Interactive whiteboards and all that jazz: the contribution of musical metaphors to the analysis of classroom activity with interactive technologies

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Interactive whiteboards and all that jazz: the contribution of musicalmetaphors to the analysis of classroom activity with interactivetechnologiesGary Beauchampa; Steve Kennewellb; Howard Tannerb; Sonia Jonesb

a University of Wales Institute Cardiff (UWIC), Cardiff, UK b Swansea Metropolitan University,Swansea, UK

Online publication date: 08 July 2010

To cite this Article Beauchamp, Gary , Kennewell, Steve , Tanner, Howard and Jones, Sonia(2010) 'Interactive whiteboardsand all that jazz: the contribution of musical metaphors to the analysis of classroom activity with interactivetechnologies', Technology, Pedagogy and Education, 19: 2, 143 — 157To link to this Article: DOI: 10.1080/1475939X.2010.491217URL: http://dx.doi.org/10.1080/1475939X.2010.491217

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Technology, Pedagogy and EducationVol. 19, No. 2, July 2010, 143–157

ISSN 1475-939X print/ISSN 1747-5139 online© 2010 Association for Information Technology in Teacher EducationDOI: 10.1080/1475939X.2010.491217http://www.informaworld.com

Interactive whiteboards and all that jazz: the contribution of musical metaphors to the analysis of classroom activity with interactive technologies

Gary Beauchampa*, Steve Kennewellb, Howard Tannerb and Sonia Jonesb

aUniversity of Wales Institute Cardiff (UWIC), Cardiff, UK; bSwansea Metropolitan University, Swansea, UKTaylor and FrancisRTPE_A_491217.sgm10.1080/1475939X.2010.491217Technology, Pedagogy and Education1475-939X (print)/1747-5139 (online)Original Article2010Association for Information Technology in Teacher [email protected]

The teacher’s role has often been described as one of ‘orchestration’, and thismusical analogy is a powerful one in characterising the manipulation of featuresin the classroom setting in order to generate activity or ‘performance’ whichleads to learning. However, a classical view of orchestration would fail torecognise the extent to which effective teaching and learning make use ofserendipity and improvisation – characteristics more often associated with jazz.This paper uses the characteristics of various musical genres to characteriseteaching approaches observed in the authors’ work in two research projectsinvestigating the use of ICT in mathematics classrooms. In particular the authorsdemonstrate how jazz and other musical analogies can be useful when describingsome of the more effective classrooms in which serendipitous events wereexploited and performances were improvised by pupils as well as teachers. Theydiscuss the ways in which teachers were able to use ICT to establish conditionsunder which more jazz-like performances were likely to occur, offeringopportunities for more creative, improvised teaching and learning. They alsoexamine lessons that can be learned by examining differences between musicaland pedagogical settings.

Keywords: whole-class interactive technologies; orchestration; improvisation

Introduction

In the course of two funded studies (see Kennewell, Tanner, Beauchamp, et al., 2009;Kennewell, Tanner, Jones, et al., 2009), a framework of classroom use of ICT wasdeveloped (Beauchamp & Kennewell, 2010; Tanner, Jones, Kennewell, & Beauchamp,2005) which examined the orchestration of activity settings (Tharp & Gallimore, 1988)by teachers and pupils. During this time, interactive whole-class technologies (IWCTs)such as interactive whiteboards (IWBs) have become increasingly prevalent in UKclassrooms, and our research has enabled us to explore the influence of these technol-ogies on teaching and learning. What emerged from this work was the need for aframework to take account of serendipity in learning situations. In such situations,teachers and learners, in episodes of varying length, moved outside the constraints ofa pre-determined orchestration and began to improvise. In examining such episodes,it proved fruitful to extend the musical analogy, suggested by the concept oforchestration, in analysing how teacher and pupils were able to use IWCTs to support

*Corresponding author. Email: [email protected]

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improvisation. This paper draws on our observations over the last few years of primaryand secondary mathematics lessons in Wales to set out some new insights generatedfrom this analysis and it reflects on the potential for further development and applica-tion of the ideas.

Context of the exploration

There is general agreement from all studies of the use and impact of IWBs thatteachers see them as valuable in gaining and maintaining the attention of students andthat it is easier to collate a variety of resources for instant selection and display duringthe course of lesson activity (Smith, Higgins, Wall, & Miller, 2005). Many studieshighlight more specifically the multimodal nature of these resources (or ‘texts’ – seeMoss et al., 2007) in engaging learners through visual and dynamic ‘shared represen-tation of content’ (Gillen, Kleine Staarman, Littleton, Mercer, & Twiner, 2007,p. 254).

The contribution of the interactive characteristics of these technologies is lessclear, however. Beauchamp and Kennewell (2008) suggest that the key affordance foraction during learning tasks is the immediate, contingent feedback to the studentswhich is characterised as ‘interactivity’. The term ‘interactive’ is used in differentways in the literature concerning whole-class teaching, however, and Smith et al.(2005) helpfully distinguish technical interactivity (physical interaction with thedevice) and pedagogic interactivity (interaction between students and others in theclassroom designed to bring about learning). It is this pedagogical interactivity whichseems crucial to the development of effective practice, and models of pedagogicchange have been proposed by Beauchamp (2004), Haldane (2005), and Lewin,Somekh, and Steadman (2008). These models all characterise development from astage of using IWBs to replicate traditional practices through to the transformation ofpractices with the aid of IWCTs.

The mediating role of the teacher is thus crucial in studying the impact of IWCTson teaching and learning (Hennessy, Deaney, Ruthven, & Winterbottom, 2007), andpedagogical rather than technical interactivity has been the focus of most studies inthe field. Smith, Hardman, and Higgins (2006) noted that lessons with IWBs are moredominated by whole-class teaching than those without and demonstrated a more rapidrate of interaction between teacher and students (‘pace’), albeit at a rather superficiallevel. When a focus on interactivity as a technical process took precedence overpedagogic purpose, some relatively mundane activities became over-valued (Mosset al., 2007). It has also been noted that the fluency of lessons which the IWBpotentially facilitates depends on a certain level of skill in using the features on thepart of the teacher and, where they are involved, the students (Kennewell, Tanner,Jones, & Beauchamp, 2008).

Tanner et al. (2005) identified a scale of pedagogical interactivity in whole-classteaching, ranging from the ‘lecture’ approach with a high level of teacher control atone end of the scale through ‘funnelling questioning’, ‘probing questioning’ and‘focusing and uptake questioning’ to the category with greatest student control,‘collective reflection’, at the other end. This scale has been used to help characterisedifferences between lessons with and without the use of ICT, and there is someevidence that shifting the nature of pedagogical interactivity towards greater studentinfluence may be more important in improving the quality of learning (Kennewell,Tanner, Beauchamp, et al., 2009).

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Indeed, a number of studies have focussed on the role of IWCTs in facilitatingmore dialogic interaction. Gillen et al. (2007, p. 254) suggest that ‘the most effectiveuse of IWBs seems … likely to involve striking a balance between providing a clearstructure for a well-resourced lesson and retaining the capacity for more spontaneousor provisional adaptation of the lesson as it proceeds’. Furthermore, Hennessy et al.(2007, p. 298) claim that ‘the strength of the IWB lies in its support for sharedcognition, especially articulation, collective evaluation and reworking of pupils’ ownideas, and co-construction of new knowledge’. A number of related ideas haveemerged from attempts to characterise the contribution that the IWB can make to asetting in which effective dialogic interaction takes place:

● shared representation of content (Gillen et al., 2007)● site for collective reflection (Kennewell et al., 2008)● dynamic and manipulable object of joint reference (Hennessy et al., 2007)● dialogic space (Wegerif, 2007)● development of idiosyncratic knowledge into common/collective knowledge

(Sutherland et al., 2004).

In analysing teacher mediation of ICT and other resources in the classroom, theidea of ‘orchestration’ is particularly valuable (see, for example, Kennewell et al.,2008; Mercer, Hennessy, & Warwick, 2010, this issue). This construct extends themore familiar idea of ‘scaffolding’ and concerns the planned and responsive manipu-lation by the teacher of the features of the classroom setting (including students,resources, and less tangible features such as culture and ethos) to support the goal-related actions carried out by students and the development of common or collectiveknowledge.

In some circumstances, such as when the culture of the classroom or the featuresof the task and the technology support it, students may orchestrate features of thesetting for themselves and their peers. We have been able to associate particular typesof orchestrating action on the part of the teacher and students with different categoriesof pedagogical interactivity (Beauchamp & Kennewell, 2010) in order to assistfurther research on this matter. Furthermore, we have noticed that other aspects ofmusical theory may be able to help us understand the phenomena that we observe inclassrooms.

Extending the musical analogy

The musical analogy is a powerful one in characterising the manipulation of featuresin the classroom setting in order to generate activity or ‘performance’ which leads tolearning. The style of orchestration can reflect a variety of classroom settings andpractice according to which musical tradition is considered.

Although definitions of orchestration in the musical sense vary, the commontheme is that it is essentially a systematic, (pre-)considered and deliberate organisationof instruments or voices (Scholes, 1980). This includes making decisions about howthey will be combined and sequenced to produce textures (combinations of differentinstruments and groups of instruments) and timbres (individual ‘voices’ of instru-ments) in a variety of melodic, rhythmic and harmonic variations to achieve a finishedcomposition. This is especially true in what may be considered the classical tradition.In the classroom analogy this could be equated to how the teacher chooses how to

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combine and sequence different textures (features of the setting) and timbres (studentor teacher voices).

In addition, a classical musician orchestrating a piece will normally result in thechoices being written down in a score which is largely fixed, although the conductormay interpret this in different ways, just as teachers can interpret a lesson plan. In theclassroom, the use of a fixed ‘score’ for a lesson has been reinforced with the wide-spread use of ICT for prepared slide presentations (Beauchamp & Parkinson, 2005).In the classical music genre, once a piece of music (lesson) is orchestrated (planned)and notated in a score (lesson plan), the success of musical performances (lesson) isnormally attributed to the conductor (teacher) and not to the players (learners). Thisreflects the locus of control in such a setting. Although the players (learners) are stillindividuals, they must adapt their performance to that of the conductor (teacher).While the classical music analogy offers a way of looking at lessons, it does not fit sowell with more open and flexible approaches to teaching which demonstrate a degreeof improvisation by participants, particularly when supported by the use of more‘interactive’ technologies such as IWBs and handheld communication devices.

Teachers do not always plan classroom activity as rigidly as the classical scoreabove and other musical genres offer a better analogy to explore the nature andpotential of interactive and dialogic teaching, including the use of ICT resources as‘instruments’ allowing pupils to have a voice. Whilst having clear objectives for learn-ing and a broad plan of how the activity might be structured, we have found(Kennewell, Tanner, Beauchamp, et al., 2009) that the most effective teachers allowfor a considerable degree of learner influence over the course of activity with anapproach described by Alexander (2004) as ‘dialogic’ teaching. This involves theteacher stimulating learners to generate and express their ideas, responding contin-gently and encouraging other learners to respond to their peers, and allowing learnersto ‘conduct’ the features of the setting so as to gain support for the pursuit of theirgoals. Underlying this process is the ‘invisible script’ which may be represented bythe resources available for access on the IWB (Lewin et al., 2008, p. 299). In musicalterms, this is more characteristic of the style of orchestration adopted in jazz and otherpopular music genres. In particular, the ability to respond to spontaneous ideas fromboth the pupil and the teacher, both with and without ICT, mirrors the musician’sunplanned response to musical stimuli in improvisation.

Jazz and improvisation

The composer Busoni outlined the constraints of a musical score when he wrote that‘notation is to improvisation as the portrait to the living model’ (cited in Karolyi,1995, p. 76). Scholes (1980, p. 509) outlines the long lineage of improvisation whenhe defines it as ‘a branch of the musical art that was for centuries considered to be ofthe highest importance yet has now dwindled to insignificance amongst seriousmusicians (though it is still ably practised by jazz musicians …)’.

Improvisation is not a simple matter to define, however, and may take differentforms in different settings. It is defined broadly by Kamoche, Cunha, and Cunha(2003) as ‘the conception of action as it unfolds, drawing on available cognitive, affec-tive, social and material resources’ (p. 2025). Kamoche et al. also cite Berliner (1994),who suggests that it involves ‘reworking precomposed material in relation to unantic-ipated ideas that emerge and are conceived in the course of the performance’ (p. 2025)and highlight a number of different forms of improvisation which have been identified

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in the literature. These ideas resonate well with observations of good teachers usinginteractive technologies (e.g. Hennessy et al., 2007), and two particular forms ofimprovisation characterised by Kernfeld (1995) seem helpful in analysing classroomactivity. ‘Paraphrase improvisation’ is characterised by the ‘ornamentation of an exist-ing theme’ whilst ‘formulaic improvisation’ is characterised by the ‘artful weaving offormulas’ (p. 131–58). This latter type of improvisation corresponds closely to theprocess of orchestration, the difference from more classical forms being that it isdynamic and responsive. In the classroom, we will therefore refer to this as ‘dynamicorchestration’, in which planned activities are rearranged and redesigned during thelesson in response to matters that arise, whereas paraphrase improvisation involvesideas on subject matter being elicited and developed within a planned lesson structure.

For example, a teacher we observed was using software from NGfL Cymru(http://www.ngfl-cymru.org.uk) to teach a class of 13 to 14 year-old pupils aboutreflection. This software allows shapes and mirror lines to be drawn and dragged ona grid, and generates reflections in specified lines, together with construction lines ifrequired. The lesson started with a triangle displayed on the IWB. The class wasasked to talk in pairs to predict the position of the reflection. A volunteer (male) waschosen to come to the board to draw the reflected triangle in approximately thecorrect position using IWB board tools.

The teacher then asked the boy to explain why he had drawn the reflection in thatposition. He struggled to explain and the teacher asked probing questions to establishhow he had visualised the reflection. The class were then asked whether he had drawnit correctly and how they could justify their claim. Suggestions included countingdiagonal distances, counting squares in the x and y directions, or drawing constructionlines. Each was considered in turn with pupils being invited to the board to demon-strate their ideas. The teacher asked probing questions about pupils’ reasoning andfocussed attention on salient features and limitations of the strategies. Finally, thesoftware was used to confirm the position of the reflection under the lines drawn bypupils and the construction lines were inserted.

The interactions here were largely dialectic (Wegerif, 2007) in character. Theteaching incorporated a degree of improvisation on the part of the teacher as sheresponded to the pupils’ unpredictable responses. The context was well structured,however, and the degree of improvisation afforded to the pupils was limited by thetask and the context. During this ‘performance’ there was an ebb and flow of controlbetween solos, instrumental sections (brass, woodwind – groups of learners) and thewhole ensemble (class).

The pattern of interaction described above was repeated with more examplesbefore setting a paper-and-pencil exercise based on a worksheet of similar, butprogressively more difficult, tasks. The final one was a challenging example in whicha polygon crossed over a mirror line which was at 45° to the axes. This example wasdiscussed in a plenary review and displayed on the IWB. Pupils volunteered ideas butno one gave an accurate answer immediately and class discussion followed, withpupils arguing their case and being questioned by the teacher. Eventually two pupilscame to the board together and with the help of advice from the class managed toconstruct an accurate reflection.

At this stage, the task demanded significant improvisation from the pupils, albeitwithin an environment structured by the task and the technology. Extensive modifica-tions were made to the process in a complex, but structured, conversation betweenmultiple voices. The discussion was dialogic in character, with pupils making

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exploratory and tentative suggestions, some of which were taken up and made thefocus of discussion by the teacher. Other comments by pupils were cumulative incharacter as the board became a space for collective thinking.

The teacher then invited the class to reflect on what made a question hard and whatthey had learned about strategies for constructing reflections, drawing out the weak-ness of purely intuitive approaches in the more complex questions. In the discussionthat followed, the teacher orchestrated the contributions from a range of voices, in acomplex dialogue that summarised the learning that had occurred. At this stage,the orchestration demanded improvisation from pupils as well as the teacher in acumulative dialogue.

Relating musical genres and pedagogical approaches

Although the jazz metaphor has often been used in the context of business organisa-tions, many of the dilemmas facing managers also face classroom teachers and theirpupils, particularly in the adoption of new technologies. When teachers adopt newtechnology or new facets of a technology (such as a new feature of the IWB), they arefaced with ‘environmental turbulence, [where] there is a tendency to fall back onhabitual responses … [managers] are tempted to repeat what they do well rather thanrisk failure if they depart from what is proven to work’ (Barrett, 1998, p. 608). Jazzmusicians, and improvisers in most other musical styles, face a challenge in balancingthe risk of failure with the creative tension involved in embracing mistakes andreacting to them to form creative new pathways for action. This parallels researchcontrasting positive teaching approaches, that are apparently safer in their productionof clear arguments, with those based on cognitive conflict in which the production oferroneous conceptions is actively sought. The relative success of conflict-basedapproaches demonstrates the value of exposing such errors (see, for example, Bell,1993; Muller, Bewes, Sharma, & Reimann, 2008). It could be argued that mistakes aremore likely in a minimal structure, such as the chord (lead) sheet of a song, rather thana fully notated classical score. However, such ‘mistakes’ can also provide the catalystfor creativity as new and unexpected situations present themselves.

The creative potential of using a jazz metaphor in teaching is outlined by Flodenand Chang (2007) who argue that jazz provides a balance of guidance for teachers andcreativity in teaching, although they do not fully explore the impact on, or involve-ment of, learners. Like the sources above, they argue that jazz allows freedom withinconstraints of structure. Zack (2000) challenges this argument by suggesting that,although the jazz metaphor is useful, the elements open to improvisation need to bepushed further. He introduces the notion of examining organisations and jazz usingconversation as a framework, suggesting how this could work in a range of genresfrom the classical (similar to a prepared speech with little deviation from the script) topostbop (spontaneous, interactive conversation). In mapping musical genres he makesa useful distinction between them using Konitz’s stages (cited in Zack, 2000) whichreflect Beauchamp and Kennewell’s (2010) categories of classroom interaction andinteractions with ICT (see Table 1).

Neyland (2004) has also explored and used the jazz metaphor in the context ofethical maths teaching. He suggests an interdependent set of characteristics of the jazzmetaphor: (i) complexity (not complicatedness), (ii) an optimally minimal structure,(iii) the primacy of creative and spontaneous improvisation, (iv) challenging (‘playingoutside’) established structures, (v) pursuit of ideals, and (vi) ethical know-how. Some

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Tabl

e 1.

Mus

ical

gen

res

and

clas

sroo

m i

nter

acti

ons.

Mus

ic g

enre

Kon

itz’

s st

ages

Com

mun

icat

ion

met

apho

rC

ateg

ory

of i

nter

acti

onIn

tera

ctio

n w

ith

ICT

Cla

ssic

al –

min

imal

im

prov

isat

ion

Inte

rpre

tati

onF

orm

al p

re-d

efin

ed, l

inea

rA

utho

rita

tive

Fac

tual

rec

all,

foll

owin

g st

anda

rd

proc

edur

e or

bro

wsi

ng f

ixed

hy

pert

ext

Tra

diti

onal

jaz

z/sw

ing

– co

nstr

aine

d im

prov

isat

ion

wit

hin

a w

ell-

stru

ctur

ed c

onte

xt

Em

bell

ishm

ent

Pre

dict

able

but

fle

xibl

e sc

ript

s;

stri

ct t

urn

taki

ng a

nd u

se o

f ad

jace

ncy

pair

s –

high

ly

pred

icta

ble

stat

emen

t an

d re

spon

se p

airs

Dia

lect

icC

onst

ruct

ing

prod

uct

to s

peci

fied

br

ief,

inv

olvi

ng s

elec

tion

of

opti

ons

and

sour

ces

Beb

op –

ext

ensi

ve m

odif

icat

ion

of t

he

tune

usi

ng w

ide

rang

e of

not

es a

nd

rhyt

hms

and

som

e m

odif

icat

ion

to

harm

onic

str

uctu

re

Var

iati

onC

ompl

ex b

ut s

truc

ture

d co

nver

sati

onD

ialo

gic

Dev

elop

ing

prod

uct,

requ

irin

g in

form

atio

n se

ekin

g, h

ypot

hesi

s te

stin

g, c

ompa

riso

n an

d el

abor

atio

n of

mat

eria

lP

ostb

op/f

ree

jazz

– m

axim

al

impr

ovis

atio

n of

the

str

uctu

re,

cont

ent a

nd r

ules

of i

mpr

ovis

atio

n –

‘fun

ctio

nal

anar

chy’

Impr

ovis

atio

nE

mer

gent

, spo

ntan

eous

, in

tera

ctiv

e, m

utua

lly

cons

truc

ted

conv

ersa

tion

Syn

ergi

stic

Ope

n pr

oble

m-s

olvi

ng o

r cre

atin

g pr

oduc

t inv

olvi

ng id

enti

fica

tion

of

con

text

/mat

eria

l, an

alys

is,

refl

ecti

on

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150 G. Beauchamp et al.

of these characteristics echo those already outlined previously, but the final one alsointroduces the notion of ‘effortless mastery’, which is a mode of learning rather thana condition. This process is quite different from repetitive practice of techniques, andleads to effortless (but not habitual) performance in which new ideas are created,seemingly independent of conscious effort. In terms of IWB use, this matchesBeauchamp’s (2004) synergistic user.

In all styles of orchestration, the ICT equipment could be considered as instru-ments that the players have at their disposal, additional to the more traditional ones ofvoice, pen/paper, wipeboard, and so on. Some instruments will be better quality thanothers, some players will have a greater skill level than others – with ICT and withtalk, writing, and so on – and the role of the orchestrator in classical, jazz and othermusical genres is to try and draw the best from the instruments and players at theirdisposal by allowing varying degrees of freedom within a structured environment. Theextent of this structure can vary and loosening this is one feature of the move towardsmore improvisatory use of ICT. This is analogous to the jazz or blues musician who,when performing a piece, may have a fixed sequence to follow, such as the chordstructure and progression with associated melodic phrases, but the musical score isonly a starting point or guide and not an end in itself. Whilst still necessary in somecases, it only provides a loose framework for performance and contrasts strongly withthe current fashion in teaching guidance for tightly pre-determined objectives. One ofthe challenges for using ICT in this context is exploiting its ability to provide thecontingent responses which are characteristic of improvisation.

Another feature of this greater freedom of approach is that there may be no apparentconductor, although in reality one of the players is likely to be leading. The conductorhas signalled a change of control by becoming one of the band. Similarly, class teach-ers may temporarily hand over the direction of the lesson to pupils and this is oftensignalled by them relinquishing their position at the front of the class – ‘standing away’from the board (Lewin et al., 2008, p. 297).

An example of improvisation and change of control was seen during a lesson with10-year-old pupils who had undertaken a practical investigation to find out the totalscores obtained when throwing two dice 50 times. The scores obtained by each groupwere then collated on the IWB to find the overall frequency with which each total hadoccurred. As the totals were displayed some pupils spontaneously began to suggestreasons for the emerging patterns:

Pupil: Sir, 7 will be the most likely total as you can make 7 in lots of ways, but a 2 youcan only get in one way.

Although the teacher had not planned to do this analysis until the subsequentlesson he improvised in a contingent response to these suggestions and invited onepupil to explain:

Teacher: Go on, please explain. I’m interested in your ideas. Can you use the board toshow us what you mean? (He offered her the board pen as the pupil got upand moved to the board.)

Teacher: Come on, you take over. I’ll sit in your seat (and he moves towards her seatas the class grin and turn their attention to the pupil).

The pupil then addressed the class who listen attentively whilst she repeated herreasoning and started to write out the possible number pairs:

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2 = 1 + 1

but

7 = 4 + 37 = 1 + 6…

After she finished her explanation she looked to the teacher for comment and hethen stepped back towards the front and took back ‘control’.

The pupil had also been improvising as her contribution was volunteered andunplanned. The teacher continued to improvise as he asked the class for comments andchose another pupil to explain how other scores could be generated. In this lessonsequence, as in a performance, all players (learners and teacher) were listening to andresponding to what others are playing (contingent response). In addition, on occasionsthere may be solos (learners at the front of the class on the IWB) but others may becontent to maintain their place in the band – although they still have to be listeningand responding to the soloist. The lesson also had elements of Sawyer’s (1995)characteristics of improvisation in that it had an unpredictable outcome, with moment-to-moment contingency and the next dialogue turn depending on the one just before.

Differences between musical and pedagogical settings

Not all of the ideas drawn from musical orchestration transfer comfortably to theeducational arena, however. The use of a rehearsal to familiarise the players with thepiece and with each other’s ideas, for instance, is normal in some forms of music butdoes not have an equivalent in education. Some of these differences have generatedinsights into classroom events.

Goals and success criteria

Where a group of musicians have a goal of performing a piece of music well, they arelikely to have a shared understanding of this goal and the criteria for a successfuloutcome. It is beyond the scope of this article to discuss what these criteria might bein different genres, but it seems clear that there is a key difference from when a groupof students carry out curriculum tasks in a classroom under the supervision of ateacher. In the latter case, there are two sets of goals: those concerned with learning,and those concerned with completing the task. Whilst the teacher will be pursuing thelearning goals, students may only have the goal of task completion (for morediscussion of this point, see Kennewell et al., 2008). The success criteria can be quitedifferent for these two types of goal, with pupils merely seeking to produce a correctanswer to a question, or a product meeting superficial requirements, rather thanachieving the intended learning outcomes.

The following lesson excerpt is taken from a lesson with 32 pupils aged 13 in amixed comprehensive school. The teacher had planned a circus of three activitieswhich were to be studied in turn by each of three groups of about 11 pupils. Eachactivity was to be completed in approximately 15 minutes. We focus here on one ofthe activities – sequences.

The lesson had started with the teacher demonstrating all three of the activities tothe whole class and leaving the sequences activity on the IWB for the first group of

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11 pupils to attempt. The software gave sequences of numbers that were connected byan unknown, two-part, linear function such 2n + 3:

5 7 9 11 13

Two ‘sliders’ underneath the sequence allowed pupils to adjust the coefficients ofthe two terms in the sequence in an expression that appeared in a box marked‘answer’. When an expression was entered, the sequence for that expression appearedunderneath the original sequence for comparison.

The teacher told the pupils to copy down the sequences and use whatever methodthey wished to calculate the sequence. He showed them how to use the method ofdifferences if they could not spot the expression by inspection. The first person tocalculate the sequence would then take the pen and slide the sliders to demonstratethat their expression gave the required sequence.

In a subsequent interview, the teacher said that he wanted them to be competitive,racing each other to be the first to finish and get the pen. He hoped that this wouldmotivate the pupils to work quickly, getting through a lot of examples in 15 minutes,perhaps as many as eight.

When demonstrating the task, the teacher’s communication metaphor was largelyformal, using a pre-determined linear sequence of funnelling questions such as:

If you find the difference between each of the terms, what do you notice?

What does that tell us about the ‘n’ term?

What are we adding on each time?

When an expression was suggested, ICT was used to confirm whether or not theexpression was valid. When pupils gave a wrong or unexpected answer he modifiedhis response to take account of their thinking, demonstrating why they were wrong.Pupils who proved able to state the expression by inspection were congratulated andasked to explain how they had done it.

During the demonstration of the task, the genre varied between classical andtraditional, following a fairly predictable script embellished with the use of ICT butallowing a small degree of improvisation, constrained by the need to construct theproduct to brief. When the pupils worked on the task during the ‘circus’ phase of thelesson, they were competitive and motivated to be the one to enter the data at the IWB.They tried to work as fast as they could and some quickly realised that they couldsubvert the process and generate the solution without completing the calculation. Twoboys realised early on that they could calculate the difference between two terms on

5 7 9 11 13 Answer5 8 11 14 17 3n + 2

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5 −4 −3 −2 −1 0 1 2 3 4 5

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the way to the board, set the first slider to the difference and then slide thesecond slider until the numbers matched, without ever calculating the expression forthemselves.

The focus of the activity for these pupils was to construct the product as briefed –large numbers of sequences and expressions, confirmed as correct by the IWB.Unfortunately this focus on product rather than learning had led to an improvisationthat avoided some of the mathematics. The solution provided by the board was author-itative and classical in character, with some pupils doing little more than watching andcopying and few, if any, thinking mathematically.

In this case, the features of ICT have afforded a degree of improvisation(paraphrase in the first case, and dynamic orchestration in the second case) which hasbeen effective in meeting the students’ success criteria without meeting the teachers’expectations of learning from the activity. Whilst this phenomenon is not a novel one,and may not be directly caused by ICT, it seems that there is greater potential forsubversion because of the ease with which students can operate powerful tools. Thismastery can also be harnessed in the cause of learning goals, of course.

For example, a mathematics class was taken to a computer room to use Autographsoftware to explore reflections on individual PCs. Worksheets with polygons drawnon graph paper demanded the construction of a mirror line such as y = x, y = 2x ory = −x, followed by the construction of a reflected image. Pupils were then asked towork in small groups to check their answers by constructing the shapes in Autographand reflecting in their mirror line. At this stage, pupils’ discussions developed a moredialogic character as they sought to explain any discrepancies between their answersand those generated by the ICT.

During this phase, many pupils made errors in plotting points and/or selecting thecorrect mirror lines. These errors often challenged pupils to reconsider their ideasthrough dialogue with their partners, experimentation within the software and/ordiscussion with the teacher. This more dialogic tone was developed further in thelesson plenary.

Several pupils had also seized the opportunity to subvert the set task and to use theaffordances of the software to create their own shapes and reflection patterns, oftencreating dynamic and attractive symmetrical patterns. Unlike the pupils described inthe previous sequence, however, the intention of these pupils was not to get to theright answer, but to play, and in so doing, they improvised their own mathematicalwork.

Here, the affordances of the software constrained them towards patterns whichwere mathematical in character, many of which offered opportunities for further learn-ing. When the teacher noticed this off-task behaviour, instead of admonishing thepupils, she chose to ask them to present some of their designs to the rest of the class.Discussion of the construction of the designs provided an opportunity for collectivereflection about some of the key strategies being taught in the lesson. In this phase ofthe lesson, the improvisation of the ‘subverters’ resulted in a loosening of control anda move to a more improvisatory format in which the pupils assumed a degree of‘functional anarchy’ and offered a performance of their own ideas.

In this plenary, the teacher was orchestrating a range of voices in an emergent andspontaneous, mutually constructed conversation that linked mathematical ideas withthe aesthetics of art and design. Perhaps most importantly, it was pleasurable andexposed the joy of mathematics. The performance had some of the characteristics of‘effortless mastery’. The lesson also displayed characteristics of improvisation which

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have been identified in studying children’s play which are useful in analysingimprovisation in lessons:

● unpredictable outcome, rather than a scripted, known endpoint● moment-to-moment contingency: the next dialogue turn depends on the one just

before● open to collaboration● an oral performance, not a written product● embedded in the social context of the performance (Sawyer, 1995).

Skills

What is evident from the above is that ICT use does not always accord with the overallorganisational genre (orchestration technique) planned by the teacher. Indeed, thepotential of ICT to subvert the teacher’s intention can result in greater improvisationby the pupils as in the ‘slider’ example. This does, however, require a certain degreeof confidence and fluency with relevant ICT tools. Any orchestrator needs to at leastunderstand the potential of an instrument or voice to be able to perceive how they canbe used in compositions or arrangements. Whilst they do not necessarily need to beable to play an instrument to a high standard, they do need to have heard it played toa high standard and understand how certain sounds can be achieved. They also needto know how specific instruments or voices sound in combinations. Most textbookson musical orchestration spend much time outlining what is, and is not, possible toachieve on individual instruments and how different musical textures can be createdby combining specific instruments. One classic text states:

The technical equipment of both composer and orchestrator must include a thoroughknowledge of the individual instruments, their capabilities and characteristics, and amental conception of the sound of each. Then the effects and resources of instrumentalcombination must be learned, involving such matters as balance of tone, missed tonecolors, clarity in texture, and the like. (Piston, 1976, p. vii)

In the teaching context, both teacher and pupil have the ability to orchestrate anactivity, and understanding the capability of ICT resources, as with sound sources inmusic, is crucial. When considering the use of ICT, it seems that a successful orches-trator, or indeed subverter of the orchestration, needs a good understanding, if notpractical skill, of the resource. This is not to say that pedagogic vision and understand-ing is not important, although on its own it may not be enough to ensure a goodorchestration with ICT. It may be conjectured that being prepared to take a risk inimprovising during a lesson, both pedagogically and with ICT resources, can lead tonoticing the potential for better orchestrations in the future. Evidence from the lessonsabove suggests that if teachers accept such risk taking, by players and conductors,soloists and supporters, it is possible to make sense of unexpected outcomes and tobreathe new life into existing forms and structures.

Conclusion

In this paper we have argued that the musical analogy suggested by orchestration inthe classroom is a powerful one in characterising the manipulation of features in the

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classroom setting in order to generate activity or ‘performance’ which leads tolearning. This can range from a highly controlled and pre-planned ‘classical’ style oforchestration to a range of more improvisatory orchestrations – all of which canpotentially be found in one lesson at various times. We have suggested that a classicalview of orchestration would fail to recognise the extent to which effective teachingand learning makes use of serendipity and improvisation – characteristics more oftenassociated with jazz. The use of jazz and other musical analogies can be useful whendescribing how serendipitous events are exploited and performances are improvisedby pupils as well as teachers. There is an important role for ICT in establishingconditions under which more jazz-like performances are likely to occur, offeringopportunities for more creative, improvised teaching and learning. The dynamic andcontingent properties of ICT can facilitate the exploration of ideas and improvisationby both pupils and teachers within and beyond the set task and the use of IWCTsprovides easier sharing of ideas with the whole class. Moreover, the dynamicproperties of ICT allow demonstration of the thinking process and not just the finishedproduct.

Unfortunately, within the current school system, the emphasis is on the achieve-ment of externally set, pre-specified targets which often require a reproduction ofstandard procedures, rather than helping pupils to critically apply their learning tonovel contexts and improvisation. It may be that until this emphasis is changed, pupilswill be largely restricted to playing someone else’s tunes.

AcknowledgementsThe projects which contributed to this paper were funded by the Economic and Social ResearchCouncil (Research Grant RES-139-25-0167) and Becta: they were respectively ‘The Use ofICT to Improve Learning and Attainment through Interactive Teaching’ and ‘The Impact ofPrior Technological Experiences on Children’s Ability to Use Play as a Medium for Develop-ing Capability with New ICT Tools’. The authors wish to thank the other members of theresearch teams (John Parkinson, Nigel Norman, Lynne Meiring, Alex Morgan, GerranThomas, Helen Denny, Bethan Jones, Cheryl Anthony, Anne Loughran, Helen Lewis), all theteachers who contributed to the projects, and the anonymous reviewers who commented on anearlier version of the paper.

Notes on contributorsGary Beauchamp is a professor of education and Director of Research at the University ofWales Institute Cardiff (UWIC). His research interests focus on the use of interactive technol-ogies, particularly the interactive whiteboard, and their role in effective learning and teaching.

Steve Kennewell teaches an initial teacher education course for ICT specialists and researchesthe use of ICT to enhance teaching and learning. He is editor of Technology, Pedagogy andEducation, convenor of the Pedagogies for Interactive Technologies Research Group and amember of two International Federation for Information Processing working groups.

Howard Tanner is reader in education at Swansea Metropolitan University. He teaches on themathematics Postgraduate Certificate in Education, Master of Research and PhD programmesand researches into dialogical pedagogies.

Sonia Jones is a senior lecturer in Mathematics Education at Swansea Metropolitan University.Her research interests lie in mathematics education with a particular focus on interactiveteaching and ICT.

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