How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc!...

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One Way to Overcome the Math Barrier with NonSTEM Majors How My Students Determined the Fate of the Universe Steve Cederbloom University of Mount Union

Transcript of How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc!...

Page 1: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

ì  

One  Way  to  Overcome  the  Math  Barrier  with  Non-­‐STEM  Majors  

How  My  Students  Determined  the  Fate  of  the  Universe  

                           Steve  Cederbloom  University  of  Mount  Union  

Page 2: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Outline  

ì  The  challenge  

ì  A  framework  for  meeDng  the  challenge  

ì  My  soluDon  

ì  New  exploraDons  

Page 3: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

The  challenge  

ì  A  course  for  the  “IntegraDve  Core”  –  “Einstein’s  Universe:    The  Big  Bang,  Black  Holes,  and  Beyond”  

ì  Cosmology  is  an  observa(onal  science,  not  an  experimental  science  

ì  How  do  I  get  students  to  DO  cosmology?  

Page 4: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Authentic  science  practice  in  the  classroom    (Edelson,  1997)  

ì  APtudes  

ì  Tools  and  techniques  

ì  Social  interacDons  

Page 5: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Why  is  Inquiry  Inherently  Difficult?  

ì  “The  GePng  on  Board  Problem”  (Meyer  and  Avery,  2010)  ì  ObservaDons  generate  the  need  to  describe,  

organize,  and  explain  ì  The  resulDng  paradigm  suggests  new  observaDons  

to  make  

Page 6: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Why  is  Inquiry  Inherently  Difficult?  

ì  “The  GePng  on  Board  Problem”  (Meyer  and  Avery,  2010)  

Empirical  data   TheoreDcal  knowledge  

Page 7: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Why  is  Inquiry  Inherently  Difficult?  

ì  “The  GePng  on  Board  Problem”  (Meyer  and  Avery,  2010)  ì  ObservaDons  generate  the  need  to  describe,  

organize,  and  explain  ì  The  resulDng  paradigm  suggests  new  observaDons  

to  make  

ì  How  do  you  break  into  this  cycle?  ì  New  Ph.D  students  start  by  joining  ongoing  work  of  

mentors  

Page 8: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

A  framework  for  meeting  the  challenge  

ì  Choose  a  topic  for  the  students  to  explore  ì  The  expansion  of  the  universe  

ì  Choose  the  tools  to  use  ì  Euler’s  method  ì  Excel  

ì  Backwards  design  -­‐  scaffolding  

Page 9: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Scaffolding  

ì  Making  a  graph  ì  Using  only  data  at  first  ì  Using  equaDons  also  

ì  EquaDons  in  Excel  ì  Cell  addresses  ì  Copy  and  drag  ì  SePng  up  constants  

ì  Trendlines  and  slopes  

Page 10: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

The  topic  

The  universe  is  expanding    The  curvature    is  linked  to  its  history  &  desDny  

Page 11: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

The  “scale  factor”  of  the  Universe,  R,  is  governed  by  the  Friedmann  equaDon:  

Page 12: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

SoluDons  tell  us  the  possible  history  of  the  Universe  

•  Depend  on  amounts  of  ma_er,  radiaDon,  dark  ma_er,  &  dark  energy  

Page 13: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna
Page 14: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

The  “scale  factor”  of  the  Universe,  R,  is  governed  by  the  Friedmann  equaDon:  

ρ  changes  according  to  conservaDon  laws  

Page 15: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Start  with  V  and  change  to  slope:  

1! !

!= !8!"3 ! − !!!

!

!! + !Λ3!

1RΔRΔt

"

#$

%

&'2

=8πG3

ρ −kc2

R2+Λ3

Page 16: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Euler’s  method  

ΔRΔt

=R2 − R1t2 − t1

R2 = R1 +ΔRΔt

t2 − t1( )

Page 17: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Start  with  “Now”  

Page 18: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Type  in  equations  for  one  time  step  

Page 19: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

The  past    

Page 20: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

The  future  and  the  past  

Page 21: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

New  explorations  –  two  dimensions  

ì  Can  these  histories  lead  the  students  to  new  quesDons?    

ì  Are  there  other  quesDons  that  students  could  invesDgate  with  these  tools  and  techniques?  

Page 22: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

Embedding  diagrams  

Page 23: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna
Page 24: How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc! Science!Learning!Through!the!AdapDon!of! Sciencfic !PracDce. In!K.!Tobin!&!B.!Fraser!(Eds.),!! Interna

References  

ì  Edelson,  Daniel  C.  (1997).    Realising  AuthenDc  Science  Learning  Through  the  AdapDon  of  SciencDfic  PracDce.    In  K.  Tobin  &  B.  Fraser  (Eds.),    Interna(onal  Handbook  of  Science  Educa(on.  Kluwer,  Dordrecht,  NL.    

ì  Meyer,  Daniel  Z.  &  Avery,  Leanne  M.  (2010).    Why  Inquiry  is  Inherently  Difficult…and  Some  Ways  to  Make  it  Easier.  Science  Educator,  19(1),    26-­‐32.