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## Problem Solving and Teamwork: Engagement in Real World Mathematics Problems

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Title: 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
• 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 womens 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/lo
gic development
• Computer Tools Excel/MATLAB

11
Factory Layout MEA
• The general manager of a metal fabrication
• 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?
• 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
15
Team Effectiveness Scale
• Student-reported questionnaire to measure team
functionality
• 25-item Likert scale
• Given immediately following MEA
• Internal reliability measured
• Cronbachs Alpha gt 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 clients 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
• 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_at_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