Group Size in Mathematical Problem Solving

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Group Size in Mathematical Problem Solving

• Action Research
• Conducted By Stephanie Williamson
• UNC-Asheville Education Dept.
• Tuesday November 29, 2005

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About the Project

• My Question Does Group Size influence students
  problem solving abilities in math class?

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Research

• Polya- Problem solving
• Constructivism
• Piaget
• Vygotsky

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Study Design

• North Carolina public rural middle school
• Study lasted four weeks
• 6th grade math class

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Instruments Used

• Pre- Survey
• Daily questionnaire
• Post Survey
• Journal

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Pre-Survey

• Given the day before research period began
• Five question agree or disagree survey

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(No Transcript)
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Daily Questionnaire

• Given Daily
• Five questions
• What size group?
• Used a strategy?
• Come up with a solution?
• Was the solution correct?
• Rate you problem solving experience today.

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Post-Survey

• Given the after the research period ended
• Five question agree or disagree survey, same
  survey as pre-survey

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Pre compared to Post
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Conclusions

• Majority of students preferred to work in small
  groups
• Working in groups did increase the number of
  answers students came up with and also the number
  of correct answers.
• Thus, group size does influence students problem
  solving abilities in math class!!
• Best to use a variety of both, see what would
  best meet the needs of your students.

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Recommendations Future Ideas

• Longer time period
• Have a control group
• Use more than one class
• Look at gender differences in group size
  preferences
• Look at learning styles in relation to group size
  preferences
• I will definitely incorporate small group
  learning for problem solving in my own classroom.

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Citations

• Blumenfeld, P., R. Marx, E. Soloway, J.
  Krajcik. (1996). Learning with peers From small
  group cooperation to collaborative communities.
  Educational Researcher, 25, 37-40. Retrieved
  February 14, 2005, from JSTOR database.
• Gillies, R. M. (2003). The behaviors,
  interactions, and perceptions of junior high
  school students during small-group learning
  Electronic version. Journal of Educational
  Psychology, 95, p. 137-147.
• Hackman, J., N. Vidmar. (1970). Effects of
  size and task on group performance and member
  reactions. Sociometry, 33, 37-54. Retrieved
  March 2, 2005, from JSTOR database.
• Heartland Area Education Agency II (2003).
  Small-Group Learning. Retrieved February 16,
  2005, from http//www.aea11.k12.ia.us/E2T2/smallgr
  ouplearning.html
• Kroll, L., Masingila J., S. Mau. (1992).
  Cooperative problem solving But what about
  grading? (1992). Arithmetic Teacher. Retrieved
  February 16, 2005, from http//www.enc.org/profess
  ional/learn/research/journal/math/document.shtm?in
  putENC-002228-2228
• Manners, G. (1975). Another look at group size,
  group problem solving, and member consensus.
  Academy of Management Journal, 18, 715-724.
  Retrieved March 2, 2005, from JSTOR database.
• Messemer, C., A. Arora. (2002). Problem-Solving
  in groups. Retrieved March 2, 2005, from
  http//depts.washington.edu/cidrweb/TeachingLearni
  ngBulletin.html
• Mulryan, C. (1994). Perceptions of intermediate
  students cooperative small-group work in
  mathematics. Journal of Educational Research,
  87, 280-292. Retrieved March 2, 2005, from Ebsco
  Host-Academic Search Elite.
• National Council of Teachers of Mathematics.
  (2000).Principles and Standards for School
  Mathematics. Problem Solving Standard for Grades
  6-8. Retrieved September 13, 2004, from
  http//www.unca.edu/nruppert/e-standards/chapter6
  /prob.htm
• Peterson, S., J. Miller.(2004). Comparing the
  quality of students experiences during
  cooperative learning and large-group instruction.
  The Journal of Educational Research, 97, 123-134.
  Retrieved March 2, 2005, from JSTOR database.
• Slavin, R. (1980). Cooperative learning. Review
  of Educational Researcher, 50, 315-342. Retrieved
  March 2, 2005, from JSTOR database.
• Vobejda, B. (1987). A mathematicians research on
  math instruction. Educational Researcher, 16,
  9-12. Retrieved March 2, 2005, from JSTOR
  database.
• Wilson, J. W., M..L. Fernandez, N. Hadaway.
  (1993). Mathematical problem solving. In P. S.
  Wilson (Ed.), Research Ideas for the Classroom
  High School Mathematics (p. 57-78). New York
  MacMillan.

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Questions??
Thank you for coming have a nice day!!!