problem solving and teamwork: engagement in real world mathematics problems tamara j. moore purdue...
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Problem Solving and Teamwork: Engagement in Real World Mathematics Problems
Tamara J. Moore
Purdue University
February 8, 2006
Background and Research Interests
High School Mathematics Teacher Mathematics in Context Problem Solving Engineering Classroom Research
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
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
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
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
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
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
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?
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
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
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
Purpose of the Study
Investigate relationships between: student team functioning team performance on Model-
Eliciting Activities
Interventions and Relationships
Team Functioning MEA Performance
Observations
Team Effectiveness Scale
MEA Reflection
Team Function Rating
MEA TeamResponse
Response Quality Score
Quality Assurance Guide
Is there a connection?
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
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
Quality Assurance Guide
Does the product meet the client’s needs?
Performance Level
How useful is the product?
1 Requires redirection
The product is on the wrong track. Working longer or harder won’t work.
2 Requires 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.
3 Requires only minor editing
The product is nearly ready to be used. It still needs a few small modifications, additions or refinements.
4 Useful 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.
5 Sharable 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.
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
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
Preliminary Results
MEA Score vs. Self-Reported Team Rank
R2 = 0.29
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Self-Reported Team Rank
ME
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Sco
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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
Preliminary Results
MEA Score vs. Observed Team Rank
R2 = 0.31
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Observed Team Rank
ME
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lity
Sc
ore
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
Preliminary Results
MEA Score vs. Aggregate Teaming Rank
R2 = 0.63
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Aggregate Team Effectiveness Rank
ME
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lity
Sc
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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
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
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
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?
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?
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
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.
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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.
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