View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Aston Publications Explorer   The  Electronic  Journal  for  English  as  a  Second  Language     June  2011—Volume  15,  Number  1     Classrooms  as  Complex  Adaptive  Systems:  A  Relational  Model   Anne  Burns   Aston  University,  Birmingham,  UK,  and  University  of  New  South  Wales,  Australia   <a.c.burns@aston.ac.uk>   <nne.burns@unsw.edu.au>     John  S.  Knox   Department  of  Linguistics,  Macquarie  University,  Sydney,  Australia   <john.knox@mq.edu.au>     Abstract   In  this  article,  we  describe  and  model  the  language  classroom  as  a   complex  adaptive  system  (see  Logan  &  Schumann,  2005).  We  argue  that   linear,  categorical  descriptions  of  classroom  processes  and  interactions   do  not  sufficiently  explain  the  complex  nature  of  classrooms,  and  cannot   account  for  how  classroom  change  occurs  (or  does  not  occur),  over  time.   A  relational  model  of  classrooms  is  proposed  which  focuses  on  the   relations  between  different  elements  (physical,  environmental,  cognitive,   social)  in  the  classroom  and  on  how  their  interaction  is  crucial  in   understanding  and  describing  classroom  action.       Introduction   Diane  Larsen-­‐Freeman’s  seminal  paper  (1997)  on  parallels  in  chaos/complexity  theory   and  the  study  of  second  language  acquisition  engendered  new  directions  in  thinking   about  language  learning  processes  and  caused  a  re-­‐evaluation  among  second  language   acquisition  researchers  of  some  of  the  basic  assumptions  in  the  field  (e.g.,  de  Bot,  Lowie   &  Verspoor,  2005a,  2005b;  Ellis  &  Larsen-­‐Freeman,  2006;  Herdiner  &  Jessner,  2002;   Larsen-­‐Freeman  &  Cameron,  2007).  Larsen-­‐Freeman  identified  a  number  of  areas   where  it  might  be  profitable  to  reconceptualize  some  of  the  essential  questions  raised  in   SLA  and  to  re-­‐envisage  them  from  the  perspectives  offered  through  chaos  and  complex   systems  theory  in  the  social  sciences.  More  recently,  de  Bot  et  al.  (2005a,  2005b)  have   put  dynamic  systems  theory  to  productive  use  to  explain  instability  and  variability  in   TESL-EJ 15.1, June 2011 Burns & Knox page 1 the  development  of  language  knowledge,  according  to  the  nature  of  the  interaction  of   individual  factors  (such  as  age,  attitude,  motivation,  intelligence,  early  learning   experiences),  and  argue  that  it  is  ‘impossible  to  extract  and  measure  single  factors  that   contribute  to  SLA  because  they  all  interact’  (2005a,  p.  76).     Schneider  (1997,  2001)  utilizes  chaos  theory  to  explain  dialect  variability  and  change,   arguing  that  the  properties  of  chaotic  systems  help  to  explain  the  ‘alternation  between   areas  or  periods  of  relative  stability  and  areas  or  periods  of  “chaotic  variability”’  (2001)   as  well  as  the  unpredictability  and  aperiodicity  of  language  acquisition.  Schneider   builds  on  earlier  work  by  Bernadez  (1994),  Lightfoot  (1991)  and  Wildgen  (1982)   among  others.  Looking  at  language  learning  from  the  perspective  of  human  language   development,  Smith,  Brighton  &  Kirby  (2003)  argue  that  Chomskyan  innatist  and   adaptionist  models  of  language  fail  to  explain  the  development  of  compositionality,   which  they  see  as  a  fundamental  structural  property  of  language  acquisition  (cf.  Ke  &   Holland,  2006).  A  theory  of  language  evolution,  they  argue,  requires  an  understanding   of  the  complex  adaptive  interactions  of  biological  evolution,  learning  and  culture.  Their   Iterated  Learning  Model  seeks  to  demonstrate  that  compositional  language  emerges   from  a  “bottleneck”  in  cultural  transmission,  which  leads  to  an  adaptive  breakthrough   in  language  development.   The  related  theoretical  approaches  underpinning  the  studies  on  language  learning  and   language  evolution  cited  above  share  a  number  of  features,  such  as  context-­‐sensitivity,   interrelatedness  among  elements,  and  non-­‐linearity,  and  a  number  of  discussion  papers   which  consider  the  relevance  of  such  theories  to  language  education  more  broadly  have   also  appeared  (e.g.,  Hill,  2003;  Hodge,  2003;  Mallows,  2002).  Yet  despite  these   developments,  very  few  studies  have  applied  such  theoretical  perspectives  to  analysing   classrooms  (though  see  Finch,  2001;  Lemke  &  Sabelli,  2006;  Senior,  2006;  van  Lier,   1996).  In  this  paper,  we  present  a  relational  model  which  we  have  developed  in  an   attempt  to  map  the  complexity  of  two  language  classrooms  and  to  account  for  the   changes  that  we  have  observed  in  the  teachers’  classroom  practice,  and  their  thinking   about  their  practice  (cf.  Feryok,  2010).  This  model  conceptualizes  the  classroom  not  as   a  machine  where  inputs  are  processed  and  outputs  generated,  not  as  a  space  where   activity  takes  place,  and  not  as  a  an  activity,  but  as  a  convergence  of  different  elements   which  stretch  beyond  the  temporal  and  spatial  location  of  a  given  classroom,  and  which   combine  in  dynamic  relationships.   In  presenting  this  model  we  build  on  a  number  of  areas  of  research  within  Applied   Linguistics,  and  conceptualize  classrooms  as  complex  adaptive  systems  (see  Logan  &   Schumann,  2005),  which  comprise  ‘multiple  agents  dynamically  interacting  in   fluctuating  and  combinatory  ways’  (Rogers  et  al.,  2005,  p.  3).   Our  aim  is  to  use  these  concepts  as  a  metaphor  (Bowers,  1990;  Kramsch,  2002a;   Larsen-­‐Freeman,  1997;  Larsen-­‐Freeman  &  Cameron,  2007)  to  better  understand   classrooms,  and  in  particular  the  conditions  under  which  classroom  processes  might   become  sensitive  to  changes  in  a  teacher’s  thinking.  The  ultimate  aim  of  such  an   approach  will  be  to  work  towards  a  better  understanding  of  how  teacher-­‐educators   TESL-EJ 15.1, June 2011 Burns & Knox page 2 might  bring  about  changes  in  teachers’  classroom  practice,  and  a  positive  change  in   classrooms  overall.   In  the  following  section,  we  describe  the  study  from  which  the  model  presented  in  this   paper  developed.  Following  that,  we  provide  a  discussion  of  relevant  research  and   theory.  We  then  look  at  data  from  the  study,  and  outline  the  classroom  model.  After   considering  the  limitations  of  the  model,  we  finally  discuss  its  implications  for  research   on  classrooms  more  broadly.   The  study   Our  focus  in  this  article  is  less  on  the  study  we  describe  in  this  section  (which  has  been   reported  in  Burns  &  Knox,  2005),  and  more  on  the  relational  model  we  have  developed   in  our  reflection  on  its  implications.  Nevertheless,  data  from  the  study  are  presented  in   the  section  on  ‘Modeling  the  dynamism  of  the  classroom’    in  order  to  support  and   illustrate  our  contentions.  In  this  section,  we  aim  only  to  provide  sufficient  detail  about   the  study  to  illustrate  how  the  research  became  the  basis  for  our  model.   We  researched  the  classrooms  of  two  teachers,  who  had  completed  a  unit  in  a  Master  of   Applied  Linguistics  program.  We  co-­‐taught  the  unit,  which  focused  on  systemic   functional  linguistics  (SFL)  and  its  applications  to  the  language  classroom  over  a   semester  consisting  of  26  hours  of  on-­‐campus  classes.  The  students  of  the  teachers  we   observed  were  mostly  young  adult  learners  studying  in  intensive  university-­‐based  pre-­‐ sessional  English  classes.  The  aim  of  the  research  was  to  explore  i)  how  and  to  what   extent  the  theoretical  concepts  of  SFL  impacted  on  the  teachers’  knowledge  about   language  (KAL);  and  ii)  what  impact  this  knowledge  had  on  their  classroom   practices.    The  observations  and  interviews  took  place  six  months  after  the  teachers   had  completed  the  unit.   Procedures   The  main  procedures  used  in  the  study  were  as  follows:   1. Before  the  first  observation  the  teachers  were  asked  to  write  a  brief  description   of  their  class.  We  also  asked  them  to  describe  their  greatest  challenge  in  teaching   grammar.   2. Four  lessons  with  each  teacher  were  observed  and  audio-­‐recorded  by  the   researchers  over  a  period  of  six  weeks.  In  total  eight  hours  of  teaching  by  each   teacher  were  observed.   3. Immediately  before  each  lesson,  the  teachers  were  interviewed  briefly  and  asked   to  describe  their  overall  goals  and  any  other  details  about  the  lesson  they  wished   to  clarify.  All  interviews  for  the  study  were  audio-­‐recorded.   4. Immediately  after  each  lesson,  the  teachers  were  interviewed  for  up  to  30   minutes  to  obtain  their  immediate  reactions  to  the  lesson.   5. Approximately  five  days  after  the  first  observation,  the  researchers  conducted   an  hour-­‐long  interview  with  each  teacher.  A  second  long  interview  (90  minutes)   was  held  approximately  one  month  after  the  subsequent  lesson  observations,   TESL-EJ 15.1, June 2011 Burns & Knox page 3 and  transcripts  were  supplied  to  the  teachers  in  advance.  Parts  of  the  transcripts   were  used  in  a  stimulated  recall  procedure  during  the  interviews,  where  the   teachers  were  asked  to  comment  on  specific  teaching  sequences.   To  analyse  the  data  we  scanned  the  classroom  and  interview  transcripts  using  a   continual  iterative  process  to  develop  major  themes  and  categories  (cf.  Bogden  &   Biklen,  1998).   Findings   We  focus  here  on  the  themes  that  arose  from  our  observations  of  the  classrooms,  the   classroom  transcripts,  and  the  interview  data  where  the  teachers  explicated  their   practices  and  the  factors  that  influenced  and  mediated  them.  Our  initial  analysis  led  us   to  the  typology  in  Table  1.   It  was  already  obvious  from  the  typology  in  Table  1  that  to  gain  a  full  appreciation  of   the  nature  and  processes  in  the  teachers’  KAL,  it  was  not  enough  to  consider   pedagogical  practices  in  isolation.  As  the  data  analysis  proceeded  it  became  apparent   also  that  the  static  and  fixed  categories  of  this  typology  could  not  adequately  reflect  the   (re-­‐)emergent  and  shifting  nature  of  the  teachers’  KAL  across  the  four  lesson   observations.  Their  understandings  of  the  theoretical  concepts  of  SFL  and  how  these   related  to  their  teaching  were  in  a  state  of  flux,  and  this  instability  was  clearly  related  to   changes  we  were  observing  in  their  pedagogical  practices.  In  addition,  the  presence  of   researchers  (who  were  previously  their  teachers)  in  their  classrooms,  together  with  the   reflexive  and  conversational  nature  of  the  interviews  were  external  factors  that  were   inevitably  causing  perturbations  and  pushing  existing  beliefs  and  practices  into   disequilibrium.     Table  1:  Typology  of  factors  influencing  classroom  practices     Institutional   Pedagogical   Personal   Physical    exam  pressures      previous  lesson(s)      language  learning    heat     experiences      time  tabling  and  time    student  needs      physical  size  and   pressures      student  skills/language   previous  training  as   layout  of  class     (language)  teacher      changes  of  rooms      course  aims  and   ability     syllabus    newness  of  student    previous  teaching    student  movement  in   requirements     experiences  of  tertiary   experience     and  out  of  class     study      required  materials      existing  practices      presence  of    course  focus  on    online  classroom    theories  of  teaching     researchers  in   tertiary  entry/study     decision-­‐making      theories  of  learning     classroom      time  available  for    student  age      recent  study  (of  SFL)     preparation      teacher-­‐student    current  study   relationships     commitments      focus  of  the  research    personal  lives  and   project     relationships     (source:  Burns  &  Knox,  2005,  p.  254)     TESL-EJ 15.1, June 2011 Burns & Knox page 4 In  order  to  depict  such  dynamism  we  recognised  progressively  that  we  needed  to  be   able  to  map  interrelatedness,  fluidity  and  unpredictability,  rather  than  construct   distinct,  separate  and  fixed  categories.  In  other  words,  we  needed  somehow  to  capture   this  kaleidoscopic  process  holistically  rather  than  in  parts.  As  we  did  so,  we  drew  on   theoretical  concepts  from  a  number  of  strands  of  research  in  Applied  Linguistics,  which   we  outline  in  the  following  section.     Research  perspectives  on  classrooms   We  began  the  research  study  outlined  above  with  a  focus  on  teachers’  KAL  and  the   impact  of  changes  in  KAL  on  classroom  practices.  Initially,  our  approach  was  informed   primarily  by  research  into  teacher  cognition,  and  to  a  lesser  extent  research  into   classroom  discourse.   Studies  of  language  teacher  cognition  focus  on  the  relationship  between  teachers’   practices  and  the  rationale  informing  or  underlying  this  practice  (see  Borg,  2003,   2006).  It  is  a  common  assumption  that  teachers  must  be  observed  in  action  in  the   classroom  in  order  for  researchers  to  make  valid  claims  regarding  their  decision-­‐ making,  and  many  studies  bring  the  social  context  of  teachers’  practice  into   explanations  of  decision-­‐making  (e.g.,  Burns,  1992,  1996;  Burns  &  Knox,  2005;  Breen  et   al.,  2001;  Freeman  &  Johnson,  1998;  Johnson,  1996;  Richards  &  Pennington,  1998;   Woods,  1996).   Studies  which  have  focused  explicitly  on  the  relationship  between  teacher  cognition   and  teachers’  classroom  practice  have  collectively  shown  that  ‘language  teachers’   classroom  practices  are  shaped  by  a  wide  range  of  interacting  and  often  conflicting   factors’  (Borg  2003,  p.  91).  Some  scholars  have  concluded  that  teachers’  cognition   studies  are  ‘unreliable’  (e.g.,  Basturkmen,  Loewen  &  Ellis,  2004;  Tabachnick  &  Zeichner,   1986)  as  teachers’  beliefs  and  practices  often  appear  to  be  contradictory.  However,  if   classrooms  are  viewed  as  complex  adaptive  systems,  it  can  be  argued  that  contradictory   research  findings  are  not  so  much  unreliable  as  reflective  of  the  fact  that  teachers’   understandings  of  classrooms  and  their  own  actions  are  both  context-­‐dependent,  and   subject  to  continual  re-­‐organisation  in  interaction  with  their  environment  (cf.  Borg,   2006).   Our  project  was  also  informed  by  research  on  classroom  discourse,  which  has  become   well-­‐established  and  generated  a  rich  body  of  empirical  work  (e.g.,  Breen,  2001a;   Cazden,  2001;  Chaudron,  1988;  Christie,  1999;  Hall  &  Verplaetse,  2000;  Mehan,  1979;   Pica,  1987;  Sinclair  &  Coulthard,  1975;  van  Lier,  2001).  Some  of  this  research  has   connected  with  the  work  of  sociologists  such  as  Bernstein  and  Bourdieu,  describing   ways  in  which  discursive  patterns  of  action  and  interaction  and  the  social  roles  of   teacher  and  learner  are  both  reflective  and  constitutive  of  the  larger  structure  of  the   curriculum,  and  social  structures  where  patterns  of  wealth  and  social  class  are   systematically  related  to  educational  resources  and  opportunities  (e.g.,  Breen,  2001a;   Christie,  1999,  2002;  Lin,  2001;  O’Halloran,  2004;  van  Lier,  1996).   TESL-EJ 15.1, June 2011 Burns & Knox page 5 As  we  observed  the  changes  taking  place  in  the  two  teachers’  classrooms,  it  became   increasingly  apparent  that  these  classrooms  were  not  merely  the  context  of  teacher   practice  (cognitive  and  discursive),  but  were  themselves  the  phenomena  in  which  the   teachers  were  playing  a  part.  Existing  research  findings  of  connections  between   teachers’  decision-­‐making  and  social  context,  and  between  discursive  action  and   broader  social  structures,  were  influential  in  our  decision  to  draw  increasingly  on   classroom-­‐based  research  in  applied  linguistics  which  has  taken  a  social  (and  later  an   ‘ecological’)  turn.   Much  of  this  socially-­‐oriented  classroom-­‐based  research  is  strongly  grounded  in  the   discursive  tradition  described  above.  Breen’s  (2001b)  paper  (first  published  in  1985)   draws  on  the  work  of  Malinowski  to  describe  classrooms  as  ‘coral  gardens’  –  the   language  class  ‘is  an  arena  of  subjective  and  intersubjective  realities  which  are  worked   out,  changed,  and  maintained.  …  [These  activities]  continually  specify  and  mould  the   activities  of  teaching  and  learning’  (Breen,  2001b,  p.  128).  Work  by  scholars  who  have   taken  a  social  and  cultural  view  of  classrooms  (e.g.,  Canagarajah,  2001;  Holliday,  1994;   Kramsch,  1993)  shows  how  language  classrooms  can  provide  a  ‘third  space’  for   language  learners  (and  teachers)  to  explore  and  negotiate  their  linguistic  and  social   identities  (see  also  Coleman,  1996;  Gieve  &  Miller  2006;  Senior,  2006),  and  has  been   paralleled  by  work  in  sociocultural  theory,  which  takes  a  Vygotskian  perspective  on   learning  and  teaching  (e.g.,  Lantolf,  2000;  Lantolf  &  Thorne,  2006).   Researchers  who  approach  classrooms  as  multifaceted  and  organic  sites  of  social   activity  draw  on  a  range  of  paradigms,  including  those  already  discussed,  and  take  what   have  become  known  as  ecological  perspectives  on  classrooms  (see  Kramsch,  2002b;  van   Lier,  2000,  2004).  Such  researchers  find:   [I]n  the  notion  of  “ecology”  a  rallying  framework  to  voice  the   contradictions,  the  unpredictabilities,  and  paradoxes  that  underlie  even   the  most  respectable  research  in  language  development.  By  embracing  an   ecological  perspective  they  do  not  intend  to  replace  existing  metaphors.   Instead,  …  they  seek  new  ways  of  conceptualizing  the  nature  of  the   relationship  between  the  dancer  and  the  dance.  (Kramsch,  2002,  pp.  4-­‐5)   We  found  the  notions  of  embracing  contradiction  and  unpredictability,  of  providing  a   complementary  metaphor,  and  of  reconceptualizing  the  relations  in  classrooms  to  be   consistent  with  what  we  were  observing  in  our  own  research,  and  also  consistent  with   our  growing  interest  in  complex  adaptive  systems,  and  the  potential  such  a  theoretical   approach  appeared  to  provide  in  describing  the  process  of  change  in  the  classrooms  of   the  two  teachers.   In  addition  to  the  research  perspectives  discussed  above,  then,  the  model  we  present  in   this  paper  draws  on  the  notion  of  complex  adaptive  systems,  which  has  been  applied   increasingly  in  the  field  of  Applied  Linguistics  (see  ‘Introduction’  above).  The  features  of   complex  adaptive  systems  that  we  focus  on  here  are  interaction,  emergence,  non-­‐ linearity,  and  nestedness.   TESL-EJ 15.1, June 2011 Burns & Knox page 6 Complex  adaptive  systems  (language  classrooms  in  the  case  of  this  paper)  consist  of   multiple  variables  that  are  constantly  in  interaction.  As  each  variable  ‘affects  all  the   other  variables  contained  in  the  system  and  thus  also  affects  itself’  (van  Geert,  1994,  p.   50),  the  interaction  of  the  variables  in  the  system  produces  an  inherent  potential  for   instability  and  also,  inevitably,  change  over  time.  Thus,  it  is  unproductive  to  isolate   individual  variables  as  a  way  of  describing  a  system.  Rather,  the  trajectory  of  complex   adaptive  systems  can  be  best  mapped  by  the  description  of  emergent  patterns  of   behaviour.   Emergent  behavior  is  behaviour  in  a  system  which  comes  as  a  result  of  the  interactions   between  different  elements  of  the  system,  and  which  cannot  be  explained  by  looking  at   the  elements,  but  must  take  into  account  their  relations  and  interaction  in  situ  (see  Ellis   &  Larsen-­‐Freeman,  2006).  Thus,  the  interactions  between  elements  in  a  complex   adaptive  system  emerge  as  ‘higher-­‐order’  patterns  of  behaviour  in  a  ‘larger’  system  that   operates  on  a  different  scale  (see  Lemke,  2000,  2002).  Emergent  behaviour  cannot  be   predicted  by  looking  at  what  parts  of  a  system  do  in  isolation,  nor  by  identifying  cause   and  effect  relationships  between  variables.     Another  feature  of  complex  adaptive  systems  is  that  they  develop  in  a  dialectic  manner   that  is  sensitive  to  initial  conditions,  and  changes  in  systems  are  non-­linear  and   aperiodic.  While  there  may  be  periods  of  relative  stability,  there  will  also  be  times  when   the  system  becomes  disturbed  by  the  appearance  of  new,  typically  external,  influences,   which  can  push  the  system  in  various  unpredictable  directions.   Finally,  complex  adaptive  systems  are  nested.  That  is,  they  are  interconnected  with   other  larger  macro-­‐systems  systems  or  smaller  subsystems  (Folke  &  Folke,  1992).  The   various  systems  are  themselves  dynamic  and  are  in  continuous  interaction  with  each   other.  For  example,  classrooms  are  subsystems  within  a  whole  school  system,  which  in   turn  is  a  subsystem  of  a  state  or  national  educational  system.  The  educational,  social,   political,  and  physical  variables  within  a  classroom  interconnect  with  those  in  ‘higher’   (social-­‐semiotic)  and  ‘lower’  (e.g.,  chemical,  physical,  and  biological)  systems  and   interact  with  them  (Lemke,  2000,  2002).   We  found  that  viewing  classrooms  as  complex  adaptive  systems  was  at  once  consistent   with  the  research  in  Applied  Linguistics  on  which  we  had  drawn,  and  helpful  in   furthering  our  understanding  of  classrooms  as  relational.  In  closing  this  section,  we   adapt  a  description  of  dynamic  systems  theory  (‘the  science  of  the  development  of   complex  systems  over  time’  –  De  Bot  et  al.,  2005a,  p.  116)  which  resonates  with  our   own  perspective  on  classrooms.  Table  2  describes  classrooms  as  complex  adaptive   systems.       TESL-EJ 15.1, June 2011 Burns & Knox page 7    Table  2:  Classrooms  as  complex  adaptive  systems   de  Bot,  Lowie  &  Verspoor  (2005a)   Burns  &  Knox  (2005)   Complex  systems  are  sets  of  interacting   variables.   Classrooms  are  sets  of  interacting  variables.   In  many  complex  systems,  the  outcome  of   development  over  time  cannot  be  predicted  …   because  the  variables  that  interact  keep   changing  over  time.   In  many  classrooms,  the  outcome  of   development  over  time  cannot  be  predicted  …   because  the  variables  that  interact  keep   changing  over  time.   Dynamic  systems  are  always  part  of  another   system,  going  from  submolecular  particles  to   the  universe.   Classrooms  are  always  part  of  another  system,   going  from  classroom,  to  institution,  to  an   entire  society.   As  they  develop  over  time,  dynamic   subsystems  appear  to  settle  in  specific  states,   which  are  preferred  but  unpredictable,  so-­‐ called  ‘attractor  states.’   As  they  develop  over  time,  classrooms  appear   to  settle  in  specific  patterns  of  practice,  which   are  preferred  but  unpredictable,  so-­‐  called   ‘typical  classes.‘   Systems  develop  through  iterations  of  simple   procedures  that  are  applied  over  and  over   again,  with  the  output  of  the  preceding   iteration  as  the  input  of  the  next.   Classrooms  develop  through  iterations  of   simple  procedures  that  are  applied  over  and   over  again,  with  the  output  of  preceding   iterations  as  the  input  of  latter  ones.   The  development  of  a  dynamic  system   appears  to  be  highly  dependent  on  its   beginning  state.  Minor  differences  at  the   beginning  can  have  dramatic  consequences  in   the  long  run.  …   The  development  of  a  classroom  appears  to  be   highly  dependent  on  its  beginning  state.  Minor   differences  at  the  beginning  can  have   dramatic  consequences  in  the  long  run.  …   In  dynamic  systems,  changes  in  one  variable   In  classrooms,  changes  in  one  variable  have  an   have  an  impact  on  all  other  variables  that  are   impact  on  all  other  variables  that  are  part  of   part  of  the  system:  systems  are  fully   the  class:  classrooms  are  fully  interconnected.   interconnected.   In  natural  systems,  development  is  dependent   on  resources:  …  all  natural  systems  will  tend   to  entropy  when  no  additional  energy  is   added  to  the  system.   In  classrooms,  development  is  dependent  on   resources:  …  all  classrooms  will  tend  to   entropy  when  no  additional  energy  is  added   to  the  class.   Systems  develop  through  interaction  with   their  environment  and  through  internal  self-­‐ reorganisation.   Classrooms  develop  through  interaction  with   their  environment  and  through  internal  self-­‐ reorganisation.   Because  systems  are  constantly  in  flow,  they   will  show  variation,  which  makes  them   sensitive  to  specific  input  at  a  given  point  in   time  and  some  other  input  at  another  point  in   time.   Because  classrooms  are  constantly  in  flow,   they  will  show  variation,  which  makes  them   sensitive  to  specific  input  at  a  given  point  in   time  and  some  other  input  at  another  point  in   time.     TESL-EJ 15.1, June 2011 Burns & Knox page 8 Modelling  the  dynamism  of  the  classroom   Throughout  the  process  of  our  research  project,  we  were  faced  with  a  number  of   factors,  some  predictable,  some  unexpected,  some  difficult  to  account  for.  In  our  first   observation  with  each  teacher  (coincidentally  the  last  lesson  in  the  first  of  two  courses   each  taught  respectively  during  the  research),  neither  applied  any  of  the  principles  of   SFL  in  their  grammar  instruction.  In  later  lessons,  they  did  so  increasingly.  There  were  a   number  of  factors  related  to  the  process  of  change  in  teaching  approaches  we  observed.   For  one  of  the  teachers,  the  difference  in  the  syllabus  of  the  courses  she  taught  was  an   important  factor:   T:                          We  had  like  a  plan  already  designed  for  us  [in  the  first  course].  …   On  that  plan  it  says  whatever  we  have  to  teach  on  each  day  …   I:                              So  you  didn’t  really  have  a  choice?   T:                          So  in  this  case,  I  really  didn’t  have  a  choice,  no.  In  the  other   [course],  yeah  because  it’s  a  general  English  course,  …  we  have  like  a   framework  but  it’s  a  very  open  framework.  So  you  can  teach  things  that   are  included  there  but  there  are  so  many  things  that  you  can  decide  when   to  do  it,  why  to  do  it  and  how  to  do  it.  [1]     Another  factor  was  our  own  presence  in  their  classrooms,  which  in  various  ways   ‘tipped  the  scales’  in  favour  of  implementing  change.  In  a  post-­‐lesson  interview,  one  of   the  teachers  commented:  ‘because  I  had  to  present  a  lesson  to  you  I  put  in  the  work  that   I  probably  otherwise  wouldn’t  put  in  to  quite  this  degree.’  Similarly,  in  the  final   interview,  the  other  teacher  responded  to  a  question  on  her  participation  in  the   research:   I  think  that  it  helped  me  become  more  …  conscious  about  or  more   confident  with  this  new  approach,  because  as  I  said  to  you,  at  the   beginning  I  felt  like  I  really  did  not  know  how  to  put  this  into  practice  …   so  it  helped  me  see  how  I  could  put  that  into  practice  ….   Simultaneously,  many  other  factors  which  were  observed  by  us  and  commented  on  by   the  teachers  were  related  to  the  changes  we  observed  (see  Table  1).  We  have   documented  the  process  of  change  over  time  for  these  two  teachers  elsewhere  (Burns  &   Knox,  2005).  Here,  we  look  at  an  extract  from  the  last  observed  class  of  one  of  the   teachers.  The  first  lesson  we  observed  (the  last  of  that  particular  course)  had  had  a   grammar  focus  on  phrasal  verbs  and  the  possible  combinations  between  certain  verbs   and  prepositions.  Her  second  lesson  (with  a  new  class,  teaching  a  new  course)  looked  at   cohesion  by  analysing  a  text  written  by  one  of  the  students  in  the  class.  In  the  third   lesson,  she  examined  conjunction  and  signposting  in  a  number  of  model  texts  in   response  to  problems  she  had  identified  in  the  students’  writing.  In  the  final  lesson,  the   focus  on  grammar  in  relation  to  discourse  which  had  been  established  in  the  second   and  third  lessons  continued.   T:                          Okay.  All  right.  So  what  I’ve  done  at  the  back  of  this  sheet  the   main  uses  of  modals.  Have  you  got  that  page?  Flip  it  over…Martin  have   TESL-EJ 15.1, June 2011 Burns & Knox page 9 you  got  a  copy?  You’ve  got,  oh  no,  you’re  copying  out  your  essay.  That’s   alright.   S:                          [inaudible  sentence]   T:                          Alright.  Um  okay  so  it  gives  you  the  three  possible  sort  of,  three   general  times.  Hi  Ivy…ah…right…I  can  tell  everybody’s  getting  tired.  They   are  coming  to  class  more  and  more  slowly  …  Okay  we’ll  just  go  through   the  modal  verbs  very  quickly.  Actually  flip  that,  yeah  that  side  …  So  what   do  we  mean  by  attitude  …  ’cos  it  says  here  ‘attitude  to  information.’  What   do  we  mean  by  attitude?   [7  secs]   S:                          [inaudible  sentence]   T:                          A  which?  Opinion  did  you  say?  Sort  of  yes  it’s  a  bit  like  opinion   but  it’s  it’s  what,  how  you  feel  about  how  you  react  towards  opinion  …   Okay  so  when  you’re  giving  information  you  might  use  modals  to  show   how  certain  you  are  that  your  information  is  true,  so  and  these  are   comments  that  I’ve  put  in  here  so  you  must  be  the  only  one  who  did  their   homework  or  …  so  ‘must’  gives  the  …  is  anyone  listening?  Ethel?  …   Concentrate.  So  it’s  actually  very,  why  do  you  think  we’re  doing  so  much   on  modals  right  now?  [inaudible  word]   [7  secs]   T:                          Why  would  we  be  doing,  what’s  the  point  of  doing  all  this  work   on  modals?  …  It’s  not  just  to  fill  in  the  time.  It’s  not  only  because  Anne  and   John  are  here  …  Okay  think  back  to  your  first  draft  …  of  your  essay.  What   was  one  of  the  things  I  wrote  a  lot  on  your  first  draft?   [10  secs]   T:                          Modals  modals  modals  …  because  in  academic  writing  you  often   can’t  say  something  is  100%  so.  So  often  when  we’re  giving  information   even  when  we’re  giving  opinion  we  have  to  use  modals.  We  have  to,  and   sometimes  it’s  it’s  in  the  verb  form  like  the  ‘would’  the  ‘could’  the  ‘might.’   Sometimes  it’s  by  adding  ‘perhaps’  or  ‘possibly’  because  usually  you  know   you  can’t  say  ‘television  is  always  bad  for  children’  …  you  know,  it  can  be,   you  know  it  could  have  bad  effects  on  children  because  you  can’t  always   say  100%.  So  so  …  Good  afternoon,  May.  So  actually  we’re  looking  at  the   back  of  that  sheet  for  the  moment.  So  so  this  is  why  we’re  doing  modals.   Because  when  we’re  giving  information  or  opinions  we  often  put  it  with   modals  to  show  that  there  are  other  possibilities  as  well.  Okay  then  there   is  intention.  So  it  tells  us,  unlike  all  the  other  verbs,  the  other  verbs  tell  us   if  things  are  in  the  past  or  if  things  are  in  the  future  or  if  things  are   happening  now  or  if  things  …  ah!  I  will  lock  the  classroom  door.  People   won’t  be  able  to  come  in  anymore.   TESL-EJ 15.1, June 2011 Burns & Knox page 10 S:                          I’m  sorry  I’m  late.   T:                          Okay.     This  extract  gives  an  indication  of  the  language  focus  of  the  lesson,  and  also  of  the   nature  of  the  interaction  throughout  this  lesson.  The  students  did  not  appear  to  be   responsive  to  the  teacher  during  this  lesson,  even  though  the  teacher  explained  to  us   later  that  the  language  focus  was  chosen:   …  because  of  the  exam  essay  plus  the  major  assignment  that  they’ve  done   that  there  really  needs  to  be  more  kind  of  modulation  in  their  language  …   and  I  think  it’s  one  of  the  major  areas  of  improvement  as  they’re  going   into  this  business  course,  the  next  course  up.   In  our  observation  notes,  one  of  us  wrote:  ‘silent  resistance  or  subversion  is  hanging  in   the  air.’  When  we  interviewed  the  teacher  immediately  after  the  lesson,  she  identified  a   number  of  factors  relevant  to  the  students’  attitude  towards  the  lesson,  including  their   age,  the  fact  that  they  were  now  near  the  end  of  the  course,  and  an  incident  between  her   and  a  student  in  a  previous  class  where  she  had  confronted  the  student  about   plagiarism  in  an  assignment,  a  confrontation  which  resulted  in  a  significant  conflict  and   disrupted  the  entire  class.  Factors  such  as  cultural  differences  in  teacher  and  learner   roles,  and  different  understandings  of  what  constitutes  plagiarism,  were  obviously   relevant  to  that  conflict,  and  also  therefore  to  the  extract  above,  and  were  in  fact   discussed  in  this  context  in  the  post-­‐lesson  interview.   Thus,  a  combination  of  factors  meant  that  the  teacher’s  careful  preparation  and   planning  were  negated  by  the  students’  agendas,  and  the  lack  of  responsiveness  led  to  a   high  level  of  teacher  talk  as  student  responses  were  very  difficult  to  elicit.  When  asked   how  she  felt  about  the  lesson,  she  responded:   T:                      Flat  really!  [laughs]  Um  …  just  I  mean  a  sense  of  disappointment   that  I  couldn’t  galvanise  them  more  but  yeah  um  …  I  just  didn’t  feel   frightfully  fresh  today  so  it  was  just   I:                          one  of  those  days   T:                      hard  to  yeah  yeah  and  it’s  an  awkward  time  like  because  they’ve   got  all  these  things  coming  up,  they’re  really  preoccupied  with  that  too.     This  lesson  unfolded  according  to  the  interaction  among  a  number  of  factors,  including   but  not  limited  to:   • The  syllabus  (embodying  institutional  expectations  of  what  was  to  be  learned   and  taught)   • The  materials  the  teacher  had  developed  (in  response  to  the  learners’  needs)   • The  agendas  of  the  teacher  (e.g.,  preparing  the  students  for  assessment  and  their   next  course,  satisfying  the  researchers)   TESL-EJ 15.1, June 2011 Burns & Knox page 11 • The  agendas  of  the  students  (e.g.,  possibly  showing  displeasure  with  the  teacher,   and/or  solidarity  with  the  student  who  had  been  involved  in  the  conflict  in  the   previous  lesson)   • The  presence  of  the  researchers.   The  challenge  we  faced  was  to  integrate  these  different  factors  into  something  more   coherent  and  explanatory  than  Table  1.  That  is,  what  we  observed  was  not  something   that  could  be  explained  simply  by  listing  more  and  more  ‘inputs’  to  account  for  an   ‘output.’  The  social  action  we  witnessed  emerged,  in  real  time,  from  the  dynamic   relations  between  factors  in  the  immediate  temporal  and  spatial  environment  (e.g.,  the   researchers,  the  students,  the  materials),  and  as  part  of  a  longer  term  process  in  the   trajectories  of  the  students,  teacher  and  researchers  as  individuals  with  institutional,   cultural,  and  social  identities  (incorporating,  for  example,  the  evolving  demands  of  the   curriculum,  understandings  of  language,  and  experiences  of  teaching  and  learning  in   different  social  and  institutional  contexts).  In  addition  to  these  factors,  the  physical   environment  (such  as  the  size  and  layout  of  the  classroom,  light,  heat)  had  been   repeatedly  observed  by  us  and  mentioned  by  the  teachers  as  impacting  on  what  took   place  during  lessons.   In  order  to  capture  this  relational  perspective  on  classroom  action,  we  wanted  to   construct  a  model  by  which  we  could  approach  the  classrooms  we  observed  as   confluences  of  elements  and  processes.  We  viewed  the  classroom  not  as  a  ‘machine’   where  these  various  elements  are  processed,  but  more  as  an  ‘organism’  characterised   by  emergent  patterns  of  behaviour  which  are  brought  into  existence  by  the  dynamic   relationship  between  such  elements  over  time  (cf.  Kramsch,  2002a).  Our  attempt  to   visually  represent  this  way  of  understanding  and  describing  the  classrooms  we   observed  is  shown  in  Figure  1.  The  arrows  indicate  that  all  elements  are  dynamic,  and   that  these  elements  of  the  system  can  only  be  properly  understood  in  terms  of  their   interactions  and  relations  with  other  elements  in  and  beyond  the  system,  and  not  in   isolation.  That  is,  the  model  is  relational.   TESL-EJ 15.1, June 2011 Burns & Knox page 12    Figure  1:  Classroom  as  a  complex  adaptive  system   In  this  model,  the  classroom  is  seen  neither  as  a  space  nor  an  activity,  but  as  a   convergence  of  a  number  of  crucial  elements  which  combine  in  multiple,  dynamic,   context-­‐specific  relationships.  What  is  captured  in  this  particular  description  is  what   came  into  focus  through  the  lens  of  our  particular  research  methodology,  our  questions,   and  the  classrooms  we  observed.  We  would  expect  that  studies  of  other  classrooms   may  identify  different  elements  combining  in  different  ways.  That  is,  while  some   consistency  between  classrooms  is  always  to  be  expected,  there  will  also  be  individual   variation  between  different  classrooms,  and  in  the  same  classroom  over  time:  we  are   not  claiming  that  these  factors  (nor  this  combination  of  factors)  will  generalise  to  every   classroom.  Thus,  the  elements  in  this  model  are  not  monolithic,  but  will  be   (re)constituted  by  the  particular  constraints  and  variations  in  context  at  any  given  time.   In  this  sense  our  model  is  in  line  with  Borg’s  (2006,  p.  275)  argument:   The  elements  which  constitute  these  realities  are  potentially  many,  inside   the  classroom,  the  school  and  beyond;  some  will  be  temporary  (e.g.   excessive  heat  on  a  particular  day),  others  more  permanent  (e.g.   institutional  policy).   Shifting  the  focus  of  our  model  from  the  classroom  to  the  teacher,  we  viewed  the   teachers  we  observed  as  social  actors  playing  a  particular  set  of  roles  in  their   classroom.  Our  data  identified  a  number  of  personal  factors  that  interacted  to  influence   both  teachers’  action  in  their  classrooms.   TESL-EJ 15.1, June 2011 Burns & Knox page 13 For  instance,  the  teacher  in  the  extract  above  was  born  in  Eastern  Europe,  and   emigrated  first  to  Western  Europe  and  then  to  a  Pacific  Island  state  as  a  young  child,   before  later  moving  again  to  Australia.  She  raised  her  experience  as  an  immigrant  and  a   language  learner  a  number  of  times,  on  one  occasion  in  relation  to  student  attitudes   towards  spelling  and  grammar.   I  actually  start  the  patter  from  the  very  earliest  classes  so  that  they’re,   they  have,  ‘cos  I  remember  my  mother  taught  me  English  in  [the  Pacific   Island]  and  the  absolute  frustration  of  wondering  where  the  hell  this   grammar,  well  spelling  etcetera  was  coming  from.  So  I  think  it’s  sort  of,  to   me  it  kind  of  stops  people  feeling  too  anxious  about  it  too.  About  language   learning.   In  the  classroom  extract  above,  her  professional  development  experience  and  KAL  had   influenced  her  decision  about  what  needed  to  be  taught  in  this  particular  lesson.  Also   her  own  educational  experience  was  important,  and  she  pointed  out  in  the  post-­‐lesson   interview  that  she  ‘felt  from  [my]  own  education  that  nobody  had  scaffolded  stuff   enough  –  it  was  sit  down  and  write  an  essay  rather  than  telling  you  how  an  essay  was   constructed.’   Throughout  the  interviews,  both  teachers  talked  about  their  personal  histories,  and  at   times  related  their  moment-­‐to-­‐moment  decision-­‐making  to  experiences  distant  both   spatially  and  temporally.  Personal  factors  which  became  apparent  from  observations   and  interviews  included  the  teachers’  experiences  as  language  learners,  their  emotional   state  on  a  given  day  at  a  given  time,  their  teaching  experience,  their  KAL,  and  their   education  and  professional  development.  Once  again,  it  was  not  these  elements  per  se   that  stood  out,  but  the  relations  between  them,  and  how  these  relations  gelled,  shifted,   and  sometimes  dissolved  as  they  interacted  with  other  elements  of  the  classroom.   Using  the  same  modelling  principle,  we  constructed  a  visual  representation  of  the   teachers  in  the  classroom  as  shown  in  Figure  2.  Again,  this  representation  shows  the   factors  identified  in  our  research;  we  are  not  claiming  that  these  are  factors  which  are   generalisable  to  every  teacher,  nor  to  every  context.   TESL-EJ 15.1, June 2011 Burns & Knox page 14    Figure  2:  Teacher  factors  in  a  relational  classroom  model   All  the  lessons  we  observed  took  place  during  a  blazing  Australian  summer,  and  the   impact  of  the  heat  on  the  classroom  was  tangible.  After  one  lesson  where   communicative  activities  had  been  planned,  one  teacher  commented:   I  think  that  in  this  case  the  environment  didn’t  help  today.  The  heat  and   the  weather  has  affected  us  because  otherwise  they’re  usually  really   talkative  and  they’re  energetic….   In  addition,  different  rooms  had  different  arrangements  of  furniture,  lighting  and  so  on.   One  of  the  teachers  commented:   It’s  a  very  difficult  classroom  that  one.  It’s  very,  it  was  a  frustrating   classroom,  mind  you  the  one  here  is  exactly  the  same  but  because   everybody  has  to  sit  around  the  edges,  it’s  a  very  finite  limited  space.  …  in   that  classroom  they’re  just  around  the  edge  so  you  can’t  even  walk  behind   them  so  my  one  on  one  was  a  lot  less  than  it  normally  would’ve  been  in  a   bigger  classroom  where  I  can  manoeuvre  better  and  where  it’s  easier  to   set  up  tables.  I  would  be  much  more  flexible.   The  combination  of  factors  in  the  physical  environment  was  crucial.  Some  of  the  lessons   we  observed  took  place  in  a  portable  classroom  located  in  a  parking  lot.  The   combination  of  cramped  space,  intense  heat,  and  relatively  poor  light  produced  a   physical  environment  conducive  to  certain  activities  (such  as  perspiring  and  dozing)   and  not  to  others  (such  as  milling  activities,  role  plays,  or  teacher-­‐learner   conferencing).  As  with  the  descriptions  given  above,  it  was  necessary  to  consider  the   TESL-EJ 15.1, June 2011 Burns & Knox page 15 relationships  between  the  various  factors  rather  than  each  one  in  isolation.  A  visual   representation  of  the  prominent  elements  in  the  physical  environment  through  the  lens   of  our  research  is  given  in  Figure  3.     Figure  3:  Physical  and  environmental  factors  in  a  relational  classroom  model   The  relational  model  (and  its  visual  representations)  outlined  above  has  enabled  us  to   better  understand  and  account  for  teacher  change  in  the  classroom.  Our  study  began   with  the  aim  of  exploring  the  development  of  two  teachers’  KAL  and  its  impact  on  their   respective  classroom  practice.  The  relational  approach  described  led  to  our  revisiting   unquestioned  assumptions  of  ‘what  a  teacher  is,’  and  ‘what  a  classroom  is.’  As  is  evident   in  Figure  2  above,  we  came  to  view  the  two  teachers,  from  the  perspective  offered  by   this  model,  as  social  actors  whose  actions  could  be  best  understood  as  emergent   behaviours  from  a  range  of  factors  that  interact  dynamically  and  continuously.  A   teacher  is  a  person  playing  a  social  role  in  a  particular  time  and  place,  and  the  playing  of   that  role  means  that  certain  social  and  cognitive  factors  (e.g.,  KAL,  language  learning   experience,  teaching  experience)  come  to  the  fore  as  the  teacher  interacts  with  other   factors  in  the  classroom  (such  as  students,  researchers,  the  physical  environment).  This   is  represented  visually  in  Figure  4,  which  shows  how  Figures  1-­‐3  combine  relationally   and  visually.   TESL-EJ 15.1, June 2011 Burns & Knox page 16    Figure  4:  Expansion:  Classroom  as  complex  adaptive  system   Viewed  in  this  way,  the  classroom  and  the  action  therein  is  a  product  of  the  relations   between  different  elements:  some  immediate,  some  distant;  some  obvious,  some   hidden;  some  direct,  some  indirect.  Each  element  of  the  model  exists  in  a  set  of  dynamic   relations,  each  of  which  affects  and  is  affected  by  other  sets  of  relations  in  the  model.   Thus,  we  can  see  the  classroom  as  a  complex  adaptive  system,  where  changes  in   relations  between  variables  can  impact  on  the  entire  system.  Viewing  factors  in   categorical  isolation  cannot  provide  the  same  descriptive  power.   In  the  case  of  the  classroom  extract  above,  the  teacher  was  (by  her  own  admission)   relatively  unsuccessful  in  scaffolding  the  students  into  an  exploration  of  the  use  of   modality  in  academic  writing.  For  future  lessons  in  this  classroom,  this  experience  may   have  had  implications  for  the  way  that  activities  were  conducted,  for  student  attitudes   about  this  aspect  of  academic  writing,  for  the  amount  of  lesson  preparation  this  teacher   was  willing  to  do,  for  personal  relations  between  teacher  and  students,  and  for  many   other  factors.   Focusing  solely  on  the  teacher,  this  teacher  told  us  during  the  research  that  she  often   develops  her  understanding  of  grammar  in  part  by  teaching  it.  Thus,  her  experience  in   this  lesson  seems  likely  to  feed  back  into  her  knowledge  about  this  linguistic  feature  in   unpredictable  ways  (perhaps  that  it  is  difficult  to  teach,  difficult  for  students  to   understand,  or  perhaps  that  it  is  something  she  is  more  determined  to  teach  well   and/or  learn  about).  In  this  way,  her  KAL  is  seen  not  as  a  static  entity  residing  in  her   TESL-EJ 15.1, June 2011 Burns & Knox page 17 mind  and  ‘brought  into’  the  classroom,  but  in  constant  interaction  with  the  other   elements  identified  in  the  description  in  Figure  4.   This  perspective  on  KAL  is  fundamentally  different  from  that  embodied  in  our  original   research  questions  as  cited  above,  which  asked  firstly  how  our  teaching  of  SFL  impacted   on  the  teachers’  KAL,  and  secondly  how  changes  in  KAL  affected  classroom  practice.   While  these  questions  do  not  assume  that  this  research  process  is  simple,  nor  that  it  is   decontextualised,  it  nonetheless  does  presume  a  linear  cause-­‐effect  relationship  as   Figure  5  illustrates.       Figure  5:  Linear  understanding  of  the  relationship  between  teacher  education  and   classrooms     The  limitations  in  this  approach  (cf.  Figure  4)  apply  regardless  of  whether  teacher   knowledge  is  language  teachers’  KAL  or  subject  teachers’  subject  knowledge,  or  of   whether  this  knowledge  is  conceptualised  as  declarative  or  procedural  knowledge.   Knowledge  of  ‘what’  and  knowledge  of  ‘how  to’  (if  indeed  they  can  be  separated)  are   both  relational:  teachers’  knowledge  and  classroom  practice  exist  in  a  complex  web  of   interactions,  and  classroom  practice  also  impacts  on  how  teachers  construct  and   develop  their  own  knowledge.   This  dialectic  extends  also  to  classrooms  (physical  and  virtual)  where  teacher  education   takes  place,  and  following  this  research  project  we  incorporated  a  problem-­‐based   approach  into  our  teacher-­‐education  course,  in  which  students  drew  on  their  own   teaching  contexts  and  collectively  investigated  ways  in  which  SFL  could  be  applied.  This   is  one  way  in  which  teachers’  professional  contexts  can  be  integrated  in  the  teacher   education  classroom,  and  the  complexity  of  classrooms  can  be  explored  in  relation  to   new  subject  knowledge.   Conclusions   This  paper  has  presented  a  relational  model  of  classrooms,  drawing  on  a  number  of   strands  of  research  in  and  beyond  Applied  Linguistics.  The  argument  presented  is  that   the  model  provides  a  perspective  on  classrooms  which  can  add  to  existing  research.   Nonetheless,  this  model  does  have  a  number  of  limitations.   The  factors  identified  in  the  model  are  a  direct  product  of  a  particular  research  focus   and  methodology.  The  research  project  described  in  this  paper  relied  on  classroom   observation  and  interviews  with  teachers.  Other  data  such  as  interviews  with  students,   video  data,  and  multimodal  analyses  of  classroom  interactions  would  have  yielded   greater  explanatory  power  and  probably  a  broader  range  of  relevant  factors.  This   TESL-EJ 15.1, June 2011 Burns & Knox page 18 limitation  can  be  explained  in  part  by  the  small-­‐scale  nature  of  the  study:  larger  projects   with  more  funding  would  be  able  to  collect  and  analyse  more  data,  using  a  wider  range   of  methodologies,  than  was  possible  in  this  case.  Further,  the  research  was  not  designed   to  model  classrooms,  but  to  investigate  language  teachers’  KAL.  The  model  arose  from   the  research  process,  and  therefore  this  limitation  is  also  a  product  of  our  starting   point,  and  can  be  addressed  by  future  research  which  builds  on  the  approach  we  have   outlined  here.   As  discussed  earlier,  the  classroom  is  a  ‘nested’  system.  In  the  study  described  in  this   paper,  the  starting  point  was  individual  teachers’  KAL,  which  has  been  modelled  here  as   a  factor  relevant  to  the  complex  adaptive  system  of  the  classroom.  This  raises  questions   of  how  best  to  investigate  and  model  different  system  levels,  and  how  their  interaction   can  be  adequately  described.  The  ways  in  which  classrooms  can  be  modelled  in  relation   to  ‘higher-­‐order’  systems  such  as  institutions,  and  ‘lower-­‐order’  systems  such  as   individuals  requires  considerably  more  investigation.   Finally,  the  model  attempts  to  capture  the  dynamic  relationships  between  different   elements  which  converge  in  classrooms.  However,  our  two-­‐dimensional  visual   representation  of  it  is,  temporally  at  least,  static.  We  would  liken  this  to  the  paradox  of   viewing  light,  which  can  be  seen  either  as  particle,  or  wave,  but  not  both   simultaneously.  As  presented  in  this  paper,  the  model  privileges  a  ‘particle’  view  of   classrooms  (Laskowsi,  2006  offers  a  complementary  visual  representation  of  the   professional  development  of  teachers  over  time).  Constructing  visual  representations  of   classroom  change  over  time  adds  another  dimension  of  complexity,  and  is  likely  to   require  animation,  and  perhaps  three-­‐dimensional  graphics.  This  implies  the  need  to   assign  numerical  values  to  both  the  elements  in  the  model  and  their  relations,   something  which  may  become  possible  in  future  developments  (cf.  O’Halloran,  2005).   Despite  these  limitations,  this  model  builds  on,  and  extends  existing  classroom-­‐based   research  in  Applied  Linguistics,  and  affords  a  relational  view  of  the  classroom  in  which   there  is  no  a  priori  start  or  end  point;  classrooms  are  convergences  that  reach   backwards  and  forwards  temporally,  discursively,  socially,  cognitively,  and  culturally.   Such  a  view  allows  us  to  incorporate  a  range  of  factors  into  our  account  of  action  in  the   classroom,  including  how  an  immigrant  child’s  experience  of  learning  English  from   their  mother  on  a  Pacific  island  can  impact  on  their  decision-­‐making  decades  later  in  a   suburban  [location  of  research]  classroom,  and  how  the  furniture  in  that  same  room,   and  the  attitudes  of  the  students  towards  a  given  activity  can  combine  with  the   teacher’s  experience  and  affect,  and  other  factors,  to  contribute  to  the  success  or  failure   of  that  activity.   This  dynamism  is  a  typical  feature  of  classrooms,  and  means  that  there  is  an  inherent   potential  for  instability  and  unpredictability  in  classrooms,  even  highly  structured,   teacher-­‐centred  ones  where  this  potential  may  rarely,  if  ever  be  realized.  Classroom   action  can  unfold  in  a  relatively  predictable  manner  and  in  such  cases  linear  methods  of   description  appear  to  work  well  (see  Hodge,  2003,  p.  10).  But  as  with  any  complex   adaptive  system,  unforeseen  (and  unidentified)  factors  can  have  an  unpredictable   impact,  and  when  classrooms  and  the  participants  in  them  are  in  a  state  of  flux,  linear   TESL-EJ 15.1, June 2011 Burns & Knox page 19 cause-­‐and-­‐effect  descriptions  cannot  comprehensively  account  for  what  emerges  (see   Burns  &  Knox,  2005;  Laskowski,  2006).   Post-­‐experience  teacher  education  aims  to  add  to  teachers’  knowledge  and  improve   their  teaching  practice.  In  a  field  where  in-­‐service  teacher  education  frequently  fails  to   achieve  change  in  teachers’  classroom  practices  (Lamb,  1995;  Waters,  2006,  p.  33),  and   where  the  majority  of  curriculum  innovations  flounder  over  time  (Fullan,  1999;   Markee,  2001),  there  is  a  need  for  a  sound  theoretical  basis  for  explaining  classroom   change,  or  its  lack.  Our  model  suggests  that  in  order  to  effect  change,  the  work  done  by   teacher  educators  needs  to  have  sufficient  influence  on  teachers  to  change  the  relations   between  different  elements  in  their  classrooms,  and  that  teacher  education  programs   and  courses  need  to  be  designed  and  implemented  with  this  important  consideration  in   mind  (see  Borg,  2003,  p.  106).   Helping  teachers  to  develop  specific  areas  of  their  knowledge  and  practice  (e.g.,  KAL)   may  be  enough  to  effect  classroom  change.  However,  it  is  more  likely  that  teachers  (and   therefore  teacher  educators)  will  need  to  act  on  a  range  of  classroom  variables  in  order   to  change  the  relations  and  move  the  classroom  productively  out  of  a  comfortable  state   of  equilibrium.  This  implies  a  need  to  understand  and  study  classrooms  in  a  way  that   recognises  and  accounts  for  their  complexity,  rather  than  one  that  reduces  it.   Occam’s  razor  states  that  simpler  explanations  are  to  be  preferred  over   more  complex  ones,  so  long  as  they  account  for  the  data.  But  the  razor  is   in  fact  a  double-­‐edged  sword,  since  in  practice  there  may  be  a  ‘conspiracy’   effect  between  the  explanation  and  the  data.  The  ‘simplest  explanation   that  accounts  for  the  data’  is  applied  to  data  that  have  been  extracted   from  complex  processes  because  of  prior  assumptions  about  their  (the   data’s)  significance.  Thus  the  data  encourage  the  ‘simplest  explanation’   and  the  ‘prior  assumptions’  to  become  identical.  As  a  result  research  runs   the  danger  of  becoming  locked  into  a  reductionism  from  which  it  may  be   hard  to  break  away.  (van  Lier,  2000,  p.  248)   In  this  short  passage,  van  Lier  presents  a  challenge  to  ‘build  in’  complexity  rather  than   reduce  it.  This  is  a  considerable  task  for  classroom  researchers,  and  requires  new  ways   of  understanding  the  phenomena  we  investigate.  The  approach  outlined  in  this  article   represents  a  metaphor  (Kramsch,  2002a)  that  allowed  us  to  see  classrooms  in  a  new   light  (Bowers,  1990),  and  to  better  incorporate  the  complexity  of  the  classrooms  we   observed  into  our  analysis  and  description.  We  hope  others  will  be  able  to  apply  and   adapt  this  metaphor  in  exploring  the  complexity  of  their  own  sites  of  investigation.     Acknowledgement   The  research  on  which  this  paper  is  based  was  funded  by  a  Macquarie  University   Research  Grant.       TESL-EJ 15.1, June 2011 Burns & Knox page 20 Note      [1]  T  =  teacher;  I  =  interviewer     About  the  Authors   Anne  Burns  is  Professor  of  TESOL  at  the  University  of  New  South  Wales,  Sydney  and   Professor  of  Language  Education  at  Aston  University,  Birmingham.  She  has  published   extensively  in  the  field  of  applied  linguistics/TESOL  and  supervises  PhD  and  Masters   students  in  these  areas.  She  was  recently  appointed  Series  Advisor  for  Oxford   University  Press  Applied  Linguistics.   John  S.  Knox  is  a  Lecturer  in  the  Department  of  Linguistics,  Macquarie  University,   Sydney,  where  he  teaches  on  the  Postgraduate  Programs  in  Applied  Linguistics.  His   primary  research  interests  are  in  the  areas  of  language  in  education  (including  teacher   education),  systemic  functional  linguistics,  multimodal  discourse  analysis,  and  media   discourse.     References   Basturkmen,  H.,  Loemen,  S.,  &  Ellis,  R.  (2004).  Teachers’  stated  beliefs  about  incidental   focus  on  form  and  their  classroom  practices.  Applied  Linguistics,  25(2),  243-­‐272.   Bernadez,  E.  (1994).  Can  catastrophic  theory  provide  adequate  explanations  for   linguistic  change?  In  F.  Fernandez,  M.  Fuster  &  J.  J.  Calvo  (Eds.),  English  historical   linguistics  1992.  Amsterdam:  Benjamins.   Bogden,  R.,  &  Biklen,  S.  K.  (1998).  Qualitative  research  for  education:  An  introduction  to   theory  and  methods  (3rd  ed.).  Boston:  Allyn  and  Bacon.   Borg,  S.  (2003).  Teacher  cognition  in  language  teaching:  A  review  of  research  on  what   language  teachers  think,  know,  believe,  and  do.  Language  Teaching,  36,  81-­‐109.   Borg,  S.  (2006).  Teacher  cognition  and  language  education.  Research  and  practice.   London:  Continuum.   Bowers,  R.  (1990).  Mountains  are  not  cones:  What  can  we  learn  from  chaos?  In  J.  E.   Alatis  (Ed.),  Linguistics,  language  teaching  and  language  acquisition:  The   interdependence  of  theory,  practice  and  research.  Georgetown  University  Round  Table  on   Languages  and  Linguistics,  1990.  Washington,  D.C.:  Georgetown  University  Press.   Breen,  M.  P.  (2001a).  Navigating  the  discourse:  On  what  is  learned  in  the  language   classroom.  In  C.  N.  Candlin  &  N.  Mercer  (Eds.),  English  language  teaching  in  its  social   context:  A  reader  (pp.  306-­‐322).  London:  Routledge.   Breen,  M.  P.  (2001b).  The  social  context  for  language  learning:  A  neglected  situation?  In   C.  N.  Candlin  &  N.  Mercer  (Eds.),  English  language  teaching  in  its  social  context:  A  reader   (pp.  122-­‐144).  London:  Routledge.   TESL-EJ 15.1, June 2011 Burns & Knox page 21 Breen,  M.  P.,  Hird,  B.,  Milton,  M.,  Oliver,  R.,  &  Thwaite,  A.  (2001).  Making  sense  of   language  teaching:  Teachers’  principles  and  classroom  practices.  Applied  Linguistics,   22(4),  470-­‐501.   Burns,  A.  (1992).  Teacher  beliefs  and  their  influence  on  classroom  practice.  Prospect,   7(3),  56-­‐66.   Burns,  A.  (1996).  Starting  all  over  again:  From  teaching  adults  to  teaching  beginners.  In   D.  Freeman  &  J.  C.  Richards  (Eds.),  Teacher  learning  in  language  teaching  (pp.  154-­‐177).   Cambridge:  Cambridge  University  Press.   Burns,  A.,  &  Knox,  J.  S.  (2005).  Realisation(s):  Systemic-­‐functional  linguistics  and  the   language  classroom.  In  N.  Bartels  (Ed.),  Applied  linguistics  and  language  teacher   education  (pp.  235-­‐259).  New  York:  Springer.   Canagarajah,  S.  (2001).  Resisting  linguistic  imperialism  in  English  teaching.  Oxford:   Oxford  University  Press.   Candlin,  C.  N.,  &  Mercer,  N.  (Eds.).  (2001).  English  Language  Teaching  in  its  Social   Context:  A  Reader.  London:  Routledge.   Cazden,  C.  (2001).  Classroom  discourse:  The  language  of  teaching  and  learning  (2nd  ed.).   Westport,  CT.:  Heinemann.   Chaudron,  C.  (1988).  Second  language  classrooms:  Research  on  teaching  and  learning.   New  York:  Cambridge  University  Press.   Christie,  F.  (Ed.).  (1999).  Pedagogy  and  the  shaping  of  consciousness:  linguistic  and  social   processes.  London:  Cassell.   Christie,  F.  (2002).  Classroom  discourse  analysis.  London:  Continuum.   Coleman,  H.  (Ed.).  (1996).  Society  and  the  language  classroom.  Cambridge:  Cambridge   University  Press.   de  Bot,  K.,  Verspoor,  M.,  &  Lowie,  W.  (2005a).  Dynamic  systems  theory  and  applied   linguistics:  The  ultimate  “so  what”?  International  Journal  of  Applied  Linguistics,  15(1),   116-­‐118.   de  Bot,  K.,  Verspoor,  M.,  &  Lowie,  W.  (2005b).  Second  language  acquisition:  An  advanced   resource  book.  London:  Routledge.   Ellis,  N.  C.,  &  Larsen-­‐Freeman,  D.  (Eds.).  (2006).  Applied  Linguistics  (Special  issue  on   Language  Emergence),  27(4).   Feryok,  A.  (2010).  Language  teacher  cognitions:  Complex  adaptive  systems?  System,   38(2),  272-­‐279.   Finch,  A.  (2001).  Complexity  in  the  classroom.  Secondary  Education  Research,  47,  105-­‐ 140.  [Available  online  at:  http://www.finchpark.com/arts/,  accessed  July  19,  2005.]   Folke,  G.,  &  Folke,  C.  (1992).  Characteristics  of  nested  living  systems.  Journal  of   Biological  Systems,  1(3),  257-­‐274.   TESL-EJ 15.1, June 2011 Burns & Knox page 22 Freeman,  D.,  &  Johnson,  K.  E.  (1998).  Reconceptualizing  the  knowledge-­‐base  of   language  teacher  education.  TESOL  Quarterly,  32(3),  397-­‐417.   Fullan,  M.  G.  (1999).  Change  forces.  The  sequel.  New  York:  Routledge.   Gieve,  S.,  &  Miller,  I.  K.  (Eds.).  (2006).  Understanding  the  language  classroom.   Hampshire:  Palgrave  Macmillan.   Hall,  J.  K.,  &  Verplaetse,  L.  (2000).  Second  and  foreign  language  learning  through   classroom  interaction.  Mahwah,  NJ:  Lawrence  Erlbaum   Herdina,  P.,  &  Jessner,  U.  (2002).  A  dynamic  model  of  multilingualism.  Perspectives  of   change  in  psycholinguistics.  Clevedon:  Multilingual  Matters.   Hill,  K.  A.  (2003).  Quantum  linguistics:  A  response  to  David  Mallows.  ELT  Journal,  57(2),   175-­‐178.   Hodge,  R.  (2003).  Chaos  theory:  An  introduction  for  TESOL  practitioners.  English   Australia  (EA)  Journal,  21(1),  8-­‐16.   Holliday,  A.  (1994).  Appropriate  methodology  and  social  context.  Cambridge:  Cambridge   University  Press.   Johnson,  K.  E.  (1996).  The  role  of  theory  in  L2  teacher  education.  TESOL  Quarterly,   30(4),  765-­‐771.   Ke,  J.,  &  Holland,  J.  H.  (2006).  Language  origin  from  an  emergentist  perspective.  Applied   Linguistics,  27(4),  691-­‐716.   Kramsch,  C.  (1993).  Context  and  culture  in  language  teaching.  Oxford:  Oxford  University   Press.   Kramsch,  C.  (2002a).  Introduction:  “How  can  we  tell  the  dancer  from  the  dance?”  In  C.   Kramsch  (Ed.),  Language  acquisition  and  language  socialization:  Ecological  perspectives   (pp.  1-­‐30).  London:  Continuum.   Kramsch,  C.  (Ed.).  (2002b).  Language  acquisition  and  language  socialization:  Ecological   perspectives.  London:  Continuum.   Lamb,  M.  (1995).  The  consequences  of  INSET.  ELT  Journal,  49(1),  72-­‐80.   Lantolf,  J.  P.  (Ed.).  (2000).  Sociocultural  theory  and  second  language  learning.  Oxford:   Oxford  University  Press.   Lantolf,  J.  P.,  &  Thorne,  S.  (2006).  Sociocultural  theory  and  the  genesis  of  second  language   development.  Oxford:  Oxford  University  Press.   Larsen-­‐Freeman,  D.  (1997).  Chaos/complexity  science  and  second  language  acquisition.   Applied  Linguistics,  18(2),  141-­‐165.   Larsen-­‐Freeman,  D.,  &  Cameron,  L.  (2007).  Complex  Systems  and  Applied  Linguistics.   Oxford:  Oxford  University  Press.   Laskowski,  T.  E.  (2006).  Conceptualizations  of  three  junior  high  school  Japanese  English   teachers’  (JTEs)  teaching  practices.  Unpublished  Ph.D.,  Macquarie  University,  Sydney.   TESL-EJ 15.1, June 2011 Burns & Knox page 23 Lemke,  J.  L.  (2000).  Material  sign  processes  and  ecosocial  organization.  In  P.  B.   Andersen,  C.  Emmeche  &  N.  O.  Finnemann-­‐Nielsen  (Eds.),  Downward  causation:  Self-­ organization  in  biology,  psychology,  and  society  (pp.  181-­‐213).  Aarhus:  Aarhus   University  Press.   Lemke,  J.  L.  (2002).  Language  development  and  identity:  Multiple  timescales  in  the   social  ecology  of  learning.  In  C.  Kramsch  (Ed.),  Language  acquisition  and  language   socialization:  Ecological  perspectives  (pp.  68-­‐87).  London:  Continuum.   Lemke,  J.  L.,  &  Sabelli,  N.  (2006).  Complex  systems  and  educational  change:  Towards  a   new  research  agenda,  Paper  presented  at  AERA  2006,  San  Francisco.  [Available  online   at:  http://www-­‐personal.umich.edu/~jaylemke/papers/complexity&ed2006.htm,   accessed  December  15,  2006.]   Lightfoot,  D.  L.  (1991).  How  to  set  parameters:  Arguments  from  language  change.   Cambridge,  MA:  MIT  Press.   Lin,  A.  M.  Y.  (2001).  Doing-­‐English-­‐lessons  in  the  reproduction  or  transformation  of   social  worlds?  In  C.  N.  Candlin  &  N.  Mercer  (Eds.),  English  language  teaching  in  its  social   context:  A  reader  (pp.  271-­‐286).  London:  Routledge.   Logan,  R.  K.,  &  Schumann,  J.  H.  (2005).  The  symbolosphere,  conceptualization,  language,   and  neo-­‐dualism.  Semiotica,  155(1-­‐4),  201-­‐214.   Mallows,  D.  (2002).  Non-­‐linearity  and  the  observed  lesson.  ELT  Journal,  56(1),  3-­‐10.   Markee,  N.  (2001).  The  diffusion  of  innovation  in  language  teaching.  In  D.  R.  Hall  &  A.   Hewings  (Eds.),  Innovation  in  English  language  teaching:  A  reader  (pp.  118-­‐126).   London:  Routledge.   Mehan,  H.  (1979).  Learning  lessons:  Social  organization  in  the  classroom.  Cambridge:   Harvard  University  Press.   O’Halloran,  K.  L.  (2004).  Discourses  in  secondary  school  mathematics  classrooms   according  to  social  class  and  gender.  In  J.  A.  Foley  (Ed.),  Language,  education  and   discourse:  Functional  approaches  (pp.  191-­‐225).  London:  Continuum.   O’Halloran,  K.  L.  (2005).  Mathematical  discourse:  Language,  symbolism  and  visual   images.  London:  Continuum.   Pica,  T.  (1987).  Second  language  acquisition,  social  interaction  and  the  classroom.   Applied  Linguistics,  8(1),  3-­‐21.   Richards,  J.  C.,  &  Pennington,  M.  (1998).  The  first  year  of  teaching.  In  J.  C.  Richards  (Ed.),   Beyond  training  (pp.  173-­‐190).  Cambridge:  Cambridge  University  Press.   Rogers,  E.  M.,  Medina,  U.  E.,  Rivera,  M.  A.,  &  Wiley,  C.  J.  (2005).  Complex  adaptive   systems  and  the  diffusion  of  innovations.  The  Innovation  Journal:  The  Public  Sector   Innovation  Journal,  10(3).  [Available  online  at:  http://www.innovation.cc/volumes-­‐ issues/vol10-­‐no3.htm,  accessed  June  13,  2007.]   TESL-EJ 15.1, June 2011 Burns & Knox page 24 Schneider,  E.  W.  (1997).  Chaos  theory  as  a  model  for  dialect  variability  and  change?  In   A.  R.  Thomas  (Ed.),  Issues  and  methods  in  dialectology.  Bangor:  Department  of   Linguistics,  University  of  Wales.   Schneider,  E.  W.  (2001).  Chaos  theory  as  a  model  for  dialect  variability  and  change?,   Dictionary  Research  Centre  Occasional  Seminar  Series.  Macquarie  University,  Sydney.   Senior,  R.  M.  (2006).  The  experience  of  language  teaching.  Cambridge:  Cambridge   University  Press.   Sinclair,  J.,  &  Coulthard,  M.  (1975).  Towards  an  analysis  of  discourse:  The  English  used  by   teachers  and  pupils.  Oxford:  Oxford  University  Press.   Smith,  K.,  Brighton,  H.,  &  Kirby,  S.  (2003).  Complex  systems  in  language  evolution:  The   cultural  emergence  of  compositional  structure.  Advances  in  Complex  Systems,  6(4),  537-­‐ 558.   Tabachnick,  B.  R.,  &  Zeichner,  K.  M.  (1986).  Teacher  beliefs  and  classroom  behaviours:   Some  teacher  responses  to  inconsistency.  In  B.  Ben-­‐Peretz,  R.  Bromme  &  R.  Halkes   (Eds.),  Advances  of  research  on  teacher  thinking  (pp.  84-­‐96).  Lisse,  Netherlands:  Swets   and  Zeitlinger.   van  Geert,  P.  (1994).  Dynamic  systems  of  development:  Change  between  complexity  and   chaos.  New  York:  Harvester  Wheatsheaf.   van  Lier,  L.  (1996).  Interaction  in  the  language  curriculum:  Awareness,  autonomy,  and   authenticity.  New  York:  Longman.   van  Lier,  L.  (2000).  From  input  to  affordance:  Social-­‐interactive  learning  from  an   ecological  perspective.  In  J.  P.  Lantolf  (Ed.),  Sociocultural  theory  and  second  language   learning  (pp.  245-­‐259).  Oxford:  Oxford  University  Press.   van  Lier,  L.  (2001).  Constraints  and  resources  in  classroom  talk:  Issues  of  equality  and   symmetry.  In  C.  N.  Candlin  &  N.  Mercer  (Eds.),  English  language  teaching  in  its  social   context:  A  reader  (pp.  90-­‐107).  London:  Routledge.   van  Lier,  L.  (2004).  The  ecology  and  semiotics  of  language  learning:  A  sociocultural   perspective.  New  York:  Kluwer  Academic  Publishers.   Waters,  A.  (2006).  Facilitating  follow-­‐up  in  ELT  INSET.  Language  Teaching  Research,   10(1),  32-­‐53.   Wildgen,  W.  (1982).  Catastrophic  theoretic  semantics.  Amsterdam:  Benjamins.   Woods,  D.  (1996).  Teacher  cognition  in  language  teaching.  Cambridge:  Cambridge   University  Press.       Copyright  ©  1994  -­‐  2011  TESL-­‐EJ,  ISSN  1072-­‐4303   Copyright  rests  with  the  authors.     TESL-EJ 15.1, June 2011 Burns & Knox page 25