Mathematical Problem Solving and Persistence
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Mathematical Problem Solving and Persistence

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Mathematical Problem Solving and Persistence Mathematical Problem Solving and Persistence Presentation Transcript

  • Exploring How Complex Instruction Affects  Mathematical Problem Solving Persistence Presentation by Marilyn Gilman  March 13, 2010  
  • Why is Persistence in  Mathematical Problem Solving   Important?  Real World  Problems  Achievement Tests  Creative  Persistence   
  • Research on Problem Solving   Schooling Effects (Schoenfeld, TIMMS)    Metacognitive Factors (Francisco & Maher) − Self­regulation − Ownership of strategies − Collaboration may improve metacognition  Affective Factors (Goldin & DeBellis, Jansen)  − Feelings and attitudes − Peer pressure   
  • Complex Instruction  Challenging Tasks   Peer Collaboration  Status & Accountability Developed by Elizabeth Cohen (1994)    
  • Complex Instruction Research  Two Studies Problem Solving Student Motivation  Successful at long   Students adopted  application tasks goal orientation   Students report  towards learning persistence is key   More persistence to  to math success face obstacles  (Boaler & Staples, 2008)   (Ben­Ari & Eliassy, 2003)
  • How does Complex Instruction Affect  Students Mathematical Problem Solving  Persistence? A Comparison of Two Classes Six classroom observations Teacher Interview Two mathematical tasks Observations Written Work Two questionnaires   
  • Study Participants Complex Instruction       Comparison      Class Class  42% school met math   55% school met math  WASL in 2008 WASL in 2008  51% low income  30% low income  Mixed ability students  Mixed ability students Both Classes:  Same curriculum, experienced teacher, 26 students,   mostly White, one or two English Language Learners  
  • Two Distinct Learning Experiences  Mathematical Task Complexity and Time  Mathematical Discussion   Accountability and Autonomy  
  • Comparison Class  Low­complexity   math problems  Short work time   Little mathematical  discourse  Individual work and  accountability   
  • Complex Instruction Class  Complex problems   Long work time  Rich mathematical  discourse  Group and  individual work  Group & individual   accountability  
  • Two Problem Solving Tasks and Questionnaires  Pairs for  problems   Surveys      individually
  • What differences were found in students  problem solving persistence between the  two classes?   Time necessary for a difficult problem  Performance while working on tasks    Mathematical strategies used   
  • A Diagram Only Solution   
  • Multiple Strategies   
  • Strategies and Correct Solutions as Indicators  of Problem Solving Persistence   Number of Groups with Correct* Solutions for the Second Research Task Four  Three  One  Diagram Only  No Correct Total Classes Two Solutions Solutions Solutions Solution Solution** Solutions Groups Complex  4 1 1 3 3 0 12 Instruction Class Comparison  1 0 0 4 3 3 11 Class   * Correct solutions used at least two mathematical strategies to explain how a solution was accurate or not accurate. ** Diagrams Only indicate students drew an accurate diagram but, didnt explain the diagram in any way  Number of Strategies used by Student Groups  TASK ONE TASK TWO Number of  Complex   Comparison   Complex  Comparison Strategies Used Instruction Class Instruction  Class None 0 0 0 1 One 2 2 1 2 Two 6 6 0 3 Three 2 2 7 4 Four 3 1 3 1 Five 0 0 1 0 Total  Groups 13 11 12 11 Strategies used: calculations, counting boxes, counting columns,     diagrams, written verbal explanations, formulas, labels,  measurements, patterns
  • Complex Instruction: A Promising Practice Confirms Boaler & Staples (2008) findings  Alternative explanations & limits of the study  
  • Questions? For a copy of the study contact me at: marilyngilman1@gmail.com