Algebra  Readiness    for  Every  Student  

NCTM  Interac:ve  Ins:tute  for  Grades  6-­‐8  July  20-­‐22,  2015  

Trena  L.  Wilkerson  Professor,  Mathema:cs  Educa:on  

Baylor  University  Trena_Wilkerson@baylor.edu  

NCTM  Board  of  Directors  

Post  Cards  with  a  View!  

•  As  you  enter  look  through  the  postcards  and  find  one  that  indicates  how  you  view  yourself  as  a  mathema9cs  teacher  leader.  

AND  THEN  •  Select  another  that  describes  something  fun  about  yourself  as  an  individual!    

•  Have  fun  geCng  to  know  one  another!  •  We  will  start  at  9  a.m.  

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Algebra  Readiness    for  Every  Student  

NCTM  Interac:ve  Ins:tute  for  Grades  6-­‐8  July  20-­‐22,  2015  

Trena  L.  Wilkerson  Professor,  Mathema:cs  Educa:on  

Baylor  University  Trena_Wilkerson@baylor.edu  

NCTM  Board  of  Directors  

Schedule  Overview  

•  Welcome  &  Goals  •  Focused  ½  day  on  professional  development  •  Daily  Reflec9on  Sessions  

– Monday:  Immediately  following  the  Ins9tute  •  4:30-­‐5:30  p.m.  

– Tuesday:  Immediately  following  the  Ins9tute  •  4:30-­‐5:15  p.m.  

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Who  we  are!  

•  Briefly  introduce  yourselves  at  your  tables.  – Name,  role,  Purpose  in  being  here  

•  Share  both  postcards  with  group  at  your  table.  •  As  a  group—be  prepared  to  share  one  observa9on  (interes9ng  thing)  with  the  whole  group  

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Algebra  Ins:tute’s  Goals  1.  gain  strategies  to  build  the  founda:on  of  knowledge  and  skills  that  lead  to  

students'  future  success  in  algebra;    2.  use  Principles  to  Ac.ons  as  a  tool  for  learning  new  instruc:onal  techniques  for  

posing  purposeful  ques9ons,  engaging  students  in  produc9ve  discourse,  and  building  student  responsibility  within  the  community  of  learners;  

3.  learn  strategies  for  implemen9ng  tasks  that  promote  reasoning  and  problem  solving  and  provide  all  students  with  opportuni9es  to  develop  strong  algebraic  reasoning  skills,  including  the  development  of  conjectures  and  generaliza9ons;  

4.  determine  the  role  of  the  Standards  for  Mathema:cal  Prac:ce  in  instruc9onal  strategies  and  assessments;  and  

5.  understand  how  concepts  within  mul9ple  domains  of  the  Common  Core  State  Standards  support  algebraic  reasoning.    

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PD  Strand  Goals  

•  Examine  models  of  professional  development  that  support  teachers  as  learners,  teachers  as  teachers,  and  teachers  as  reflec9ve  prac99oners  

•  Develop  lens  for  Ins9tute  par9cipa9on  for  professional  development  focus  

•  Make  plans  for  developing  professional  development  to  address  the  Algebra  Ins9tute’s  focus  

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PD  Strand  Ac:vi:es  

•  Engage  in  non-­‐rou9ne  mathema9cal  problem(s)  •  Examine  student  work  and  role  in  PD  •  Discuss  evidence  of  mathema9cal  prac9ces  •  Iden9fy  student  and  teacher  misconcep9ons  •  Analyze  various  professional  development  models  for  implementa9on  

•  Consider  lens  for  par9cipa9ng  in  the  ins9tute  to  support  development  of  PD  

•  Develop  PD  plan  8  

Content  Progression  

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! ! ! !!6th!Grade!

!Writing!expressions!with!!a!focus!on!variable!

!

!Solving!equations!using!!multiple!techniques!

!

!Graphing!relationships:!focus!!on!multiple!representations!

!7th!Grade!

!Writing!expressions!with!a!focus!!

on!variable!behavior!and!quantitative!relationships!

!Solving!equations!using!!multiple!techniques!

Graphing!relationships:!focus!!on!multiple!representations,!

proportional!and!!non?proportional!contexts!

!8th!Grade!

!Writing!expressions!and!equations!

!

!Solving!systems!of!equations!using!multiple!strategies!

!!!

!Graphing!relationships!with!a!focus!on!slope!and!transformations!

!

Ques:ons  to  Consider  

•  How  do  you  lead  teachers  to  engage  in  Algebraic  Readiness?  

•  What  type  of  professional  development  will  work  best  in  your  situa9on?  

•  What  type  of  leadership  model  will  be  beneficial  to  implement?  

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Brainstorming!  

•  Small  Group  Discussion    – What  types  of  professional  development  models  do  you  currently  use  and/or  have  some  knowledge  of?    

– List  on  paper  at  table  •  Share  with  whole  group  

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Types  of  PD  Models  

•  Lesson  Study  •  Ac9on  Research  •  Analysis  of  Student  Work  •  Coaching  •  PLCs  •  Grade  Level  Teams  •  Co-­‐Teaching  •  Train-­‐the-­‐Trainer    

•  Workshop  Model  •  Partnership  (ex.  HE)  •  Mathema9cs  Teacher  Circle  •  Book  Study  •  On-­‐line  Op9ons  •  Problem  Solving  •  Case  Study  Analysis  

–  “Studio”  Time  

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Iden:fying  Considera:ons  

•  What  are  specific  considera9ons  that  you  believe  you  have  to  address  or  think  about  as  you  begin  to  consider  professional  development  planning  (i.e.  dura9on  and  9ming)    

•  Discuss  in  small  groups  then  share  whole  group  

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Iden:fy  their  Considera:ons  

•  Type  &  Dura9on  (Long  term  &  On-­‐going)  

•  Timing  (Amer  school,  summer,  during  school  day)  

•  Suppor9ng  tools  •  Grade  level  configura9ons  •  Par9cipants  (resource  teachers,  others)  •  Resources  needed  •  Administra9ve  Support  needed  •  Assessing  need  and  impact  •  Effec9ve  Facilita9on  14  

CCSS-­‐M  Mathema:cal  Prac:ces  Represent  what  students  are  doing  as  they  learn  mathema:cs  

•  Make  sense  of  problems  and  persevere  in  solving  them.  •  Reason  abstractly  and  quan9ta9vely.  •  Construct  viable  arguments  and  cri9que  the  reasoning  of  •  others.  •  Model  with  mathema9cs.  •  Use  appropriate  tools  strategically.  •  Apend  to  precision.  •  Look  for  and  make  use  of  structure.  •  Look  for  and  express  regularity  in  repeated  reasoning.  

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Mathema:cs  Teaching  Prac:ces  (NCTM,  PtA  2014,  p.  10)  

1.  Establish  mathema9cs  goals  to  focus  learning.  2.  Implement  tasks  that  promote  reasoning  and  problem  

solving.  3.  Use  and  connect  mathema9cal  representa9ons.  4.  Facilitate  meaningful  mathema9cal  discourse.  5.  Pose  purposeful  ques9ons.  6.  Build  procedural  fluency  from  conceptual  understanding.    7.  Support  produc9ve  struggle  in  learning  mathema9cs.  8.  Elicit  and  use  evidence  of  student  thinking.  

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Candy  Jar  Problem  

17   Principles to Actions: Ensuring Mathematical Success for All, NCTM 201, p. 314

1.  5 minutes to work individually 2.  8 minutes to share at table (various approaches) 3.  8 minutes to record different strategies to post on wall

Candy  Jar  Problem-­‐Sample  Student  Answers  

•  260  •  360  •  40  •  26  •  340  •  50  •  240  •  270  •  I  do  not  know  

•  2600  •  65  •  100  •  38.14  •  82.3  •  30  •  87  •  250  •  I  do  not  understand  18  

•  108  •  325  •  35  

•  61  •  6.9  

•  38  •  160  •  13  

•  20  •  36  •  7  R  9  

•  50/50  •  Less  than  78  

but  more  than  

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Examining  Mathema:cal  Teaching  Prac:ces  (MTP)  

•  Small  group  ac:vity  •  A  Lens  for  Viewing  the  Algebra  Readiness  Ins.tute  Ac.vi.es  

•  Considera9ons  for  Professional  Development  •  Each  table  is  assigned  2  of  4  targeted  MTPs  to  analyze  around  two  areas  –  Iden:fy  the  key  elements  or  considera:ons  of  your  assigned  MTP  

– Analysis  of  the  Mathema:cal  Task      19  

Mathema:cs  Teaching  Prac:ces  (NCTM,  PtA  2014,  p.  10)  

•  #1  Establish  mathema9cs  goals  to  focus  learning.  

•  #3  Use  and  connect  mathema9cal  representa9ons.  

•  #6  Build  procedural  fluency  from  conceptual  understanding.    

•  #8  Elicit  and  use  evidence  of  student  thinking.  

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Gallery  Walk-­‐Focus    

•  In  what  way  is  this  MTP  important  to  you  when  considering  the  focus  of  professional  development  for  your  teachers  around  the  Algebra  Ins9tute  ideas?  – Take  post  it  notes,  one  copy  of  PtA  per  group,  way  to  record  group’s  ideas  

– 3  minutes  at  each  MTP  – Brief  whole  group  sharing  follows  

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•  hpp://www.nctm.org/Conferences-­‐and-­‐Professional-­‐Development/Professional-­‐Development-­‐Resources/  

•  hpp://www.nctm.org/PtAToolkit/    

 

NCTM  New  PD  Resources-­‐MTPs  

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Planning  PD-­‐Planning  Sheet  

•  Algebra  Readiness  Goal(s)-­‐Content  &  Process    

•  Type(s)  of  PD  •  Audience/Par9cipants  •  Timeline/Time  Allotment  •  Support  Needed  •  Resources  &  Funding  needed  

•  Assessment  &  Evalua9on  Process  

•  Poten9al  Obstacles,  Barriers,  or  challenges  

•  Ways  to  Address  (above)  •  Targeted  Principle(s)  (from  PtA)  

•  Targeted  MTP  (from  PtA)  •  BACK  PAGE:  Next  steps  &  other  thoughts  

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PD  Strand  Goals-­‐Revisited  

•  Examine  models  of  professional  development  that  support  teachers  as  learners,  teachers  as  teachers,  and  teachers  as  reflec9ve  prac99oners  

•  Develop  lens  for  Ins9tute  par9cipa9on  for  professional  development  focus  

•  Make  plans  for  developing  professional  development  to  address  the  Algebra  Ins9tute’s  focus  

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Disclaimer The National Council of Teachers of Mathematics is a public voice of mathematics education, providing vision, leadership, and professional development to support teachers in ensuring equitable mathematics learning of the highest quality for all students. NCTM’s Institutes, an official professional development offering of the National Council of Teachers of Mathematics, supports the improvement of pre-K-6 mathematics education by serving as a resource for teachers so as to provide more and better mathematics for all students. It is a forum for the exchange of mathematics ideas, activities, and pedagogical strategies, and for sharing and interpreting research. The Institutes presented by the Council present a variety of viewpoints. The views expressed or implied in the Institutes, unless otherwise noted, should not be interpreted as official positions of the Council.

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Algebra  Readiness  Ins:tute  

•  Thank  you!  Enjoy  the  ins9tute!  •  Keep  your  PD  plan  in  mind.  

– See  you  at  4:30  today  and  tomorrow  as  well!  

•  Access  the  electronic  resources  – Bibliography  of  resources  for  different  types  of  PD  – TCM  &  MTMS  ar9cles  – PowerPoint  and  handouts  

•  Feel  free  to  ask  ques9ons  any9me!  – Trena_Wilkerson@baylor.edu    

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Facilitate  Meaningful    Mathema9cal  Discourse  

Effec9ve  teaching  of  mathema9cs  facilitates  discourse  among  students  to  build  shared  understanding  of  mathema9cal  ideas  by  analyzing  and  comparing  student  approaches  and  arguments.  

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5  Prac:ces  for  Facilita:ng  Mathema:cal  Discourse  (Smith  &  Stein  2011)  

1.  An9cipa9ng  student  responses  prior  to  the  lesson  2.  Monitoring  students’  work  on  and  engagement  

with  the  tasks  3.  Selec9ng  par9cular  students  to  present  their  

mathema9cal  work  4.  Sequencing  students’  responses  in  a  specific  order  

for  discussion  5.  Connec9ng  different  students’  responses  and  

connec9ng  the  responses  to  key  mathema9cal  ideas  

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Student  Work  Analysis  

•  Using  the  student  work  sample(s)  provided  determine  what  order  you  would  sequence  them  for  Meaningful  Mathema.cal  Discourse  (MTP  #4  pages  29-­‐35  in  PtA  2014)    in  the  classroom  and  why.  –  14  Different  Student  Work  Samples  – May  not  necessarily  use  all  

•  If  9me  permits,  discuss  how  you  would  guide  students  during  their  work  9me—par9cularly  those  that  seemed  to  struggle-­‐incorrect  answers  

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