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 ft 2 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. Interventions and Relationships Team Functioning MEA Performance Observations Team Effectiveness Scale MEA Reflection Team Function Rating MEA Team Response Response Quality Score Quality Assurance Guide Is there a connection?

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? Performance Level How useful is the product? 1Requires redirection The product is on the wrong track. Working longer or harder won’t work. 2Requires major extensions or revisions The product is a good start toward meeting the client’s needs, but a lot more work is needed to respond to all of the issues. 3Requires only minor editing The product is nearly ready to be used. It still needs a few small modifications, additions or refinements. 4Useful for this specific data given No changes will be needed to meet the immediate needs of the client, but this is not generalizable to new but similar situations. 5Sharable or reusable The tool not only works for the immediate situation, but it also would be easy for others to modify and use it in similar situations.

18. Preliminary Results 11 student teams observed Correlation of rankings of: 1. 11 teams self-reporting ranking 2. 11 observation score ranking 3. 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. 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. 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 engineering education 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.