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James Calleja    



Ø To  explore  opportunities  where  the  teacher  may  shift  more  instructional   responsibilities  to  the  students  

Ø To reflect  upon  concerns  in  giving  students  more  responsibilities  over  their   learning  

Ø To understand  the  responsibilities  and  the  roles  of  students  and  the  teacher   within  a  collaborative  classroom  community    

Ø To create  an  effective  classroom  culture  based  on  habits,  rules,  expectations,   behaviours,  actions,  interactions,  beliefs  and  values  which  the  teacher  and  the   students  establish,  understand  and  share    



Teaching and  Learning  Mathematics  through  Inquiry  

LOOKING AT  YOUR  CLASSROOM  CULTURE     Mike   Ollerton   and   Anne   Watson   (2001,   p.   14)   describe   a   list   incorporating   three   elements   for   the   culture   of   a   classroom.   This   includes:   (1)   student   actions   and   behaviour;  (2)  teacher  actions  and  behaviour;  (3)  classroom  environment.     ü



Student actions  and  behaviour     Engage   purposefully   in   their   mathematical   work;   ask   and   answer   questions  of  each  other;  ask  and  answer  questions  of  the  teacher;  ask  for   and   offer   help;   take   independent   responsibility   for   their   work;   respect   each  others’  right  to  work  and  participate   Teacher  actions  and  behaviour   Have  a   working   relationship  with  students;  respond  seriously  to,  as  well   as   initiate,   interactions;   prepare   interesting   approaches   to   mathematics;   ensure   students   have   access   to   the   material   presented;   use   a   range   of   resources,  teaching  styles  and  strategies   The  classroom  environment   Be   sometimes   calm   and   at   others   vibrant,   but   always,   purposeful;   be   used   flexibly  with  people,  desks  and   chairs  rearranged  to   suit  the  mathematical   activities;   contain   a   variety   of   easily   accessible   resources;   have   displays   produced  by  students  and  teachers  

Ollerton and  Watson  (2001,  p.  15)  continue:   For   students   to   take   personal   responsibility,   opportunities   and   encouragement   must   exist   for   them   to   make   decisions   about   the   direction,  amount,  pace  and  depth  of  work  they  do.   One  very  important  question  arises…   How  is  the  teacher  to  exercise  responsibility  for  ‘covering’  the  syllabus?   1. Students   need   to   be   made   fully   aware   of   what   they   need   to   do   for   examinations   and   other   assessments,   if   they   are   expected   to   make   responsible   decisions.   Syllabus   and   assessment   criteria   need   to   be   shared   with   the   students   so   that   they   are   not   fully   dependent   on   the   teacher   for   monitoring  progress.   2. The   teacher   must   provide   opportunities   and   access   for   all   students   to   work   on  the  syllabus  topics.   3. Students   need   to   be   given   the   knowledge,   structures   and   tools   of   how   to   behave   responsibly.   More   importantly,   students   should   be   expected   and   trusted  with  being  able  to  utilize  those  tools  for  their  own  benefits.     Reference:            Ollerton,  M.  &  Watson,  A.  (2001).  Inclusive  Mathematics  11-­‐18.  London:  Continuum.  


Teaching and  Learning  Mathematics  through  Inquiry  



In most  classrooms,  it  seems  that  the  teacher  carries  much  of  the  responsibilities  for   student   learning.   And   rightly   so,   some   might   claim.   However,   teachers   seem   to   undertake   full   responsibility   for   what   goes   on   in   the   classroom,   with   students   ‘passively’  waiting  for  things  to  be  done  –  by  the  teacher,  for  the  students  –  because   that’s  the  way  it  is  and  that’s  the  way  it  should  be!   In   considering   some   of   the   key   decisions,   actions   and   expectations   traditionally   undertaken   by   teachers,   one   might   have   a   closer   look   at   the   following   six   aspects.   Teachers,  and  especially  those  of  mathematics,  are  usually  expected  to:   ⇒ Take   absolute   control   on   and   of   the   mathematical   problems,   questions   and  

exercises that  students  should  do;   ⇒ Ensure  that  students  do  all  the  work  assigned  to  them,  and  will  get  some  form  

of ‘punishment’  if  students  either  refuse,  refrain  or  forget  to  do  it;   ⇒ Collect   and   mark   all   the   work   assigned,   providing   students   with   corrections  

to any  incorrect  methods  and/or  answers;   ⇒ Resolve   the   difficulties,   struggles   and   challenges   that   students   encounter  

during a  particular  lesson;   ⇒ Help  students  study  and  do  well  in  tests,  assessments  and  examinations;   ⇒ Provide   students   with   detailed   notes   and   worked   examples   about   all   the  

topics covered  during  the  scholastic  year.   Teachers   may   feel   puzzled   about   implementing   inquiry-­‐based   learning   pedagogies   because   they   have   so   many   responsibilities   to   shoulder.   Moreover,   these   responsibilities  do  not  seem  to  resonate  well  with  IBL.  Indeed,  they  don’t!  Teachers   feel  increasing  pressures  with  ‘delivering’  mathematical  content  to  students,  with   taking  action  and  finding  support  when  students  do  not  do  their  work,  collecting   and   correcting   all   the   work   students   do   in   class   and   at   home,   resolving   the   difficulties  that  students  may  encounter  in  their  work,  and  providing  students  with   notes   about   the   topics   covered.   Especially   in   today’s   world,   these   aspects   have   become  much  more  challenging  to  implement,  realize  and  achieve.   The  idea  is  to  shift  some  of  these  responsibilities  onto  the  students  and  achieve  some   balance   in   responsibility   between   teacher   and   students.   In   classrooms   where   students   carry   more   responsibilities   for   their   learning,   students   carry   out   different  


Teaching and  Learning  Mathematics  through  Inquiry  

duties and  play  more  active  roles:  authority,  responsibility  and  agency  are  seen  to  be   constantly  shifting  between  the  teacher  and  the  students.   Another  very  important  question  arises…   But  how  can  such  a  balance  be  attained,  structured  and  negotiated?   The  table  below  identifies  potential  classroom  demands  and  teacher  dilemmas  that   you   may   want   to   address   differently   in   order   to   occasionally   shift   more   responsibility  to  your  students.     SOME  CLASSROOM   DILEMMAS  AND  DEMANDS    



What and  how  much  work   do  you  assign?  

I select  the  same  type  and   amount  of  classwork  and   homework  exercises  that  all   students  should  do  

Students select  the  amount   and  type  of  problems  and   questions  to  do  based  upon   an  assessment  of  what  each   individual  student  feels  s/he   should  focus  on  

What if  students  do  not  do   their  work?  

I make  sure  that  students  do   all  the  work  assigned,  and   they  know  that  they  will  get  a   report  for  not  doing  it  

Students have  some  degree  of   freedom  with  the  amount  of   work  they  do,  but  need  to   justify  their  decisions  

What about  correcting   students’  work?  

I collect  and  mark  all  the   work  assigned,  providing   students  with  the  necessary   corrections  

Students get  to  mark  and   correct  their  own  work,  and   the  teacher  gets  to  provide   ideas  when  students  get  stuck  

What do  you  do  when  your   students  struggle  with   mathematical  ideas  and   concepts?  

If students  do  not  manage  to   work  things  out  I  usually  tend   to  tell  them  how  to  do  

Students appreciate  that,  for   learning  to  occur,  they  need   to  struggle  and  solve  their   own  mathematical  issues  

How do  you  get  your   students  to  study  and  do   well  in  mathematics?  

I usually  plan  to  give  surprise   tests  on  a  regular  basis,  thus  I   keep  my  students  on  edge   and  prepared  for  their  exams  

Students are  aware  when  and   why  assessments  are  carried   out,  have  time  to  prepare  for   them  and  are  expected  to  be   well-­‐prepared  

What do  you  do  to  facilitate   studying  for  your  students?  

I ask  students  to  copy  notes   from  the  board,  otherwise  I   provide  a  structured  set  of   notes  that  include  definitions   and  worked  examples  for   every  topic  

Students are  encouraged  to   write  and  create  their  own   notes;  copying  whatever  they   feel  is  helpful  from  the  board  

How do  you  group  students   when  you  need  them  to   work  collaboratively?  

I always  choose  and  decide   with  whom  they  will  work  

More often  than  not,  students   are  free  to  decide  with  whom   they  will  work  


Teaching and  Learning  Mathematics  through  Inquiry  


ESTABLISHING A  DIDACTICAL  CONTRACT  WITH  STUDENTS     Teachers   might   argue   that   secondary   school   students   may   not   be   ready   to   take   responsibility   for   their   learning   –   either   because   they   are   not   used   to   undertaking   such  a  proactive  role  or  because  they  are  still  not  mature  enough  for  it.  However,  it  is   assumed   that   students   may   learn   to   become   more   responsible   if   they   are   encouraged,  allowed  and  supported  to  do  this.   The   culture   of   the   classroom,   thus,   becomes   crucial.   It   requires   teachers,   together   with   their   students,   to   create,   cultivate   and   inhabit   a   classroom   that   encourages   autonomy,   creativity,   communication,   trust   and   respect   for   one   another.   When   students   are   trusted   as   active   and   autonomous   learners,   they   are   more   likely   to   make   and   take   decisions   responsibly,   creating   more   meaningful   mathematical   learning   for   themselves.   Indeed,   Ollerton   (2006,   p.   51)   claims   that   ‘if   I   am   to   educate   my  students  to  take  responsibility,  then  I  must  also  learn  when  to  take  a  step  back,   when   to   loosen   my   grip’,   and   to   trust   that   eventually   students   will   be   in   a   better   position  to  take  more  control  of  and  over  their  learning.   Active   learning   pedagogies,   like   inquiry-­‐based   learning,   call   for   a   modified   didactical   contract   –   one   that   enhances   students’   acquisition   of   a   much   greater   sense   of   ownership,  agency  and  responsibility  over  their  learning.  For  a  start,  if  students  are   to   develop   into   active   constructors   of   mathematical   meanings   and   knowledge,   the   responsibility   for   teaching   and   learning   has   to   pass   from   the   sole   domain   of   the   teacher  to  become  one  that  is  shared  within  the  classroom  community.     This   relates   to   the   realization   that   when   students   are   trusted   with   ‘deciding   how   much   they   need   to   do   to   understand   the   mathematics   involved,   an   important   shift   takes   place:   away   from   doing   something   because   they   have   been   told   to   do   so,   and   towards   doing   something   because   they   recognize   the   value   of   making   progress’   (Ollerton,   2006,   p.   198).   When   students   are   handed   some   degree   of   control  over  what  and  how  they  learn  mathematics  (Ollerton,  2006),  they  get  a  sense   of  ownership  of  their  learning  which  helps  them,  in  turn,  to  progressively  develop  a   positive  sense  of  self  and  the  subject  (O’Neill  &  Barton,  2005).     References:           Ollerton,  M.  (2006).  Getting  the  Buggers  to  Add  Up  (2nd  Edition).  London:  Continuum.   O'Neill,  T.,  &  Barton,  A.C.  (2005)  Uncovering  student  ownership  in  science  learning:  The  making  of  a   student  created  mini-­‐documentary.  School  Science  and  Mathematics,  105(6),  292-­‐301.  


Teaching and  Learning  Mathematics  through  Inquiry  

Profile for IBL Maths

PD: Planning to Shift Responsibility  

Teacher guide to support in planning to provide agency and shift more responsibility to students

PD: Planning to Shift Responsibility  

Teacher guide to support in planning to provide agency and shift more responsibility to students

Profile for iblmaths