Comps Presentation

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Comps Presentation

  1. 1. Cooperative Learning and the Transition to Proof A dissertation proposal Martha Byrne University of New Mexico
  2. 2. To what extent can working in aCooperative Learning environmentaffect students’ acquisition anddevelopment of proof skills?
  3. 3. Proof Skills•  Proof Construction•  Proof Validation•  Concept Image (of Proof)•  Attitudes about Mathematics•  Attitudes about Proof
  4. 4. Proof Construction•  Roles of proof –  Dependent on audience –  Proofs that convince vs. Proofs that explain•  Where the students are –  Empirical evidence –  Authoritarian proof schemes Almeida (1995), Harel and Sowder (1998)
  5. 5. Proof Validation•  Structure vs. Detail•  Formal vs. Informal•  Conviction vs. Validity Segal (1999), Selden and Selden (1995, 2003), Powers et. al. (2010)
  6. 6. Concept Image (of Proof)•  Concept Image vs. Concept Definition•  Concept Image of Proof –  Imprecise definition –  Need for examples and non-examples –  Proof process Tall and Vinner (1981), Weber (2001)
  7. 7. Attitudes about Mathematics•  What comes after Calculus?•  Cultural Portrayal
  8. 8. Attitudes about Proof•  Conviction vs. Validity•  Need for Proof•  Lack of Exploration Almeida (2000), Maclane (1994), Sowder and Harel (2003)
  9. 9. Cooperative Learning (CL)•  Positive Interdependence•  Personal Accountability•  Appropriate Grouping•  Student Interaction•  Attention to Social Skills•  Teacher as Facilitator Cooper (1990), Cooper and Robinson (1994), Millis (1992), Springer (1998)
  10. 10. To what extent can working in aCooperative Learning environmentaffect students’ acquisition anddevelopment of proof skills?
  11. 11. The Seminar•  Plan A – Case Studies•  Plan B – Treatment and Control
  12. 12. The Students•  Recruitment Pools•  Majors
  13. 13. The Mathematics•  Sets and Functions•  Michael Nakamaye
  14. 14. The Measures•  Proof Construction•  Proof Validation•  Concept Image•  Attitudes
  15. 15. The Approval•  IRB•  CITI training•  Kristin Umland
  16. 16. The Timeline 2012 – 2012 – 2012 – 2013 -2011 - Fall Spring Summer Fall Spring Sept: Jan: Aug: Jan: July: preliminary materials student recruitment - IRB revision recruitment finalized recruitment control group Nov: Jan: Aug: Aug: Jan: IRB student materials seminar control submission recruitment revision begins seminar Dec: Jan: materials pilot begins draft
  17. 17. Next Steps•  Measures•  Strategies•  Materials•  IRB
  18. 18. Works Cited•  Almeida, D. (1995). Mathematics Undergraduates’ Perceptions of Proof. Teaching Mathematics and Its Applications, 14(4), p. 171-177.•  Almeida, D. (2000). A survey of mathematics undergraduates’ interaction with proof: some implications for mathematics education. International Journal of Mathematical Education in Science and Technology. 31, #6, 869-890.•  Cooper, J. (1990). What is Cooperative Learning? In Cooper, J., Robinson, P., and Ball, D. (Eds.) (2009). Small Group Instruction in Higher Education: Lessons from the Past, Visions of the Future. New Forums Press, Inc.
  19. 19. •  Cooper, J., and Robinson, P. (1994) FIPSE-Sponsored CL Research at Dominguez Hills and Community Colleges. In Cooper, J., Robinson, P., and Ball, D. (Eds.) (2009). Small Group Instruction in Higher Education: Lessons from the Past, Visions of the Future. New Forums Press, Inc.•  Harel, G., & Sowder, L. (1998). Students proof schemes. Research on Collegiate Mathematics Education, Vol. III. In E. Dubinsky, A. Schoenfeld, & J. Kaput (Eds.), AMS, 234-283.•  Millis, B. (1992). How Cooperative Learning Can fullfill the Promises of the "Seven Principles." In Cooper, J., Robinson, P., and Ball, D. (Eds.) (2009). Small Group Instruction in Higher Education: Lessons from the Past, Visions of the Future. New Forums Press, Inc.
  20. 20. •  Powers, R. A., Craviotto, C. & Grassl, R. M. (2010). Impact of proof validation on proof writing in abstract algebra. International Journal of Mathematical Education in Science and Technology, 41(4), 501-514.•  Segal, J. (1999). Learning about mathematical proof: conviction and validity. Journal of Mathematical Behavior, 18, 191-210.•  Selden, A. & Selden, J. (2003). Validations of proofs written as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 36 (1), 4-36.•  Selden, J. and Selden, A. (1995) Unpacking the logic of mathematical statements. Educational Studies in Mathematics, 29(2), 123-151.
  21. 21. •  Sowder L., Harel G. (2003) Case Studies of Mathematics Majors Proof Understanding, Production, and Appreciation Canadian Journal of Science, Mathematics and Technology Education 3(2)•  Springer, L. (1998). Research on Cooperative Learning in College Science, Mathematics, Engineering, and Technology. In Cooper, J., Robinson, P., and Ball, D. (Eds.) (2009). Small Group Instruction in Higher Education: Lessons from the Past, Visions of the Future. New Forums Press, Inc.•  Tall, D. and Vinner, S. (1981) Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, Vol.12 (No.7). pp. 151-169.
  22. 22. •  Weber, K. (2001). Student difficulty in constructing proofs: The need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101-119.

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