Integrating Numerical Computation into the Modeling ... - arXiv

most high school computer science courses, which typically focus on programming and procedural abstractions rather than solving science problems.
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Integrating  Numerical  Computation  into  the  Modeling  Instruction  Curriculum  

Marcos  D.  Caballero,  Michigan  State  University,  East  Lansing,  MI   John  B.  Burk,  St.  Andrew's  School,  Middleton,  DE   John  M.  Aiken  and  Brian  D.  Thoms,  Georgia  State  University,  Atlanta,  GA   Scott  S.  Douglas,  Erin  M.  Scanlon,  and  Michael  F.  Schatz,  Georgia  Institute  of  Technology,  Atlanta,  GA     Numerical  computation  (the  use  of  a  computer  to   emphasizes  the  practice  of  “Developing  and  using   solve,  simulate,  or  visualize  a  physical  problem)   models”  highlighted  by  the  NRC  K-­‐12  science   has  fundamentally  changed  the  way  scientific   standards  framework.1  Coupling  computational   research  is  done.  Systems  that  are  too  difficult  to   experiences  with  Modeling  Instruction  enables  the   solve  in  closed  form  are  probed  using   modeling  practice  and  the  computational  thinking   computation.  Experiments  that  are  impossible  to   practice  to  reinforce  each  other.    To  achieve  this   perform  in  the  laboratory  are  studied  numerically.   synergy,  we  taught  9th-­‐grade  students  to  use  the   Consequently,  in  modern  science  and  engineering,   VPython  programming  environment3,4  within  a   computation  is  widely  considered  to  be  as   Modeling-­‐Instruction-­‐based  physics  course.5  We   important  as  theory  and  experiment.       found  that  numerical  computation  within  the     Modeling  Instruction  curriculum  provides   Unfortunately,  most  high  school  students  today   coherence  among  the  different  models  within  the   are  never  introduced  to  computation's  problem-­‐ curriculum,  links  the  various  representations  that   solving  powers.    Computer  usage  is  widespread  in   the  curriculum  employs,  and  extends  the   high  school  STEM  courses  (e.g.,  obtaining  lab  data   curriculum  to  include  real-­‐world  problems  that   using  computer  acquisition  hardware/software),   are  otherwise  inaccessible  using  a  purely  analytic   but  such  usage  rarely  involves  students   approach.     constructing  a  computational  representation  of  a   Modeling  Instruction  &  numerical  computation   science  problem.    The  lack  of  computation  in   The  Modeling  Instruction  curriculum  employs  a   domain-­‐specific  STEM  courses  is  not  addressed  in   coherent  framework  of  scientifically  testing  the   most  high  school  computer  science  courses,  which   limits  of  physical  models  (i.e.,  “the  modeling   typically  focus  on  programming  and  procedural   abstractions  rather  than  solving  science  problems.     cycle”)  by  engaging  students  in  the  construction   and  comparison  of  different  representations  of   In  recognition  of  these  shortcomings,  the  recently   physical  phenomena.6,7  Each  modeling  cycle  is   published  National  Research  Council's  (NRC)   built  on  a  set  of  modules;  these  modules  promote   framework  for  next-­‐generation  K-­‐12  science   scientific  thinking  through  observation,   standards  lists  “computational  thinking”  as  one  of   experimentation,  and  discourse.  By  observing   the  fundamental  “practices”  that  should  be   physical  phenomena,  representing  those   incorporated  into  future  K-­‐12  science  curricula.1   phenomena  in  a  variety  of  ways,  and  making   The  framework  acknowledges  that  experience   with  computational  thinking  is  crucially  important,   predictions  of  similar  but  not-­‐yet-­‐observed   phenomena,  students  construct  a  working  model   not  only  for  developing  future  scientists  and   that  is  able  to  fully  describe  the  phenomena  they   engineers,  but  also  for  providing  all  citizens  with   observe.  A  full  description  of  the  modeling  cycle  is   general  insight  into  the  science  behind  proposed   available  in  Refs.  6  and  7.  Because  of  its  emphasis   solutions  to  technically  co