Integrating technology in the classroom - Group Scribbles - National ...

Original articledoi: 10.1111/j.1365-2729.2009.00323.xIntegrating technology in the classroom: a visualconceptualization of teachers’ knowledge, goalsand beliefsjcal_323 1..19F.-H. Chen, C.-K. Looi & W. ChenNational Institute of Education, SingaporeAbstractKeywordsIn this paper, we devise a diagrammatic conceptualization to describe and represent thecomplex interplay of a teacher’s knowledge (K), goals (G) and beliefs (B) in leveraging technologyeffectively in the classroom. The degree of coherency between the KGB region and theaffordances of the technology serves as an indicator of the teachers’ developmental progressionthrough the initiation, implementation and maturation phases of using technology in the classroom.In our study, two teachers with differing knowledge, goals and beliefs are studied as theyintegrated GroupScribbles technology in their classroom lessons over a period of 1 year. Ourfindings reveal that the transition between the teacher’s developmental states (as indicated bycoherency diagrams) is nonlinear, and thus the importance of ensuring high coherency right atthe initiation stage. Support for the teacher from other teachers and researchers remains animportant factor in developing the teacher’s competency to leverage the technology successfully.The stability of the KGB region further ensures smooth progression of the teacher’s effectiveintegration of technology in the classroom.teacher change, technology in the classroom, technology integration.IntroductionThere is much consensus that technology is now aninevitable and integral part of our everyday life, workand home experiences. Concomitantly, the call forschools to move to a more technologically integratedapproach to teaching and learning has been resonatingamong ministries or departments of education invarious countries. It is an undeniable fact that teachersplay a central role in integrating technology in the classroom.In our previous paper (Chen & Looi 2008), wehave argued that the coherency between a teacher’sknowledge, goals and beliefs, i.e. ‘KGB’ and the affordancesof the technology is the main key in leveragingAccepted: 3 June 2009Correspondence: Fang-Hao Chen, National Institute of Education, 1Nanyang Walk, Singapore 637616. Email: fanghao.chen@nie.edu.sgtechnology successfully in the classroom. By viewingthe teacher’s developmental trajectory through the threephases of initiation, implementation and maturation, weexplore the different interplay mechanisms between ateacher’s KGB and the affordances of the technology.In this paper, we investigate the different knowledge,goals and beliefs of two teachers in a primary (elementary)school as they integrate a technology calledGroupScribbles (GS) in their lessons that seeks toemploy collaborative and constructivist pedagogiesbased on the concepts of Rapid Collaborative KnowledgeBuilding (DiGiano et al. 2006). In addition, wehave devised representations of ‘KGB diagrams’ andcoherency diagrams to better illustrate the complexinterplay of teacher’s knowledge, goals and beliefs intheir developmental trajectories as they developed theircompetencies in using the technology in the classroom.At the end of this comparative study, we make some© 2009 Blackwell Publishing Ltd Journal of Computer Assisted Learning 1

2 F.-H. Chen et al.notable assertions from our research and draw some recommendationsfor helping teachers integrate technologymore effectively in the classroom.Literature reviewVarious research works have established that teachers’beliefs play an important role in influencing teachers’instructional decisions and classroom practices (Cohen1990; Pajares 1992; Calderhead 1996; Ertmer 1999,2005). Aguirre and Speer (2000) argues that beliefs playa central role in a teacher’s selection and prioritizationof goals and actions in her teaching. Moreover, beliefsshape how teachers perceive and interpret classroominteraction which influences their responses anddecision-making processes in the classroom.With the view that teacher’s beliefs have a profoundimpact on teaching practices, a series of studies has beendone to investigate the relationships between a teacher’sbeliefs and technology use in classroom. Ertmer (1999)describes two barriers to technology integration,namely, first-order barriers and second-order barriers.Second-order barriers are intrinsic to the teacher andthey include teachers’ beliefs which are harder to overcomethan first-order extrinsic barriers such as lack ofaccess to software, support and time. Therefore, theteacher’s beliefs have to be addressed adequately first inorder to have meaningful technology integration.Extending from this, Becker (2000) and Niederhauserand Stoddart (2001) indicate that teachers who holdmore constructivists beliefs tend to use technology moreoften than those who held more teacher-centred beliefs.The research of Schoenfeld (1999, 2006) shows thatit is not only the teacher’s beliefs but the teacher’sknowledge and goals that play an important role inevery pedagogical decision that the teacher makes. Indeveloping a comprehensive model of the teacher’sdecision-making process, Schoenfeld (1999) considers‘how goals, beliefs and knowledge serve to select andshape courses of action taken by the teacher.’The teacher’sknowledge, goals and beliefs influence each otherin a complex manner in every decision processembarked on by the teacher in the classroom. This formsthe underlying architecture behind the TMG’s (TeacherModel Group) model. The basic idea is that a teacher’sdecision-making and problem solving is a function ofthe teachers’ knowledge, goals and beliefs (Schoenfeld1999, 2006).Schoenfeld and the Teacher Model Group have utilizedthe TMG model in analysing, explaining and diagnosingmany complex and widely varying teachingepisodes (Arcavi & Schoenfeld 1992; Schoenfeld 1999;Schoenfeld et al. 2000) at multiple grain sizes. Themodel has thus proven to be robust (Schoenfeld 2006).However, there seems to be little work on the complexinterplay of the teacher’s knowledge, beliefs and goalsrelated to the integration of IT in the classroom in theTMG model. In this study, we seek to explore theseissues further using the KGB diagram and coherencydiagram mechanisms.Visual conceptualizationThe KGB diagramIn seeking to represent the complex interplay betweenteachers’ knowledge, goals and beliefs or ‘KGB’, wehave devised the ‘KGB diagram’ (Fig 1). In our study,the teacher’s beliefs (B) refer specifically to the epistemologicalbeliefs of the teachers. In other words, thesebeliefs concern teachers’ views about the nature ofknowledge and how knowledge is learned (Hofer & Pintrich1997). These conceptions of knowledge impact theteaching practices of a teacher (Brownlee et al. 2002).Goals (G) are what a teacher sets to accomplish in class(Schoenfeld 1999). These goals can be intrinsic to theteacher and coherent with her beliefs, or they can beextrinsic to the teacher and imposed upon her by theschool, community, or other stakeholders. The knowledgeof a teacher (K) includes content knowledge, pedagogicalcontent knowledge and knowledge of thestudents (Bransford et al. 2000).KGB regionFig 1 KGB diagram.1Teacher’sknowledge(K)5Teacher’sbeliefs (B)6 723Teacher’sgoals (G)84© 2009 Blackwell Publishing Ltd

Integrating technology in the classroom 3In the Mentored and Online Development of EducationalLeaders in Science program that supportsteachers’ professional development to implementtechnology-enhanced inquiry instruction, these knowledgecomponents (content knowledge, pedagogicalcontent knowledge and knowledge of students’ learning)have been identified as core areas of teachers’knowledge enhancement (Lee & Spitulnik 2008). Thetheoretical framework of designing these professionaldevelopment activities is founded on the KnowledgeIntegration (KI) framework (Linn 2000, 2006; Slotta &Linn 2000). Some activities include connecting teachers’existing knowledge about teaching with new waysof teaching with technology (Davis 2004) and scaffoldingteachers to make their own thinking visible via interactingwith their peers through a forum (Lee &Spitulnik 2008).The ‘KGB diagram’ represents teacher beliefs (B),goals (G) and knowledge (K) as separate circular setrepresentations. Each region in the KGB diagram iscontextualized with respect to a specific situation in theclassroom where a teacher’s K, G and B are brought tobear in her teaching, shaping her intentions, interactionsand other decisions she has to make. In Fig 1, we havedivided the KGB diagram into eight regions for clarityof explanation. Regions 1, 2 and 3 denote the intersectionof two circular sets, regions 4, 5, and 6 denote nointersection while region 7 denotes the intersection ofall three circular sets.Region 1 represents the intersection between teacher’sknowledge and teacher’s beliefs. It denotes a classroomsituation where the teacher applies selectedknowledge that is coherent with the beliefs of theteacher but may not be relevant in achieving any goals inthe classroom. This is particularly true if the goals areextrinsic to the teacher. For example, aligned with a particularbelief about collaborative learning, a teachermay implement portfolio assessment strategies in theclass. According to Gearhart and Herman (1998), portfolioscontain products of classroom instruction involving‘an engaged community in a supportive learningprocess’that is suitable for collaborative group learning.Research done by Webb (1993, 1995) suggests that anindividual’s performance in the context of group activitymay or may not represent his or her capability. In herfinding, low ability students had higher scores on agroup work than on individual work because effortswere assisted. Therefore, if the goal set for the class bythe school is to do well for high stakes individual traditionalassessments, students that did well in the portfolioassessment may or may not achieve their desiredgrades for the traditional assessments.An overlapping of K and G but not B results in region2. In this scenario, the teacher’s goals in the classroomare set by external influences such as the school, whichmay run contradictory to the teacher’s beliefs. Nevertheless,the teacher possesses the knowledge necessaryto achieve the goals. For example, a teacher mightstrongly believe in collaborative learning in the classroombut under certain constraints in the school curriculum,a teacher might revert to didactic methods or rotelearning to teach a particular lesson. A consideration ofB and G together produces region 3. In this situation, theteacher may have multiple goals for the classroom butshe has to weigh her goals according to her beliefs. Forexample, a teacher may have the dual goals of buildingan impressive portfolio for herself and having her studentslearn. However, when the goals conflict in anyparticular situation, the teacher will prioritize the goalsbased on her beliefs and this will impact the decisionmakingprocess in the classroom.Regions 4, 5 and 6 denote classroom situations inwhich the teacher’s goals, beliefs and knowledge aremutually distinct without each having any influence oneach other. Usually, these pertain to latent knowledge,goals and beliefs that were not relevant to the currentteaching and learning situation of the teacher. However,these circular sets are not static but dynamic. Anychanges to the external environment will trigger either ashift in or a resizing of any circular sets, to cause anydormant goals, beliefs and knowledge to intersect withone another. Region 8 lies outside of the KGB set. Thisregion represents the external influences and socialforces that can act on the teacher, thereby influencingthe KGB diagram. The susceptibility to these changes isstrongly subjected to the stability of the teacher’s KGB.Usually, a teacher with long teaching experiences has afar more stable KGB, as compared with a noviceteacher. Thus, their susceptibility to changes is far lessand their KGB diagram will remain relatively static ascompared with a novice teacher whose KGB diagram isrelatively more dynamic, with continual shifting andresizing of the circular sets.The central region 7 represents the intersection of theteacher’s knowledge, beliefs and goals, the KGBregion. This region denotes the teacher’s selection of© 2009 Blackwell Publishing Ltd

4 F.-H. Chen et al.knowledge, that based on goals, are prioritized by his orher beliefs. In other words, this region explains the typeof teacher’s decisions in the classroom that are alignedwith the teacher’s goals, beliefs and knowledge. In thisview, good teaching with technology requires an alignmentof the all three elements: K, G and B. In leveragingany technology effectively in teaching, the teacher mustpossess knowledge of the affordances of the technologyand how to use the technology to achieve goals that areset for the classroom.Affordances refers to both the perceivedand actual fundamental properties of technologythat determine just how the technology could possiblybe used (Norman 1990) and they are objectively measurableand independent of the individual’s ability torecognize them (Gibson 1977). Clearly in the KGBregion, the goals and knowledge of the teacher areshaped and influenced by the teacher’s beliefs. Hence,the teacher’s beliefs, in this case, provide the affectivemotivation for teacher to utilize the technology.The coherency diagramTechnology is treated as a knowledge system that isbiased (Hickerman 1990) and possesses its own propensities,biases and inherent attributes (Bruce 1993;Bromley 1998). Some technology is more suitable forcertain tasks than others. Thus, technology cannot betreated as a knowledge base unrelated from knowledgeabout teaching tasks and contexts – it is not only aboutwhat technology can do, but also, and perhaps moreimportantly, what technology can do for teachers(Koehler et al. 2007). Furthermore, for technology tobecome an integral component or tool for learning in thesubject, teachers must also develop ‘an overarchingconception of their subject matter with respect to technologyand what it means to teach with technologypedagogical content knowledge (TPCK)’ (Niess 2005).Angeli and Valanides (2009) argues that in leveragingtechnology in teaching, it is important to consider teacher’sbeliefs, in addition to knowledge (content, technologyand pedagogy). A disregard of teacher’s beliefs isconsidered as ‘naïve perceptions about the nature ofintegrating technology in teaching and learning.’(Angeli & Valanides 2009, p. 157). Hence, we need toconsider the teacher’s knowledge, goals and beliefs inrelation to the affordances of the technology in orderto study the harnessing of technology in teaching. Tocapture this relation, we introduce the coherencyThe intersection region denotes theextent of technology that is exploitedKGB regionFig 2 Coherency diagram.Affordancesoftechnologydiagram (Fig 2) as a representation to describe theextent to which technology is leveraged in teaching inrelation to the teacher’s KGB region.In Fig 2, the size of the intersection region determinesthe extent of coherency between KGB region and theaffordances of the technology. In other words, thegreater the intersection, the more effectively the affordancesof technology will be leveraged by the teacher inthe classroom. The effective usage of any technology inthe classroom must align with the knowledge, goals andbeliefs of the teacher. As the teacher develops cognitiveand affective competencies in the use of a technology,the KGB region will gradually be shifted more to theright, causing the intersection area to increase in size.On the contrary, the teacher may also develop negativeviews about the technology or misconceptions about theaffordances of the technology that may affect the KGBregion, causing it to shift to the left, thereby reducing theintersection area.The coherency diagram is dynamic and exists intandem with the teacher’s developmental trajectory inusing technology in the classroom. If we map out theentire repertoire of intersection regions, one wouldrealize that they lie in a continuum. Hence, the coherencydiagram serves as an indicator of teacher’s developmentalstate in technology competency.Four states in the continuum of coherencyAlthough the coherency diagram views the developmentalstages in a continuum, it is useful to divide thecontinuum into four distinct states shown in Fig 3.These states encompass all possible classroom scenarioswhere technology is implemented. State 1denotes pictorially that the affordances of the technol-© 2009 Blackwell Publishing Ltd

Integrating technology in the classroom 5(continuum of coherency diagram)(increasing intersection between KGB region and affordances of technology)|-----------------------------------|----------------------------|------------------------------------------------|State 1 State 2 State 3 State 4State 1: NocoherencyState 2: LittlecoherencyState 3: MuchcoherencyState 4: TotalcoherencyFig 3 Four states along the continuum inthe coherency diagram. White circle represents‘KGB region’. Grey circle represents‘Technology affordances’.There is nointersection.Technology is notleveraged at all.There is littleintersection.Technology isleveraged to a limitedextent.There is muchintersection.Technology isleveraged at a largeextent.There is totalintersection. Hence,total coherency.Many affordances ofthe technology areleveraged. This formsthe ideal state.ogy are not leveraged by the teacher at all. This stateforms one end of the continuum. As the intersectionincreases in state 2, technology is deployed to a limitedextent in the classroom. Continuing along the continuum,state 3 denotes a situation where much coherencyis depicted. In this case, technology is leveraged toa large extent. State 4 denotes the upper limit of the continuum.It is a state where all affordances of the technologyare leveraged, and there is total coherency betweenthe KGB region of the teacher and the affordances of thetechnology. This state forms the ideal state. The variousstates are not time dependent and a teacher could begin,progress, regress, or end at any state. They attempt notonly to describe a teacher’s KGB region and its relationto the leveraging of the technology’s affordances at anyone point, but also to serve as important indicators of herdevelopment progress from one state to another in usingtechnology in the classroom. The transition from onestate to another is qualitatively and quantitativelyassessed in terms of the leveraging of affordances of thetechnology in the classroom.Research contextOur focus in this study is the analysis of the teacher’spersonal experiences in using the technology in theclassroom. We adopt a case study approach in mappingout each teacher’s developmental trajectories using theCoherency diagram. This model provides a systematicframework for us to gather relevant data as to teachers’knowledge, goals and beliefs about the GS technologyat each developmental milestone, and to do comparativestudies between different implementation paths takenby each teacher.Research and intervention contextIn our research project, we have collaborated with twoteachers, namely, Lynn and May. These teachers wereselected based on their different KGB characteristics sothat a contrasting comparison can be done at the end ofour study. Lynn is an experienced primary schoolteacher in the latter stages of her successful career inteaching. In contrast with other teachers in her school,Lynn (before our study) was a technology novice, usingthe computer mainly for recording grades, email communicationsand word processing. Despite this, she volunteeredto participate in this project and was willing tomove up the technology learning curve.May is a young female teacher with about 5 years ofteaching experience. She puts in effort in her classroommanagement, cares for her students and does not neglectthe weaker students. She is under pressure to producehigh-grade students as the school faces pressure toproduce not just good students, but star students, so as toattract more parents to send their children to school.May is relatively more IT-savvy than Lynn.In Singapore, the school year starts in January andends in November. We started our study in July 2007working with Lynn and May in their primary school inSingapore. Lynn and May teach different classes ingrade 4. We started with 6 weeks of Paper Scribbles,which are activities using sticky paper notes, in theclassrooms as an initiation phase. This is a means to© 2009 Blackwell Publishing Ltd

6 F.-H. Chen et al.MathematicslessonsMathematics topicsSciencelessonsScience topicsTable 1. Topics that are taught in Lynn’sand May’s mathematics and scienceclasses.Week 1 Equivalent fractions Week 1 GenesWeek 2 Area of a triangle Week 2 Parts of a flowerWeek 3 Division of fractions Week 3 Plant pollinationWeek 4 Ratio of two quantities Week 4 Seed dispersalWeek 5 Ratio of three quantities Week 5 Plant reproductionWeek 6 Stem cuttingWeek 7 Experiment planningWeek 8 Transfer of energybegin enculturating the teachers and the students intothe practice of rapid collaborative brainstorming andcritiquing, and to developing the relevant protocols andsocial etiquettes. Easy-to-use sticky notes are adoptedto facilitate the students’ use in contributing ideas to anactivity posed by the teacher and in commenting oneach others’ postings.Subsequently, the class switched to the use of the GStechnology for 10 weeks. The students and teacherswere provided training for two sessions of an hour each.They then used GS for science lessons for another 10weeks. Each week, they had a 1 h GS science lesson inthe computer laboratory. These GS lessons formed ourprimary core data for analysis. In our instructionaldesign, we tried to incorporate the following ten principles,of which the latter five were adapted fromScardamalia (2002):• distributed cognition – designing for thinking to bedistributed across people, tools and artefacts,• volunteerism – letting learners choose what piece ofthe activity they want to participate in,• spontaneous participation – designing for quick, lightweightinteraction driven by students themselves,• multimodal expression – accommodating differentmodes of expression for different students,• higher-order thinking – encouraging analysis, synthesis,evaluation, sorting, or categorizing,• improvable ideas – providing a conducive environmentwhere ideas can be critiqued and madebetter,• idea diversity – exploring ideas and related/contrasting ideas, encouraging different ideas,• epistemic agency – encouraging students to takeresponsibility for their own and one another’slearning,• democratized knowledge – everybody participatesand is a legitimate contributor to knowledge,• symmetric knowledge advancement – expertise isdistributed, and advanced via mutual exchanges.In January 2008, we continue our involvement withthe teachers; the students are now in grade 5. Everyweek for 10 weeks, two lesson periods (totalling an hourand 10 min) for the subjects of science and mathematicsadopt GS lessons which are conducted in a computerlab. In these two classes of 40 students, each student hasan individual Tablet-PC (TPC) with a GS client softwareinstalled. In total, we have co-designed, implementedand observed five mathematics lessons andeight science lessons as shown in Table 1.GS as a technology that supports rapid collaborativeknowledge buildingThe motivation for our intervention in the school stemsfrom the realization that there is an ever-increasing needto provide students with learning experiences thatreflect the unique challenges and opportunities of the21st century. One key class of skills relates to rapid collaborativeknowledge building which include problemidentification, brainstorming, prioritizing, conceptmapping and action planning (DiGiano et al. 2006). Byharnessing these techniques in the classroom, it is possiblefor students both to learn existing subject mattermore deeply and also to become participants in 21stcentury knowledge building practices. These techniquescan be enacted with a lightweight technologysuch as GS, which enables collaborative generation,collection and aggregation of ideas through a sharedspace based upon individual effort and social sharing ofnotes in graphical and textual form.© 2009 Blackwell Publishing Ltd

Integrating technology in the classroom 7Fig 4 A Morae screenshot of the publicor group board (upper pane) and privateboard (lower pane).Table 2. GS features that support flexible collaborative work.FeaturesRepresentationallyneutralInformalLightweightMetainformatic(Re)arrangableUniqueShareableAnonymous identityDescriptionsGS can capture diagrams and drawings as well as text. Different sizes afford different kinds ofactivities.GS uses relatively small size of virtual posting pads (scribbles sheet: 3 ¥ 5 inch and label sheet:3 ¥ 3 inch) suited for quick sketches or notes rather than highly finished ideas.The scribble sheets are for concise ideas instead of lengthy explanations.The scribble sheets can annotate other representations, including other posting sheets.The scribble sheets can be positioned and repositioned to convey meaning.As a virtual artefact, each scribble sheet cannot be in more than one place at a time,suggesting turn-taking in editing or changing.The scribble sheet can be easily passed from one person to any group workspace. The samesheet can be retracted from the group workspace for refinement or elaboration.GS has the feature of veiling the user’s identity. However, access to the identity of the authorof each scribble sheet can be made available to the instructor.Adapted from DiGiano et al. 2006.GS, GroupScribbles.The GS user interface presents each user with a twopanedwindow. The lower pane is the user’s personalwork area, or ‘private board’, with a virtual pad of fresh‘scribble sheets’on which the user can draw or type (seeFig 4). The essential feature of the GS client is the combinationof the private board where students can workindividually and group boards or public boards wherestudents can view others’ work, post their work andposition it relative to others’ work, and take items backto the private board for further elaboration.Figure 4 shows a lesson activity in class in which eachstudent posts answers to the question ‘When does theheart beat faster/slower?’ in the private board, and thenmoves their answers to the public board for sharing. Thestudents’ scribble notes showed a multiplicity of ideasthey generated which enabled the teacher to initiate discussionson the interesting postings.Table 2 depicts the basic features of GS that are suggestiveof the affordances of GS for supporting studentparticipation in designed collaborative activities. In collaborativeclassrooms, groups of learners and theirteachers take on roles, contribute ideas, critique eachother’s work, and together solve aspects of larger problems(Hake 1998).© 2009 Blackwell Publishing Ltd

8 F.-H. Chen et al.Data collectionIn our collection of data, two or more researchersobserve each class and make detailed field observationnotes. One video camera is set behind the classroom torecord the classroom session, while two other videocameras are focused on two target groups of students.Screen capturing software Morae 2.0 is installed onthe TPCs to record the interaction of the students usingGS. We approach our data analysis from different perspectivesincluding uptake analysis (Looi et al. 2008), aswell as analysis of surveys, interviews and performancetests (Ng et al. 2008). We have also employed semistructuredinterviews as a method to gain access to thesubjective understanding of the teacher. This includes anhour-long interview conducted at the end of the semesterand weekly post-lesson conference sessions. In the postlessonconference sessions, the teacher is prompted toreflect on the lesson and articulate her own analysis ofthe lesson. This proves to be a useful source of data forus, as it reveals many subtle beliefs that the teacher hold.In the end of the semester, the teacher is interviewed bytwo researchers with a list of prepared interview questionsin a private location. The interview sessions arerecorded by audio and video. In the work reported in thispaper, our multifaceted data collection and analysis issituated in the frame of qualitative analysis and the casestudy formalisms of Stake (2000).AnalysisThis section discusses the use of the coherency diagramsin explaining May’s and Lynn’s various pivotaldecisions to integrate technology into the curriculum.This is done by establishing their beliefs, goals andknowledge in the first instance and then employingthem as lenses to explain and understand the variousGS-related activities in the classroom.Phases of technology implementation in the classroomIn our previous paper (Chen & Looi 2008), the differentimplementation phases of technology, namely the initiationphase, the implementation phase and the maturationphase are discussed in the context of Lynn’sdevelopmental trajectory. Each phase denotes a generaltime-based developmental milestone for integratingtechnology in the classroom. However, the timeIncrease inintersectionregionDecrease inintersectionregionFig 5 Units of developmental trajectories. White circle represents‘KGB region’. Grey circle represents ‘Technology affordances’.required to progress from each phase to another variesfrom teacher to teacher. Every teacher has a differenttrajectory with different initiation, implementation andmaturation phases, and these can be described withcoherency diagrams.The initiation phase denotes the teacher’s initialexposure to technology. The teacher must be convincedboth affectively and cognitively to accept the technologyin the classroom. In order for a teacher’s KGBregion to be coherent with the affordances of technology,i.e. state 3 of Fig 3, the perceived affordances of thetechnology must align with the teacher’s KGB. Morealignment will imply more intersection. Therefore,some practical recommendations at this phase includeopportunities for the teacher to articulate her KGBduring initial exposure to the technology and align theaffordances of technology to her KGB. In the implementationphase, the teacher proceeds to use the technologyin the classroom. If the perceived coherency inthe initiation phase is enacted successfully in the realclassroom, there will be an increase in her confidence inusing the technology. Diagrammatically, this would beindicated by an increase in intersection between theKGB region and the affordances of the technology. Ifthe converse occurs, it may signal a decrease in confidenceand motivation to use the technology. This is indicatedthen, by a decrease in the intersection region,causing a regression. These units of developmental trajectoriesare shown in Fig 5. Therefore, affirming teacher’sconfidence in the first few lessons is very importantin building confidence and increasing motivation.Lastly, the maturation phase denotes a phase wherethe teacher garners enough positive experience to usethe technology despite technical glitches of the technology.This is the final phase if the teacher has persisted inusing the technology. Another indicator is that theteacher may have found innovative ways in using thetechnology. Usually, this phase is characterized by state© 2009 Blackwell Publishing Ltd

Integrating technology in the classroom 93 or 4 of Fig 3 because it denotes certain technical competenceand confidence in the teacher. Note that in theinitiation and implementation phases, the teacher’scoherency diagram can occur at any point along the continuumof the coherency diagrams, i.e. states 1 to 4.However, there is a possibility that a teacher may notachieve the maturation phase at the end of the technologyimplementation period, especially if the teacher’sdevelopmental trajectory is regressing along the coherencydiagram continuum instead of progressing.Lynn’s developmental trajectoryLynn’s KGB is reported in our previous paper (Chen &Looi 2008). In this section, we illustrate Lynn’s developmentaltrajectory via the coherency diagrams, supportingour analysis by describing some empiricalobservations. This is summarized in Table 3.Initiation phaseIn the initiation phase, Lynn begins her developmentalpath at state 3. There is much alignment between herKGB and her perceptions of the affordance of the GStechnology. First, she believes that as a teacher, patiencewith the students is very important to help studentslearn. She expresses this belief in her own words:‘patience with the students is very important to make achild (student) learn. Raising your voice against themwill make things worse.’ This belief is fundamental toother beliefs that she holds. She firmly believes thataddressing the emotional needs of students is central tostudents’ learning, that in building a good rapport withthe students, ‘the children need to know that teacherunderstands and cares about them,’ and that it is importantto assure students that it is alright ‘not to know’.Therefore, she believes that students in her class shouldbe comfortable enough to admit that they have made amistake and that winning the hearts of the studentsis important in teaching and learning. Second, shebelieves that ‘not every student is the same’and that theypossess diverse abilities. She also resolves not to let anystudents in her class feel ‘inferior’. Students in her classhave different strengths and because of these beliefs,she has put in place a collaborative culture that is suitablefor the students to learn from each other. Lastly, shealso believes in the importance of teaching ‘thinkingskills in the classroom’. This belief motivates her toadopt pedagogies that teach cognitive skills such asposting good comments and designing questions forpeer teaching.Concerning beliefs about the use of technology in theclassroom, Lynn expresses her views succinctly: ‘it isimportant to keep up with the times. Nobody forces meto use GS in my classroom. I believe that one must bepositive in learning, especially in IT’. When askedfurther, Lynn reflects that this positive mindset is pivotalfor her in overcoming obstacles in integrating GS in theclassroom in the initiation stage and in exploiting theaffordances of GS to the fullest. This intrinsic motivationto learn has led her to be open to changes and hasresulted in good working relationship with the researchstaff.Closely linked to her beliefs are her ‘overarching’goals (Schoenfeld 1999) in integrating GS technologyin her classroom. In the interview with Lynn, sheexpresses that her main goal is ‘to see her children (students)learn because this gives a lot of satisfaction’ toher. In a conversation with her Head of Department, headds that Lynn took up GS technology because ‘it is anopportunity for her to build up her portfolio as a seniorteacher as she is competing with another seniorteacher’. We tend to infer that Lynn may hold two overarchinggoals, but her beliefs about teaching and learningmay have helped her to prioritize the goal of ‘seeingher children (students) learn’ as a more important goal.Her beliefs have also provided a focus for Lynn to selectknowledge appropriate for effective learning. Becauseof her long teaching career, Lynn possesses reasonablygood content and pedagogical content knowledge of herteaching subjects – mathematics and science. This isconfirmed in separate interviews with some of her students.One student notes that she is a ‘knowledgeableteacher who is correct most of the time’. They alsocomment that they ‘enjoyed her lessons and were able tounderstand what she was teaching’.Because of her strong belief that every child is able tolearn, Lynn has devised lessons that are relevant to thestudents and are able to leverage the affordances of GSto her advantage. Lynn perceived these affordances tobe congruent with her student-centred beliefs and goals.The affordances of GS technology complement andenhance her knowledge of content, pedagogy, and herclass. For example, the features of GS technology allowher to teach science lessons better in a collaborativesetting. In addition, although she is a technology novice,© 2009 Blackwell Publishing Ltd

10 F.-H. Chen et al.Table 3. Lynn’s developmental trajectory.Phases Lynn’s knowledge (K) Lynn’s beliefs (B) Lynn’s goals (G) Affordances of technology Coherency diagramInitiationphaseImplementationphaseMaturationphaseLynn’s knowledge aboutcollaborative learningstrategies and thedifferent abilities amongher students.Lynn’s knowledge aboutdifferent learning stylesprofiles in her students.Lynn’s knowledge aboutcollaborative learningstrategies and thedifferent abilities amongher students.Lynn’s knowledge aboutdifferent learning stylesprofiles in her students.Lynn’s increase inknowledge, e.g. workingwith researchers, PD andtraining programmes.1 Lynn’s beliefs about the valuesof the different abilities in herstudents and the importance ofpeer learning.2 She believes in the importanceof being patient with herstudent including affirming andpraising her students isimportant in learning.Lynn’s beliefs about the values ofthe different abilities in herstudents.1 Lynn’s beliefs about the valuesof the different abilities in herstudents and the importance ofpeer learning.2 Also, she believes in theimportance of being patientwith her student includingaffirming and praising herstudents is important inlearning.Lynn’s beliefs about the values ofthe different abilities in herstudents.Lynn’s goal is to create agood collaborativelearning environment.Lynn’s goal is to givestudents freedom toexpress their solutions intheir desired form.Lynn’s goal is to create agood collaborativelearning environment.Lynn’s goal is to givestudents freedom toexpress their solutions intheir desired form.Lynn’s positive learning attitudes. Lynn is determined to learnas much as possible sothat she can be anindependent competentGS technology user.Lynn perceives that theshared spaces in GSprovided a goodplatform to post, buildand improve each other’sideas to allow studentsto learn from oneanother.Lynn perceives that themultimodal affordancesof GS are aligned withher KGB.Lynn successfully utilizesthe shared space in GSfor collaborativelearning.Lynn successfullyimplementedmultimodal expressionsin her GS class lessons.Lynn is able to handletechnical glitches bydevising ‘filler’ activitiesas well as minimizingglitches.Because there is muchalignment with theLynn’s KGB and theperceived technology,Lynn starts off withstate 3.There are successes inimplementing what Lynnperceived. Hence, thereis increased confidence inusing the GS technology.This would be in state 3.Lynn is able to handletechnical glitches.Therefore, she is close tostate 4.White circle represents ‘KGB region’; Grey circle represents ‘Technology affordances’.GS, GroupScribbles; PD, professional development.© 2009 Blackwell Publishing Ltd

Integrating technology in the classroom 11Fig 6 Multimodal expressions in a Group-Scribbles science lesson.the user-friendliness features of GS gives her the confidencethat she is able to learn it well later.Implementation phaseIn the implementation phase, Lynn implements whatshe perceived as coherent in the initiation phase in theclassroom. In our case study, Lynn is able to leveragethe multimodal and shared space affordances of the GStechnology in her lessons.Multimodal expressions in GS. In many of Lynn’sscience lessons (weeks 1–5, 8; see Table 1), ‘live’specimensare used for students to sense and observe. Forexample, she brings plant seeds for lesson 4 and flowersfor lessons 2 and 3. By allowing students to observe andsense the specimens, she caters to the different learningstyles (visual, tactile, kinesthetic and audio) of the studentsin her class. This stems from her belief that everystudent learns differently, as mentioned in section 4.1.This belief also causes her to leverage on the affordanceof GS which allows students to express their answers onthe pad in different forms such as drawing or typing, i.e.the ‘representationally neutral’ feature of GS as shownin Table 2. This has produced a rich variety of answers,as shown in Figs 6 and 7. In Fig 6, some students preferto draw and colour while other students prefer to type.Some students prefer not to post anything but verbalizetheir answers during the lesson. Similarly in the mathematicslessons, different students articulate theiranswers in different modes as shown in Fig 7. Lynn’sbelief in the diverse abilities and learning styles amongher students motivates her to plan and implementlessons that cater to different learning styles of her students.In this way, the multimodal affordances of GS areleveraged upon.Shared space in GS as a platform for collaborativelearning. Lynn’s student-centred beliefs enable her tocreate a conducive environment that promotes collaborativelearning. In her lessons, students are allowed toexpress their answers without fear of criticism. This isnot only seen in verbal articulation but also in thewritten ideas on GS boards. Below is a transcript thathappened in her science lesson on transfer of energy:Lynn: What is the answer to the question? Anybodyknow?Student 1: Eagle?Lynn: Not really. However, that was a good attempt.Anybody else want to try?(students in her class begin to see that the student whoprovides an inappropriate answer will not be reprimanded,more students raises their hands)Student 2: Caterpillar.Lynn: Very good answer. Whole class give student 2 aclap. (whole class gives a clap)Lynn: Alright, everybody please write your answers onthe GS groupboard.© 2009 Blackwell Publishing Ltd

12 F.-H. Chen et al.Fig 7 Multimodal expressions in aGroupScribbles mathematics lesson.Lynn encourages her students to give constructivecomments so that their self-esteem might be boosted.She gives praise as much as possible and in her lessons,very few incidences of chiding are observed. Below isanother transcript in her science lesson on seeddispersal.Lynn: Tell me how? the seeds can be dispersed? And giveme some examples of it.Student 1: By wind. Pollen grains.Lynn: Very good! Other answers?Student 2: By water.Lynn: Any examples?Student 2: ur. . . .Lynn: Anybody can help student 2? I think student 2 hasgiven a good answer but any examples? (Lynn did notscold student 2 for being unable to give the example)Student 3: Coconut.Lynn: Excellent!In addition, her belief in the diverse abilities amongher students causes her to value every view that her studentsarticulated. She implements group collaborativelearning because she believes it is a good avenue for studentsto build upon each others’ knowledge. Shebelieves that collaboration maximizes learning, andthus is more willing to exploit the features of GS technologythat support collaborative learning shown inTable 2, e.g. viewing other group boards, peer reviewingeach other’s ideas, and posting ideas in real time asshown in Figs 6 and 7. These affordances are leveragedsuccessfully in promoting collaborative learning.Because of these reasons, we could observe substantialcollaborative results, e.g. evidences of peer learning andcritique, higher order thinking skills, richer content,etc., because of the collaborative culture that she hasbuilt in the class (Looi et al. 2008).Maturation phaseAfter a period of implementation, she has reached closeto state 4 in the maturation phase. In this phase, she hasdevised her own ways to cope with the limitations of theGS technology, such as devising suitable filler activitieswhen the technology fails, complementing GS technologywith Windows Journal, and planning GS-relatedlessons under the constraints of the GS-technology (e.g.not loading large background pictures that will ‘hang’the GS technology). Hence, as we trace the coherencydiagrams, Lynn exhibits a positive upward growth fromstate 3 to state 4 in implementing technology successfullyin the classroom. The transition from state 3 tostate 4 is a smooth and relatively easy one for Lynn.Lynn enjoys the GS technology so much that she commentsthat she will ‘use GS in her classroom even whenthe researchers are not around’.May’s developmental trajectoryInitiation phaseAt the beginning of the intervention, May holds severalprimary beliefs about teaching and learning. First, she© 2009 Blackwell Publishing Ltd

Integrating technology in the classroom 13believes that enabling the students to do well in theexaminations is the primary task of the teacher. Sheexpresses this belief in her own words, ‘I wanted mystudents to achieve academically. That is the mostimportant’. Following closely to this primary belief, herlessons have orientations towards preparing students toperform on examinations. She expects herself to finishthe syllabus on time adhering to a strict schedule calledscheme of work (SOW). Second, she believes that herstudents are ‘generally weak and unable to articulatetheir answers well enough’ and generally believes thather students ‘need to be guided and are not used to independentlearning’. This has caused her to employ didacticteaching strategies in her lessons, e.g. posing veryclose-ended questions and enacting IRE (Initiation-Response-Evaluation) episodes frequently in herlessons. Below shows a transcript in one of her sciencelesson on parts of a plant:May: Which part of the plant will form the fruit?(Initiation-close ended question)Student 1: Stigma (Response)May: Stigma? That is not really the part (Evaluationcloseended)Student 2: Style (Response)Teacher: Style? Wrong. Sorry (Evaluation)Third, she believes that strict classroom management isrequired to achieve optimal task behaviour in students.She cannot tolerate any excessive noise in her classroomand believes that discipline and orderliness is the wayfor students to learn effectively. She expects her studentsto follow her instructions in minute detail. Therefore,her goals include completing the SOW on time andexpecting a quiet, disciplined and orderly class for everylesson.Hence, May’s KGB region entails applying herknowledge of didactic strategies to ensure completionof the syllabus and preserving a disciplined class forevery lesson, based on her beliefs that her studentsshould be taught to be ‘exam-oriented’ and that they aregenerally unable to articulate their answers wellenough. Therefore, in the initiation phase, May perceivesmany of the affordances of GS technology to bemisaligned to her KGB region. The affordances of GStechnology is primarily leveraged for collaborativelearning which requires students to articulate their ideasand to work together in groups to solve open-endedquestions posed by the teacher. In addition, collaborativelearning demands more time, which will cause Maynot to complete her syllabus on time. Moreover, Mayfaces difficulty in planning collaborative learningactivities for GS-related lessons because of her limitedknowledge concerning teaching methods. Lastly, Lynnonce commented that May was ‘persuaded to join in theresearch collaboration in using GS technology’ withouther consent being sought first. All these factors points tothe incoherency between May’s KGB region and theaffordances of GS technology, and this can be aptlyindicated by state 1 as shown in Fig 1.Implementation phase (part 1)As May enacts the incoherencies perceived in the initiationphase, she is not able to leverage the technologyeffectively in the classroom. First, her fear of not beingable to complete her lessons on time has materialized insome of her GS lessons as she could not complete herintended lesson objectives. This is partly because of herpoor time management skills in a group collaborativelesson. From our classroom observations, we note thatMay constantly seeks to enforce strict discipline in herGS group collaboration lessons. This causes a lot oftension in the classroom as students tend to talk andarticulate more during these lessons while May tries tomaintain order in the classroom by giving numerousinstructions and expects her students to comply. Here isan episode of May’s strict classroom management in ascience lesson:May: Have I finished my instruction?Class: No.May (repeated again in agitated tone): Have I finished myinstruction?Class: No.May: Then why are you people starting to do your workalready?May (turned to student A): A, what did you do in X’spost?May: What was my instruction? If you draw on yourboard, how are you going to drag it on your groupboard?May (shouting): Everyone 2 fingers up! 2 FINGERS UP!May wastes much lesson time in trying to enforce disciplinein the GS lessons and she reckons that more timeis needed for collaborative group work. She succinctlyexpresses this frustration: ‘GS is time consuming anddraining. It has prevented me somehow from coveringthe syllabus.’ Second, technical glitches that have unexpectedlycropped up in her first few lessons have furtherreduced her confidence and motivation to use GS technologyin her lessons. In fact, she has attributed the poor© 2009 Blackwell Publishing Ltd

14 F.-H. Chen et al.implementation of the lesson plans to technical glitchesin the technology rather than reflecting on the misalignmentbetween her KGB region and affordances of thetechnology. Therefore, for the first half of the implementationphase, May does not exhibit any progress inleveraging technology effectively in her classroom.Basically, she seems to have stagnated at state 1.Implementation phase (part 2)Realizing May’s stagnation, we as researchers put inefforts to increase her confidence and motivation to usethe GS technology. This was done in several ways. First,we attempted to encourage her after every post-lessonconferencing. Instead of reprimanding and pointing outher mistakes, we took pains to give recognition to whatevergood practices May exhibited in the GS lessons.Second, we asked her to do some reflection of her owninstead of us criticizing her lesson directly. Third, weconducted periodic professional development sessions(PD) for the teachers (Chen & Looi 2008). These servesas communication opportunities for May to learn goodpractices from Lynn as well as serving as a platform toshare any problems they face in using GS, includingtheir KGB. In fact, we have shown her videos ofselected portions of May’s GS lesson to trigger her toreflect on the effectiveness of her teaching strategies.Surprisingly, May commented that she is not aware ofsome of the inappropriate teaching strategies she hasemployed, e.g. giving repetitive instructions. In her ownwords, ‘I think the videos showed in the PD sessionhave caused me to reflect on some of the teaching practicesseriously.’ Fourth, we have also deliberately givenMay more agency in planning collaborative lessons forGS. All these efforts have paid off when we detect somechanges in May’s KGB.First, May has shifted from IRE to probing studentsfor deeper answers, and giving opportunities for her studentsto articulate their answers more. In one of thescience lessons:May: Can anyone tell me what is wrong with the answer.Student A: Teacher, the answer is not correct.May: I do not want to know what is right or wrong, I wantto know the reason. Write your ideas on the Group-Scribbles scribble pad and post them on the groupboard.In doing so, May has leveraged on the affordance of GSas a means for the students to share their ideas. Second,May became less teacher-centred in her lessons.Instead of giving the correct answers, she chose to usestudents’ prior knowledge written on the GS scribblespad as a bridge to teach new concepts. For example, inanother science lesson on plant reproduction, Maywanted to teach the concept that seeds do not grow inplants:May read the students’ answers from the GSscribbles sheets aloud and asked students to correct anyincorrect ideas.May: The flowers have seeds? Inside it?Student A: The ‘seeds’ has not grown into a seed yet.May: Then what is it that is inside the flower?Student A: Ovule.May has better leveraged on the affordance of GS technology,e.g. ‘shareable’ feature of GS shown in Table 2,as a result of a change in her teaching strategies. Lastly,May was more able to handle certain technical glitchesthat arose in using GS. In a science lesson where therewas a glitch with the GS technology:May: All not responding? Cancel and login again.Some students talk when logging in again.May: The more people talk, the more will the computerhang (jokes).May then told students to use Window Journal to writetheir ideas and that she will restart the GS server.In summary, the external support provided by researchersto May has effected some change in her KGB.Empirical evidence discussed previously has shown thatshe is able to leverage the GS technology better becauseof a change in her teaching strategies. This can be attributedto an increase in the intersection region betweenher KGB region and the affordances of the GS technology,caused by a shift in her KGB region as indicated bystate 3.Implementation phase (part 3)One would expect May to progress towards state 4 as sheleveraged more of the affordances of the GS technology,but apparently this was not so. In one of the recent interviewswith her, she commented that ‘GS is more suitedfor higher ability students attributed to their ability toverbalize, dare to post and willing to learn from friends’.For the weaker students, she believes in ‘giving basiccontent first and use GS for enrichment due to lack oftime and lack of prior knowledge. Weaker students needto be taught exam skills instead of thinking skills’. Thisis probably because of the recent examinations results© 2009 Blackwell Publishing Ltd

Integrating technology in the classroom 15that show better results for the high ability students butnot for the weaker students. Because of the exam results,her KGB region may have shifted again and this resultsin a smaller intersection with the affordances of technology,signalling a regress into state 2.May’s developmental trajectoryIn Table 4, we attempt to tabulate May’s developmentaltrajectory according to the different phases described inthe preceding sections. May’s KGB and her changes inKGB which directly impact the affordances of GS technologyfor each phase is systematically listed in thetable. For each phase, the coherency diagram is used torepresent the leveraging of GS technology by May andthus to map out her developmental trajectory.Comparison of Lynn and May’s developmentaltrajectoryThe developmental trajectories for Lynn and May aresummarized pictorially in Table 4. In this table, we cansee the usefulness of coherency diagrams in indicatingthe different developmental stages for both Lynn andMay. In the next section, we will discuss several usefulimplications from the findings shown in Table 5.DiscussionFrom Table 4, we can make some notable assertionsconcerning a teacher’s developmental trajectory in integratingtechnology. First, the transition between eachstate is unequal. From Lynn and May’s developmentaltrajectory, the transition from state 1 to any states ismore difficult than transitions from other states. This isbecause shifting of the KGB region before they intersectat all with the affordances of the technology is a lotharder as the teacher has to change their beliefs radicallyto align with certain affordances of the technology. It iseasier to modify existing beliefs to intersect more thanreplacing existing beliefs with new beliefs, i.e. transitionfrom state 1. In May’s case, the researchers had toput in extra effort to increase her confidence and motivationduring the PD sessions, by trying to change herKGB so she can transit to a higher state.Second, it is not necessarily true that a teacher willalways exhibit progress in integrating technology. InMay’s case, she shows regression from state 3 to state 2.This regression is probably caused by external factorsthat are not within the teacher’s control. For example,the examination results have cast doubts upon the benefitsof using GS technology in May’s class, forcing herto reevaluate her KGB again.Third, it is possible to progress through multiplestates in the implementation phase without achievingthe maturation phase. For May’s case, she has not garneredenough positive experiences in integrating GStechnology in her lessons to stabilize her KGB region.As shown in Table 4, her KGB region is susceptible tochanges caused by external factors, i.e. exam results. Incontrast, Lynn’s KGB region remains relatively stable,allowing her to transit smoothly to state 4 in the maturationphase.Fourth, we conjecture a high possibility that Lynnwill stay at that stage, even when the researcher supporthas been withdrawn. This is because the high coherencybetween Lynn’s KGB region and GS affordances at thematuration phase implies that Lynn has internalized theaffordances of GS technology in her knowledge, goalsand beliefs to a degree that, without any external interventionand support, Lynn should be able to continue toleverage GS technology in her classroom lessons.Moreover, the smooth linear development trajectoryfrom state 3 to state 4 points to the high stability ofLynn’s KGB region as mentioned previously. The possibilityof regression into lower states is highly unlikely.Additional evidence gathered has supported this conjecture.Afterthe end of the research project, Lynn has beenappointed as the Head of Level for Primary 3 and hasbeen tasked to spearhead the implementation of GStechnology throughout that whole level. This includestraining and mentoring teachers to use GS in theirlessons, co-designing suitable lesson plans, and sharingwith teachers from other schools who are also interestedin using GS. In contrast, May’s volatile and unstablenonlinear trajectory poses an unpredictable situation.The low coherency between her KGB region and theaffordances of GS technology implies that May needsstable external support (from school or researcher)before she can progress from state 2 to state 4. This issupported by the fact that May is not involved in leadingany school-based GS-related projects since the end ofthe research project.Lastly, researchers have provided appropriate technical,pedagogical and psychological support in thecourse of the project, in order to accelerate upwardgrowth of the teachers’ integration of technology in the© 2009 Blackwell Publishing Ltd

16 F.-H. Chen et al.Table 4. May’s developmental trajectory.Phases May’s knowledge (K) May’s beliefs (B) May’s goals (G) Affordances of technology Coherency diagramInitiation phase 1 May possesses knowledge ofdidactic teaching strategies,i.e IRE episodes in thelessons. However, shepossesses limited knowledgeof collaborative learningteaching strategies.Implementationphase (part 1)1 May possesses knowledge ofdidactic teaching strategies,i.e IRE episodes in thelessons. However, shepossesses limited knowledgeof collaborative learningteaching strategies.1 May believes that enablingstudents to do well in theexamination is the primarytask of the teacher.2 May believes that herstudents are generally weakand are unable to articulatewell.3 May believes in strictclassroom management.4 May believes inteacher-centred approach inteaching.1 May’s goal is to completethe scheme of work(syllabus) on time.2 May’s goal is to create aquiet, disciplined andorderly class every lesson.1 May’s goal is to completethe scheme of work ontime.2 May’s goal is to create aquiet, disciplined andorderly class every lesson.There is a misalignmentbetween the affordancesof GS technology andMay’s KGB region.The perceivedincoherencies during theinitiation phase areenacted in this phase.The affordances of GStechnology are notleveraged effectively.Attributed poorimplementation totechnical glitches.Misalignment and nocoherency as shownin state 1.The perceived in theinitiation phase isenacted in theclassroom. No growth.Implementationphase (part 2)1 May learns somecollaborative learningstrategies via PD sessionsand self reflections.2 May is able to handletechnical glitches.1 May becomes lessteacher-centred.2 May is giving moreopportunities for students tospeak and articulate theirideas.1 May’s goal to usestudent’s priorknowledge as a bridge toteach new concepts.1 May leverages on GStechnology as a platformto draw students’ priorknowledge.2 May utilizes multimodalaffordance to allowstudents express theirideas.Due to a change ofteaching strategies,there are someleverages of GStechnology in state 3.Implementationphase (part 3)1 May has knowledge ofinterim examination resultsof her students.2 May realizes that she facestime constraints incompleting the curriculum.May believes that GStechnology is better suitedfor high ability students.Weaker students should betaught exam skills instead ofthinking skills.May’s goal is to allow moreof her weaker studentsto score better in testsand exams.May perceives that GStechnology may not besuitable for weakerstudents.There is a regression.White circle represents ‘KGB region’; Grey circle represents ‘Technology affordances’.IRE, Initiation-Response-Evaluation; GS, GroupScribbles; PD, professional development.© 2009 Blackwell Publishing Ltd

Integrating technology in the classroom 17Table 5. Summary of Lynn’s and May’s developmental trajectories.LynnInitiation phase Implementation phase Maturation phaseMayState 3 State 3 State 4Not attained yetState 1State 1 State 3?State 2White circle represents ‘KGB region’; Grey circle represents ‘Technology affordances’.classroom within a limited time frame. In a normalschool context, the equivalent support from schoolleaders, senior teachers, vendors and consultants canalso be given to trigger such development. We hope thatthe Coherency diagram is a generalizable mode that canbe used to analyse a teachers’ developmental trajectoryin any school context. From our studies, the Coherencydiagram points to the amount and type of supportrequired by the teacher; for example at states 1 and2, the teacher requires much more support to growprofessionally and use technology effectively in theclassroom.ConclusionIn this paper, we attempt to use the notion of Coherencydiagrams to analyse teachers’ developmental trajectoriesin integrating GS technology. Our resultsshow that the coherency between a teacher’s beliefs,goals and knowledge and the affordances of the technologyis the main key in leveraging the technologysuccessfully. The transition between each state of thecoherency diagrams is nonlinear, implying the importanceof ensuring high coherency right at the initiationstage. Support for the teacher, either from other teachersand/or researchers, remains an important factor indeveloping the teacher’s competency to leverage thetechnology successfully. The stability of the KGBregion further ensures smooth progressing of theteacher’s effective integration of technology in theclassroom.AcknowledgementsThis material is based on work supported by a grantfrom the National Research Foundation, Singapore. Wewish to thank SRI International for providing a licenseto use the GS software in Singapore, members of our GSteam for sharing their valuable insights and perspectiveswith us, and Allan Collins for proofreading this paper.We are grateful to Mayflower Primary School for collaboratingwith us on this research.© 2009 Blackwell Publishing Ltd

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