Problem Solving and Teamwork: Engagement in Real World Mathematics Problems

1. Problem Solving and Teamwork: Engagement in Real World Mathematics Problems Tamara J. Moore Purdue University February 8, 2006

2. Background and Research Interests • High School Mathematics Teacher • Mathematics in Context • Problem Solving • Engineering Classroom Research

3. What are Model-Eliciting Activities? • MEAs are authentic assessment activities that are open-ended with a fictitious client • Connect mathematical modeling to other fields • Elicit students thinking in the process of solving - Product is process • Require teams of problem solvers

4. Characteristics of MEAs • Require the design of a “novel” procedure or model to solve a problem for a real world client • Students adapt problem to their level • Incorporate self-assessment principle – students should judge based on experience/knowledge whether procedure is right

5. What Makes MEAs Different? • Iterative Design Process • Students go through multiple modeling cycles • Reading, Writing, and Presentations • Teacher Development • Assess mathematical ideas and abilities that are missed by standardized tests alone

6. What Makes MEAs Different? • Connections with Other Fields • Foundations for the Future – Lesh, Hamilton, Kaput, eds. (in press) • Multidisciplinary approaches to mathematics instruction • Each MEA addresses multiple mathematics principles and standards

7. SGMM Project • Small Group Mathematical Modeling for Gender Equity in Engineering • Increase women’s perseverance and interest in engineering via curriculum reform initiatives • Examine experiences of women in engineering in general and within the first-year specifically • Investigate engineering at first-year level

8. Lessons from SGMM • How MEAs Have Helped • Change the way faculty think about their teaching & learning environments • Increase student engagement: addressing diversity • Meaningful engineering contexts representing multiple engineering disciplines • Framework for constructing highly open-ended engineering problems • Require mathematical model development • Support development of teaming and communication skills

9. Research Questions • What relationship exists between student team functioning and performance on Model-Eliciting Activities? • What are the correlations between Model-Eliciting Activity performance and student team functioning?

10. Setting • ENGR 106: Engineering Problem Solving and Computer Tools • First-year introductory course in engineering • Problem Solving – Mathematical Modeling • Teaming • Engineering Fundamentals – statistics/economics/logic development • Computer Tools – Excel/MATLAB

11. Factory Layout MEA The general manager of a metal fabrication company has asked your team to write a memo that: • Provides results for 122,500 ft2 square layout • Total distance and order of material travel for each product • Final department dimensions • Proposes a reusable procedure to determine any square plant layout that takes spatial concerns and material travel into account

12. Teaming • What are teams? • Task-oriented • Interdependent social entities • Individual accountability to team • Why encourage teaming? • Research indicates student participation in collaborative work increases learning and engagement • Accreditation Board for Engineering and Technology (ABET) • Demand from industry

13. Purpose of the Study • Investigate relationships between: • student team functioning • team performance on Model-Eliciting Activities

14. Team Functioning MEA Performance Observations MEA Team Response Team Effectiveness Scale Quality Assurance Guide Is there a connection? MEA Reflection Team Function Rating Response Quality Score Interventions and Relationships

15. Team Effectiveness Scale • Student-reported questionnaire to measure team functionality • 25-item Likert scale • Given immediately following MEA • Internal reliability measured • Cronbach’s Alpha > 0.95 (N ~ 1400) • Subscales • Interdependency, Potency, Goal Setting, and Learning

16. Researcher Observations • Observation of one group per lab visited • Based on teaming literature • Interdependency – 3 items • Potency – 2 items • Goal Setting – 2 items • Teams received 1-5 score for 7 items • Detailed field notes also taken

17. Quality Assurance Guide Does the product meet the client’s needs?

18. Preliminary Results • 11 student teams observed • Correlation of rankings of: • 11 teams self-reporting ranking • 11 observation score ranking • Aggregate score ranking With the MEA Quality Score

19. Preliminary Results • MEA Quality Score vs.11 teams self-reporting ranking • Pearson – coefficient is -0.543 • Not statistically significant at a 0.05 level (2-tailed correlation) • Moderate degree of correlation

20. Preliminary Results

21. Preliminary Results • MEA Quality Score vs.11 teams observed ranking • Pearson – coefficient is -0.555 • Not statistically significant at a 0.05 level (2-tailed correlation) • Moderate degree of correlation

22. Preliminary Results

23. Preliminary Results • MEA Quality Score vs. Aggregate Team score ranking • Pearson – coefficient is -0.792 • Statistically significant at a 0.01 level (2-tailed correlation) • Marked degree of correlation

24. Preliminary Results

25. Preliminary Findings • Preliminary data suggests that • More work is needed in having students understand how to self-assess their teaming abilities • Research is needed to understand which of the team functioning categories are most important – especially in the observer rankings

26. Next Steps • 4 MEAs total – 100 teams per MEA • Use teaming instruments to assess team functioning – create an aggregate score • TA Observations, Team Effectiveness Scale, MEA Reflection • Look for correlation among team functionality and MEA Quality Score • 4 case studies • Collective case study

27. Significance of the Study • Answers fundamental question: • Does team functionality affect team performance? • Leads to other research questions • Which characteristics of teaming are more likely to create better solutions? • How are these team attributes best fostered in the classroom? • Contributes to the discussion on ABET and the role of teaming and problem solving in undergraduate engineeringeducation and points to NCTM Standards

28. Possible Future Directions • STEM context MEAs in secondary classrooms • How do MEAs help students progress in the NCTM Standards? • To what extent does the use of MEAs encourage female students (all students) to pursue STEM fields? • What are the correlations between teaming and MEA solution quality at the secondary level?

29. Possible Future Directions • STEM context MEAs in secondary classrooms • How do secondary students’ abilities to model mathematically complex situations compare to freshman engineering students? • What are the kinds of mathematics that each class of students use in order to solve complex modeling problems?

30. Possible Future Directions Virtual Field Experiences • Video conferencing between universities, professionals, and K-12 classrooms • Emphasis on technological tools that enhance small-group and problem-based learning (MEAs) • “Client” – Team interactions

31. Questions? • To contact me: Tamara Moore tmoore@purdue.edu

32. References • Diefes-Dux, H. A., Follman, D., Imbrie, P. K., Zawojewski, J., Capobianco, B., & Hjalmarson, M. A. (2004). Model eliciting activities: An in-class approach to improving interest and persistence of women in engineering. Paper presented at the ASEE Annual Conference and Exposition, Salt Lake City, UT. • Guzzo, R. A. (1986). Group decision making and group effectiveness. In P. S. Goodman (Ed.), Designing effective work groups (pp. 34-71). San Francisco, CA: Jossey-Bass. • Guzzo, R. A., Yost, P. R., Campbell, R. J., & Shea, G. P. (1993). Potency in groups: Articulating a construct. British Journal of Social Psychology, 32(1), 87-106. • Lesh, R., Byrne, S.K., & White, P.A. (2004). Distance learning: Beyond the transmission of information toward the coconstruction of complex conceptual artifacts and tools. In T. M. Duffy and J. R. Kirkley (Eds.), Learner-centered theory and practice in distance education: Cases from higher education. (pp. 261-282). Mahwah, NJ: Lawrence Erlbaum and Associates. • Lesh, R. A., & Doerr, H. (Eds.). (2003). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum. • Lesh, R. A., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In Handbook of research design in mathematics and science education (pp. 591-645). Mahwah, NJ: Lawrence Erlbaum. • Johnson, D. W., Johnson, R. T., Holubec, E. J., & Roy, P. (1986). Circles of learning: Cooperation in the classroom (revised ed.). Edina, MN: Interaction Book Company. • Zawojewski, J., Bowman, K., Diefes-Dux, H.A. (Eds.). (In preparation) Mathematical Modeling in Engineering Educating Designing Experiences for All Students.