EL R = 39(86.7%) R = 5(11.1%) R = 1(2.2%)Constructive TC S = 2(4.4%) S = 4(8.9%) S = 39(86.7%)Fourth EL R = 39(86.7%) R = 5(11.1%) R = 1(2.2%)Total Traditional S = 42(46.7%) S = 30(33.3%) S = 18(20%)

R = 28(31.1%) R = 15(16.7%) R = 47(52.2%)Total Constructive S = 5(5.56%) S = 9(10%) S = 76(84.4%)

R = 78(86.7%) R = 10(11.1%) R = 2(2.2%)

Note. S = selections; R = rejections; TC = teaching conception.

FIGURE 4 ANOVA means for general video preference, according to teaching conception. The vertical axis representsthe average preference for each block of videos (direct, interpretative, and constructive).

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A second analysis of variance was performed to analyze the significant effects of instructionallevel on general preference. It was found not to be significant, F(2, 116) = 0.651, p = .524,η2 = .011. Based on these analyses, we decided to continue with our second objective, to testthe effects of the variable, teaching model, which was found to be significant on general videopreference but this time on video preference by stages. This time, the scores were 1 to −1 foreach stage of planning, supervision, and evaluation (also as a result of adding one point for eachvideo selected and subtracting one point for each rejection).

Planning Stage. For our second objective, we performed an ANOVA, which showed thatteaching conception has a significant effect on video preference for the planning stage, F(2, 116)= 19.23, p < .001, direct video M = −0.43 (MD traditional M = 0.13; MD constructive M =−1.0), interpretative video M = 0.08 (MD traditional M = 0.17; MD constructive M = 0.00),constructive M = 0.32 (MD traditional M = −0.37; MD constructive M = 1.0), η2 = .472.

Supervision Stage. Here again, the ANOVA showed that teaching conception has signif-icant effects on video preference for the supervision stage, F(2, 116) = 3.06, p < .001, directvideo M = −.2 (MD traditional M = .17; MD constructive M = −.57), interpretative videoM = .00 (MD traditional M = .13; MD constructive M = −.13), constructive video M = .2 (MDtraditional M = −.3; MD constructive M = .7), η2 = .209.

Evaluation Stage. ANOVA showed that teaching conception has a significant effect onvideo preference for the evaluation stage, F(2, 116) = 10.34, p < .001, direct video M =−.38 (MDtraditional M = .1; MD constructive M = −.87), interpretative video M = .15 (MD traditionalM = .2; MD constructive M = .1), constructive video M = .23 (MD traditional M = −.3;MD constructive M = .77), η2 = .293. Table 5 summarizes the results of the ANOVAs performedin each stage:

TABLE 5ANOVA Means for the Traditional Group and the Constructive Group for Video Preference by Stages,

According to Teaching Model

Student Preferences

Stage Direct Video Interpretative Video Constructive Video

Planning MT = 0.13 MT = 0.17 MT = −0.37MC = −1.0 MC = 0.00 MC = 1.0

Supervision MT = .17 MT = .13 MT = −.3MC = −.57 MC = −.13 MC = .7

Evaluation MT = .1 MT = .2 MT = −.3MC = −.87 MC = .1 MC = .77

Note. MT = means for the traditional group; MC = means for the constructive group.

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TABLE 6Modalities of the Active Variable Teaching Conception and the Illustrative Variable Instructional Level

Test-Values of the Illustrative Modalities

Label Participants Absolute Weight Distance to the Origin Axis 1 Axis 2

Teaching conceptionTraditional TC 30 1,887.00 1.59020 −2.88 2.27Constructive TC 30 2,457.00 1.04772 2.21 −1.74

Instructional level1st EL 30 1,997.00 1.44970 −1.52 −0.794th EL 30 2,347.00 1.18822 1.30 0.67

Note. TC = teaching conception. Test values ≥ ±1.96 appear in boldface.

The Lexicometrical Qualitative Approach: How Did Students ExplainTheir Preferences?

The initial corpus of all the explanations that children provided for their video selections andrejections consisted of 12,200 total words, with 1,012 different words. After applying the fre-quency threshold = 11, the corpus was reduced to 9,448 total words and 97 different words. Thefirst two FCA factorial axes were considered because the decrease in the percentage of explainedinertia was more considerable between them than from the rest of the axes.

The results of the first FCA applied to the lexical table showed that the variables traditionalteaching conception and constructive teaching conception reached the standard test value4 (≥±1.96) on factorial Axes5 1 and 2 for global children’s discourse, while the variable instructionallevel did not (see Table 6). This shows that the lexicon differs significantly (p = .05) betweengroups according to the teaching conception they belong to, but not to their level or age, provingthat there are significant lexical differences between students from different teaching models butnot from different instructional levels.

Figure 5 shows the factorial plane formed by Axes 1 and 2 with the participants who had ahigher than average contribution (>1.67, obtained by dividing 100 by the number of participants,in this case 60 children). Students from the traditional teaching conception are represented by a

4The test value, which is calculated in a similar way to Student’s t-test, is that which determines whether the positionof a category on an axis differs significantly from the rest of the categories of the variable considered. The modalitiesfor which the absolute value of the test value is 1.96 or higher have a lexicon different from that of the others, with aprobability lower than .05.

5Following de Torres Curth (2005), the factorial plane

provides a two-dimensional graphic representation of the elements to be described called factorial plane, on whichthe modalities of the variables defined and the individuals are projected. The plane is defined by two orthogonalaxes (factorial axes); the first represents the direction of maximum data dispersal. The directions of the factorialaxes are determined by the modalities of the variables which most distinguish the individuals, such that each axiscan be characterized by the modalities which most contribute to its constitution, i.e. which are above the meancontribution of all modalities. (p. 59)

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FIGURE 5 FCA of the lexical nonaggregated table with the contributive participants and text modalities of Axis 1 and2. Letter T represents the traditional teaching conception participants, and letter C the constructive teaching conceptionparticipants.

T , and students from the constructive conception are represented by a C. The groups are fairlyhomogenous, since the two constructive participants (C22 and C53) at the upper left and lowerright of the traditional teaching conception plane are the farthest from its center of gravity. Thesame is true for the three traditional participants (T10, T33, and T34) located in the constructivegroup.

Figure 6 shows the factorial plane formed by Axes 1 and 2 with the words that had higher thanaverage contribution (>1.03, obtained from dividing 100 by the number of different words, in this

FIGURE 6 FCA of the lexical aggregate table with the contributive words and text modalities of Axis 1 and 2. OriginalSpanish has been translated into English, and verbs have been changed into the infinitive form.

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case 97 words). Although all the words that appear in the graph are contributive, the ones markedwith a larger dot made the greatest contribution and would therefore be more representative ofeach lexical group.

The analysis of the two factorial planes enabled two well-differentiated lexical groups to bedistinguished, related to the teaching conception they belong to, both in the way participants weregrouped and in their use of vocabulary. The groups are as follows:

• The traditional group is associated with participants T4, T11, T12, T13, T15, T18, C22, T35,T39, and C53 and the next contributive words: (to) be similar to, because, (to) believe, (to)change, (to) correct, doubts, exam, examples, (to) explain, (to) fail, finger, (to) get it right,(to) get the hand up, (to) have, (to) help, “maestro,” (to) make sure, mistakes, (to) place, (to)play out of tune, position, problem, (to) put, (to) realize, (to) rectify, same, (to) show, (to) stop,student, (to) teach, way, week, well, and where?

• The constructive group is associated with participants C5, T10, C19, T33, T34, C41, C44,C47, C48, C50 and C57 and these contributive words: advices, (to) ask, brain, (to) bring, (to)focus on something, her, (to) imagine, (to) learn, lesson, (to) let the student do, limit, (to) listento something, (to) memorize, more, nothing, (to) sing, (to) study, (to) think, what? and wrong.

Finally, the ASMR procedure was applied to select students’ most characteristic responses accord-ing to the variable teaching model, and the statistic chi-squared (χ2), which produced significantresults (range of χ2 distance: traditional group .731 to .837; constructive group .703 to .820).

Below we provide a qualitative description of participants’ answers, in which all the examplesare real excerpts from their discourse. Contributive words are highlighted in bold. The interviewswere conducted in Spanish, and only the contributive words that appeared in the original interviewsare highlighted in bold. Any additional occurrences of these words due to translation have notbeen highlighted. A double slash (//) separates answers from different students.

Traditional Group

The revered “Maestro.” One of the most noticeable features in the lexicon used by thetraditional group is that learning to play the instrument revolves around the figure of the “maestro,”a word used by these children to describe their favorite teacher in the videos, conferring upon hera superior position in the class hierarchy. It seems that it is possible to learn to play an instrumentsimply by exposure to the “maestra’s” explanations and that the complex underlying process willbe understood automatically:

( . . . ) because if for example, a maestro doesn’t explain it to you, you’ll do it wrong, and she hasto explain a lot to her so that she’ll do it well. // I think it would be better the way I said, to, um . . .so that she wouldn’t be so confused alone, first she explains and then she understands it and plays it.

Moreover, modeling plays a major part in teaching a scale. Indeed, these students reject theconstructive video because the teacher does not demonstrate what should be done, “Because Ithink that she didn’t tell her that she should place her hand more this way, and didn’t show herhow to do it, she only told her she should know how to do it and that’s all.”

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The importance of avoiding mistakes. These children believe that a good teacher shouldimmediately correct students’ errors so that they will not become bad habits and will not interruptthe evolution of learning:

Because she corrects her mistakes and, and helps her to tune better. // Sometimes I don’t like itbecause she doesn’t correct the hand much either, so, well . . . // Because she has told her where . . .where her mistake is, and made her correct it, made her correct the position she did badly, shetold her what the positions were and all that. // ( . . . ) and didn’t correct her and they didn’t do ittogether. // Because the girl won’t know how to do it alone without help and may acquire bad habits,the maestra should explain things, she’s the one who knows.

In this regard, it is in error correction that these children seem to show greatest autonomy:

( . . . ) you have to be sure where your finger is and you mustn’t repeat it, once you know the erroryou mustn’t repeat it. // Because the girl corrected, um . . . she was no longer out of tune, becausefor example, she played the note very badly but she corrected it.

However, the autonomy is not really such, and the students clearly understand that when they donot know how to do something, it is better for the student to ask the teacher directly and take onagain the role of nonautonomous student in class or while studying at home:

On the first day, she told her to do the scale again and on the second day she didn’t ask about thedoubts she had and didn’t know if it was high or low, and she didn’t ask about her doubts. // If youhave a doubt you should ask the teacher, she has to clarify the doubts ( . . . )

To listen or not to listen (mental representation of the sound v. repetitive psychomotorprocedures). In addition, these learning problems usually appear with regard to the tuning ofthe scale or the exact reproduction of the sound:

Because the teacher helps her a lot not to play out of tune, because she places her finger well andthey go . . . when she plays the note she hears it and when she plays out of tune she will try, shewill move her finger. //Because then she realizes that she’s out of tune because the teacher tells herto repeat it and then it comes out a little better.

These learning problems are also usually associated to incorrect placing of the hand or fingerposition rather than being related to the internal listening processes needed for the child tounderstand why the scale was out of tune:

Because she tells her where to place her fingers and . . . and all that, because she tells her where toplace her fingers and to do it again, and so on, all the time until it comes out well. //Because sheplaced the girl’s hand the way it should be placed. // Instead of just telling her that she’s going toohigh or too low, he places a “stop” for the finger so . . . so that she will know where, where it is, andnow she knows, now she remembers as if she had a block so that she doesn’t go too far up or down.

The participants from the traditional group tend to agree regarding how to correct notes that areout of tune, which, as mentioned above, is not related to the ideal, more constructive internal

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listening followed by a comprehensive learning process relating it to the placement and pressure ofthe finger on the fingerboard. Instead, the exact production of the notes of the scale is determinedby the place where the hand or finger should go, without mediation of either listening or thecomprehensive process:

( . . . ) she has to make the note go up quite a lot, a lot . . . because otherwise, it will sound out oftune and she’s made it lower. // When you’re playing and you don’t pay attention to your hand, youdon’t hear that it’s out of tune so much, and you don’t hear it so out of tune as other people do. //( . . . ) I can’t play a G major scale and place the A on a C, I have to know where my hand should go,where the first position is, where the third finger is ( . . . )

Correcting notes that are out of tune is also accomplished by repetitive practice, an activitythat becomes an order from the teacher without the mediation of the processes necessary for thechild to understand why:

Because she’s demanding, but that’s what has to be done because otherwise the student won’t holdit well and, because she’s . . . she’s making her repeat it and repeat it and repeat it until she gets it,because, um . . . she explained, she stopped her at the right moment when she did it wrong, sheexplained, in other words she explained what she had to do, she corrected many, many times. //She’s explaining it to her a little better because she makes her repeat.

Let’s ensure good results. Finally, with regard to the all above, the main and only reasonwhy the teacher corrects, explains, and selects contents and is the only mediating learning agentin her students’ learning is for the students to achieve good results in the exam:

She tells her to be careful with the tuning, to . . . to work on it well at home, so she can do it for theexam in two weeks’ time. // Because she tells her to place her fingers for the exam next week.

This seems to create in the students a desire to please the teacher by achieving the aim; thustheir motivation is extrinsic:

( . . . ) so the teacher can see you’re doing it well ( . . . ) // Because the maestro always tells you whatyou do badly and what you do well, and this one did it nearly every time), which in turn seems tocreate insecurity in the children due to the external evaluation (I’m nervous about the exam to moveup to the next level), and rejection of students who play out of tune, do not correct, or do not studyenough (Because she doesn’t study the scale for next week. // She didn’t correct, she hadn’t studiedany more and she played more out of tune.

Constructive Group

The guiding teacher. The children in this lexical group clearly understand that a goodteacher should help and guide her students in the learning and studying process both by providingadvice about how to do things, which is different from imposing the way they should be done,as happens in the other group, and by asking students for their opinion on how and what to

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study, “( . . . ) because there’s a lot of advice, very important, because of her experience and all.// Because the girl asks how things should be studied, to get an idea of where each thing hasto go in its place.” Indeed, upon rejecting the more traditional videos, they explain that if theteacher only corrects but does not help the child to reflect upon what has happened or how tosolve things so that the child herself realizes what has happened and which of her own resourcesto use, learning will not take place:

Because she says “listen to me and then you do it”, and like she doesn’t correct her much, becauseyou learn things if you do them badly so you make a mistake, because if you do them badly andsomeone corrects you, in the end you don’t learn and all this // Because she said “very good” and“see you next week”, and that doesn’t work, because she says yes, she says very good, she says studythese things at home, but she doesn’t give any advice and she doesn’t ask the girl // Well, that theteacher made . . . made the girl think, what you can’t do is not let her think and tell her everythingyourself, I mean, you have to let her think.

These children still explain the need for the teacher to be a guide in their learning processes,a figure who will ask them questions and help them think for themselves about their processes,usually represented by attention to the task and concentration on studying:

She asks her herself if she knows what needs to be studied so that she’ll pay attention. // I thinkshe should have told her . . . I don’t know . . . something more, something like how she could havestudied it at home, focus a little more on how she could have studied it. // ( . . . ) she explains thatif she sees clearly what the mistake was, she could improve at home and she could study it better,she’d focus better on what she has to do for the tune.

The importance of reflective and autonomous learners. Moreover, these processesshould be done autonomously, using, for example, recovery and transfer:

( . . . ) and then she acts as teacher, so that later, when she plays the cello, she’ll also do what shesays, because while she plays, she’ll remember what she said ( . . . ) she said “imagine something”,so then she remembers it when she’s playing and says “imagine the A in my head”, and then shedoes it well).

The learning process is also viewed, in the words of Schon (1983), as “reflection in action,”and not as mere repetitive practice:

I like the way of teaching more because the teacher makes her reflect, makes her reflect on how sheshould do it, and she answers, and that way you learn much more, I mean, if they tell you what todo, well, you do it, but if you realize what you have done badly and what you should do, well, it’smuch better, because you learn more that way; because in the others you learn too, but you learn toknow your errors ( . . . ) // ( . . . ) and she thinks of it in her head and does it slowly // Because shetells her to do something, and that’s it, to repeat it and repeat it, and she makes a “stop” and thatdoesn’t help her more.

According to these children, this type of guided, reflexive practice has direct incidence on theirdisposition or attitude to study:

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Because it’s as if the teacher tells her how they have to learn and the girl knows more, the studentknows more, um . . . and then it’s like she can . . . um . . . she can develop her brain more toplay the scale, because, well, the brain develops, the brain is more prepared to be able to play thattune, because the teacher has explained more how . . . how to rehearse and how to practice and howto study, she has also realized what they have to study and so it’s like a step towards knowing more),as well as their motivation to learn (( . . . ) also like that opportunity she gave her and . . . and that . . .that’s as if the girl was the teacher and now the teacher is the girl, and the girl corrects her, because itmight give her more strength to play and to do it better than . . . than . . . she might say “do this . . .you do this”, and perhaps she does it well because the teacher has been a student and she’s the . . .she’s the teacher.

Understanding what to do, and how and why to do it. Regarding the objectives of thelesson, these children agree that it does not make any sense to assign homework if the studentsdo not understand the reason for it, “Because the teacher said . . . said nothing she only saidwhat homework she had to bring for the next class, and that’s it.” This is because while studyingat home, the child feels lost and lacks tools to solve learning problems:

Because when she comes, she brings it well, but the thing is that she does it badly because shestudies it badly and the teacher tells her what she should do, and the next day she brings it better,but she brings better, what the teacher told her, but her finger isn’t in the right place).

As before, they do not hesitate to explain how this point should be worked on during lessonsin a more positive, constructive way for the student:

Because when she brings it, um . . . she has studied less, but when she brings it and it’s done badly,the teacher starts doing the same thing and she corrects herself as if she were the teacher, about whereshe should place her fingers, because the teacher, um . . . is playing it like she did and she realizesthat she . . . that . . . she imagines that she is the teacher so has to say how to place it.

To listen, that is the answer. Finally, this group is very interested in internal listening,which did not appear in the other group. Their learning is more centered on the process oflistening or singing than on the tuning outcome:

( . . . ) she’s not really looking at her hand, at what she’s doing, the teacher is doing it with her, butshe’s listening to her but not exactly looking at her hand. // The girl sang it in her head and it helpedher to play in tune. // Because the girl is going to sing it, to know the tuning, if you sing well youknow the tuning for the instrument.

Moreover, and unlike the other group, these students show a positive predisposition to evalua-tion as a joint process between teacher and student, “Because the girl said how it could be studiedand the teacher also gave her a kind of opportunity to see whether she had done it well or doneit badly,” rejecting the situation of the teacher performing the evaluation without providing anyexplanation, “Because the teacher says . . . says how it is, but she only says what’s wrong anddoesn’t say why she did it wrong.”

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TABLE 7Summary of Differences in Verbal Explanations of Choices and Rejections by the Two Groups of Students

Traditional Group Constructive Group

Role of the teacher Greater hierarchy “maestro”Gives ordersExplainsCorrects errors

GuidesHelpsAsks what and how to do thingsUses errors as a tool for learning

Role of the student Not autonomousAsks what to doObeys orders

AutonomousReflects on how to do thingsThinks

Teaching and learning processes Teacher-centered evaluationRepetitive practiceExtrinsic motivationModeling

Joint evaluationReflective practiceIntrinsic motivationInternal listeningManagement ofattention/concentrationRecovery and transfer

Teaching and learning results Quantity of practicePsychomotor (position of fingersand hands) to play in tunePerfect examExact production of symbolicmaterial

Quality of practiceInternal listening to play in tuneLearning to studyUnderstanding why things aredone

To sum up, the analysis of how these two groups of students explain their choice and rejectionof videos shows relevant differences in the way they understand learning and teaching. Table 7summarizes the main themes in these explanations and the differences between the groups. Aswe can see, they are similar to those described between the direct and constructive conceptions ofteaching and learning held by the teachers, upon which the selection of the two groups of studentswas based.

CONCLUSIONS AND DISCUSSION

With regard to our first objective, testing the influence of the variables teaching conceptionand instructional level on students’ conceptions of teaching and learning, we have found thatonly the teaching conception the students are exposed to produces significant differences intheir conceptions. Children whose teachers hold constructive conceptions, which focus more onstudents’ mental and metacognitive activity than on teacher-transmitted knowledge, also tend tohold more complex, internalized constructive representations. This confirms effects found in otherstudies (Bar Tikva, 2010; Pramling Samuelsson, 2006), although in our case, in contrast to thework of Pramling (1996), the effect is more profound because children exposed to constructiveteaching progress to the most complex and internalized conceptions (learning to understand),instead of only assuming intermediate levels of complexity (learning to know).

In any event, the fact that as from at least eight or nine years of age, children exposedto constructive learning absorb their teachers’ conceptions and assume greater complexity and

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internalization of the teaching–learning process shows that these more complex conceptionscan be acquired thorough practice. Although dominant conceptions among younger children arecloser to naıve behaviorism (Scheuer et al., 2006a), this may be due to the cognitive restrictionsimposed by a certain naıve epistemological realism, as reflected by the direct conception andthat has also been observed in other domains of knowledge (Hofer & Pintrich, 1997; Pozo &Gomez Crespo, 2005; Vosniadou, 2008, 2013). But it might also be due to the reproductiveand transmissive nature of the teaching and learning practices that they are exposed to in thespecific teaching contexts, in this case instrumental music teaching. Indeed, Perry, VandeKamp,Mercer, and Nordby (2002) showed that even in preschool education, when teachers foster self-regulatory activities and view errors as learning opportunities, encouraging their students to focuson their personal progress, the children begin to use more complex cognitive processes. Theseauthors showed that such young children really become involved and can perform self-regulatingactivities on their own learning, such as evaluating themselves or others, taking control of whathappens, choosing what to learn, very much in line with the characteristics of effective learners(Zimmerman, 1990): metacognition, intrinsic motivation, and strategic action.

Notwithstanding this effect of the teaching conception on children’s conceptions, our resultsshow that these conceptions do not become more complex according to children’s age and/orinstructional level, in contrast to findings in prior studies, both in young children (e.g., Scheueret al., 2006a, 2006b, 2009) and in students attending more advanced music courses (Bautista et al.,2012; Casas et al., 2014; Marın, Scheuer, et al., 2013), which found more complex conceptions inolder students and/or students at more advanced levels. Marın, Scheuer, et al. (2013) partly assignthe effect of instructional level in their results to the fact that learning music is more complexin higher courses and would therefore require teaching and learning conceptions that are morecomplex and more focused on the mental activity of students themselves. Although this may betrue in the case of instrumental music, it does not necessarily seem to be so in many higher learningcontexts, where teacher-centered rather than student-centered strategies and conceptions oftenseem to prevail (Entwistle et al., 2000; Kember, 1997). In any event, since the studies that foundinstructional level to have an effect did not also consider the effect of type of instruction received,further studies would be needed to better understand the how these two possible variables affectstudent conceptions, as well as their possible interaction.

The second aim in our study was to observe the differential effect of these variables on the threephases we have identified in the instrumental music teaching and learning processes: planning,supervision and evaluation of this learning. General results were similar for all phases. How-ever, the greatest differences between students exposed to traditional and constructive teachingwere found for the planning and evaluation phases. There are also differences between childrenregarding the supervision phase, because even though students from the traditional conceptionmainly selected the constructive conception, they did so to a lesser extent than the other group. Incontrast to these results, other authors have found that evaluation of teaching and learning is oftenthe stage at which constructive conceptions are most easily held (Bautista et al., 2012). Similarly,Siebenaler (1997) noted that the piano teachers whose children considered most effective arethose who evaluate negatively, providing information about what should be corrected and whatstrategies should be adopted for improvement, in line with the conception. In other educationalsettings, such as university teaching, the least complex conceptions appeared in the planningstage (Villalon & Mateos, 2009), whereas that difference was not found in our study, perhaps

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because teaching to play an instrument individually tends to favor greater student involvement inthe organization and design of their own learning.

But beyond these minor differences among the phases of learning, we were interested, as athird aim, in analyzing more deeply the content and meaning of the conceptions held by thestudents. The fact that students of traditional or direct teachers held equally direct conceptions,while students of constructive teachers held the same kind of conceptions as their teachers, mightbe interpreted as associative or superficial learning, as a result of modeling, and thus the studentstended to prefer the videos showing the kind of practice they were most familiar with. It wasnecessary to test the extent to which they understood the principles underlying these practices,and the extent to which they could explain their preferences to reflect that understanding. Table 7summarizes the lexicometrical analysis of these verbalizations, showing that the students not onlypreferred certain practices because they were familiar with them but also that they had internalizedthe principles underlying those conceptions and were capable of using them to make sense ofthose practices. The students in the constructive group had more elaborate conceptions, includinga greater number of processes, and greater complexity in those processes, in their own musicallearning outcomes and in the roles of teacher and student, contrasting clearly with those of thetraditional group. In fact, a comparison between Table 7 and the characterization of the conceptions(direct, interpretative, and constructive) provided earlier clearly shows that the verbal explanationsfrom students of direct teachers rest on the basic assumptions of those conceptions (dominantrole of the teacher, lack of student autonomy, little reference to cognitive and metacognitiveprocesses, repetitive practice, external evaluation, extrinsic motivation, etc.), whereas students ofconstructive teachers refer their learning to their own cognitive and metacognitive activity (theyconsider the teacher as a guide rather than a transmitter of closed knowledge, believe they learnfrom their mistakes more than by repeating the models provided, have greater intrinsic motivationand capacity for self-regulation, etc.).

It seems therefore that students have taken on a new role as learners according to the type ofteaching they are exposed to. However, there are some caveats regarding these data due to thelimitations of the study itself, and they should be considered for future research. In this study,the students were selected according to the conceptions that their teachers provided in answerto a questionnaire (Lopez-Iniguez et al., 2014). Although samples of students thus selected havealso shown differing conceptions of their own learning and teaching, matching those found intheir teachers, there may be some doubt regarding whether these conceptions really reflect theirteaching and learning practices because there is known to be some distance between what teacherssay about their practices and what in fact they do in their classrooms, both in music (Torrado& Pozo, 2008) and in other domains (Atkinson & Claxton, 2000; Olafson & Schraw, 2006).Therefore, it would be interesting to conduct new research prompting experientially teachingstrategies based on the assumptions of the constructive conception in order to confirm the causalrelationships between teachers’ conceptions and students’ conceptions.

In fact, studies on smaller samples would be needed in order to analyze the relationshipbetween observed teaching practice and student conceptions (Lopez-Iniguez & Pozo, 2014b),through, for example, discourse and best practice analysis, with teachers and students holdingdifferent conceptions and from different instructional levels. Longitudinal case studies could bealso carried out in order to analyze the effects of instructional level within different approachesto instrumental music teaching and learning on the conceptions held by the students. These kinds

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of approaches could also help to understand the relationships between conceptions and practices,since it could be assumed that the conceptions of teachers are influencing their students’ throughthe practices.

Along the same line, by having students select and reject videos showing teaching and learningpractices, we have been able to ascertain which practices the students themselves prefer andreject and the explanations for their choices. Nevertheless, it would be important to find outhow these conceptions guide the students’ own learning practices when confronted by a reallearning demand. We know that students of direct and constructive teachers conceive of learningand teaching differently, but it would be a good idea to test whether based on these differentconceptions they do in fact learn in different ways by using different learning strategies. In thesame respect, it would be interesting to analyze what conceptions students from interpretativeteachers hold, something we have specifically excluded in this investigation (as we explained inthe Objectives section), since that would help us to understand if they also conceive learning andteaching in a different way than children from traditional and constructive approaches, and if theydo so after the assumptions of the interpretative conception.

Lastly, we believe that this study could also open up a further line of research on the specificityor generality of student conceptions of teaching and learning. Since learners who are studyingmusic are at the same time learning in many other formal and informal domains, it is worthenquiring whether their conceptions are limited to the musical domain or generalized in otherdomains in which they are also learning (writing, mathematics, drawing), where they might beexposed to different teaching practices, according to the conceptions held by their teachers ineach subject. Based on the models of conceptual change, it may be assumed that change in theselearning conceptions might be related to the student’s skill in that domain, which would shed newlight on the specificity of students’ conceptions regarding knowledge and its acquisition.

We believe that in addition to our research objectives, another relevant contribution of thisstudy is the development and creation of the materials used (i.e., the nine videos showing choicesrepresenting student and teacher conceptions of teaching and learning in individual music lessons).Using these videos during the interviews helped us to gain access to student conceptions, sincechildren justified and reflected on their own selections, which probably had an effect on their ownideas about learning. In view of the results obtained with the students, we believe that these videoscould be also very useful as a starting point for reflection on the conceptions regarding learningand teaching held by currently active teachers and those attending teacher training courses, whichcould help to promote change in the conceptions and practices held by more traditional teacherstoward more student-centered learning.

ACKNOWLEDGMENTS

We are grateful for the generous participation of all the children who cooperated in the studyas well as for the logistical support of their parents and teachers in the coordination of bothtimetables and spaces at the conservatoires. We also thank Ma Jose de Dios and Amalia Casas forthe methodological advices, and our colleagues at the Interdisciplinary Seminar on Learning andEducational Change at our university for their suggestions and comments for the developmentand improvement of this research (https://sites.google.com/site/grupoconcepciones/). We extendour gratitude to the artist Rhys Turner for his inspiring drawings, and to Catalina Connon for

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helping us in the translation of this article into English. And last but not least, we thank thereviewers, executive editor, and editorial assistant of Cognition and Instruction for their time,suggestions, and insightful comments.

FUNDING

This research was financed by the Ministry of Science and Innovation, through project EDU2010-21995-C02-01, whose principal investigator is Juan Ignacio Pozo, and by the AutonomousUniversity of Madrid, through the FPU-UAM scholarship awarded to the first author.

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APPENDIX A

Video Scripts of the Planning Stage

Direct conception (The student plays the end of C Major scale in tune.)Teacher: “Very good Blanca. So, for next week, study the C Majorscale well, and remember that we’re going to play these two scales inthe exam in two weeks, so study it properly and focus on the tuning,ok Blanca?”Student: “Ok!”

Interpretative conception (The student plays the end of C Major scale in tune.)Teacher: “Good, good, Blanca, it seems you have finally realized howyou have to place your hand. So, for next lesson, study C Major well.Remember to put your hand in the correct place to play it in tune, ok?”Student: “Yes.”Teacher: “Remember also that you have to play these two scales forthe exam in two weeks, so be careful when you place your hand, sothat you can play in tune. Ok Blanca?”Student: “Ok!”

Constructive conception (The student plays the end of C Major scale in tune.)Teacher: “How is going, Blanca?”Student: “Well, it’s not good enough yet . . . my hand is still movinga little (on the fingerboard).”Teacher: “Yes, and can you think of anything else to improve it andcontrol your hand?”Student: “Singing it in tune, imagining it in my mind and listening toit while I play.”Teacher: “I think those are great ideas, so with all we have beenworking on today, what are you going to study next week?”Student: “To control my hand while I’m listening to it.”Teacher: “Very well, and because we have to prepare the concert ofscales, we could study C Major, because it also has the same thingswe practiced today, do you agree?”Student: “Sure.”

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APPENDIX B

Video Scripts of the Supervision Stage

Direct conception (The student starts playing C Major, and plays the A out of tune. The teacherstops her immediately.)Teacher: “Blanca, it’s still a little out of tune, ok? Let’s play it together to makesure it’s all right, let’s start.”(They play together, and the student focuses on the teacher’s hand movements,to imitate them. They both play it correctly, while the teacher gives thefollowing instructions:)Teacher: “And now, when playing the G-string, put the same distance betweenD and A, don’t open your fingers, that’s it!”Teacher: “Well, now it’s allright, so play it once more from the beginning,please, to make sure it goes ok, and remember when changing fingers betweenstrings to play in tune.”Student: (nods)(The student plays the scale in tune, looking at her hand.)Teacher: “Very good!”

Interpretative conception (While the student is playing C Major:)Teacher: “Now I’m going to use my hand on your fingerboard, so that you canimagine a kind of “stop” that you should not go beyond when you play A.”Teacher: “Can you feel it? (Singing: “G-A” and giving instructions while thestudent is playing:) Relax your shoulder, you’re very tense. Good, much better.Now you’ve realized that you must keep your hand in the same place all thetime, so play it yourself alone once more, and focus on tuning, please.”(The student plays the scale well.)Teacher: “Very good, Blanca. Now you know that keeping the hand in the sameposition all the time means playing correctly in tune.”

Constructive conception Teacher: “Well Blanca, with all the things we have been working on during thelesson, what are you going to remember before playing the scale once more?”Student: “I’m going to remember the feelings I had when I was pretending tobe your teacher: so that you were my student, to put my finger in the correctplace (showing it with the hand) and to know what the proper tuning is.”Teacher: “Right, let’s try it!”(The student plays the scale in tune with a slower tempo.)Teacher: “Right, what did you do to play it better?”S: “I’ve been listening to it internally, at the same time as I was playing.”Teacher: “Right, but now it is too slow, isn’t it? What could we do?”Student: “Yes, I’m going to try during next week to get to play it faster.”Teacher: “Good!”

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APPENDIX C

Video Scripts of the Evaluation Stage

Direct conception (The teacher reads the student’s homework in her diary.)Teacher: “Well, today you might play C Major . . . Please Blanca, play it forme.”(The student plays the scale, the teacher stops her immediately when she playsA out of tune:)Student: “Well, A is a little bit out of tune. Could you start again?”(The student starts again, and makes the same mistake, the teacher stops heragain:)Teacher: “That’s out of tune, it’s still a little too flat. Please, watch how I playit, ok?”(The teacher plays the scale perfectly in tune, exaggerating the gestures of thehand when playing A, the student pays attention.)Teacher: “Did you pay attention to where I put my hand? Ok, so now play italone, please.”(The student plays the scale looking at her hand, while the teacher stands upand corrects the student’s fingers so that she plays in tune.)

Interpretative conception (The teacher reads the student’s homework in her diary.)Teacher: “Well, today you might play C Major . . . Play it for me, please.”(The student plays the scale, but the teacher stops her to explain why A was outof tune:)Teacher: “Remember your hand; you’re not paying enough attention to it . . .Once again, please.”(The student plays it again wrongly. The teacher stops her again.)Teacher: “Uhmm, your hand is going up too much. That’s happening becauseyou’re not focusing on it. Please, watch how I play it, and observe carefully,alright?”(The teacher starts to play it for the student, while explaining what she isdoing:)Teacher: “Once you play D and E in their places and they’re in tune, as youalready do, the only thing you have to take care of is to put A at the sameheight, not higher up or further down. If you put it in the same place, it shouldbe perfect, right?”Student: (nods)Teacher: “Well, now I think you’ve realized how it should be done.”

Constructive conception Teacher: “Well, how did it go? Are things going a little better?”Student: “Now I control my hand much better (plays the scale slowly.)”Teacher: “Ok, what do you think? Have you improved?”Student: “I still don’t focus too well and it’s a little out of tune, but it’s gettingbetter and better.”Teacher: “And what else could we do to improve it . . . ? Perhaps we couldimagine now that you are my teacher, and let’s see what you can think of tohelp me to play in tune, do you agree?”Student: “Yes.”(The teacher plays the scale while the student puts her finger in the correctplace and says:)Student: “Imagine A in your head.” (Meaning to sing it internally.)

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like teacher, like student? conceptions of children from traditional and constructive teachers...

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