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
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Elicit students thinking in the process of solving Product is process
Require teams of problem solvers

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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

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 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

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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

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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 firstyear specifically
Investigate engineering at first-year level

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

 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?

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

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
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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

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

 Investigate relationships between:
 student team functioning
 team performance on Model-
Eliciting Activities

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

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

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Observation of one group per lab visited
Based on teaming literature
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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?
How useful is the product?
Performance
Level
1 Requires redirection
2 Requires major extensions or revisions
3 Requires only minor editing
4 Useful for this specific data given
5 Sharable or reusable
The product is on the wrong track. Working longer or harder won’t work.
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.
The product is nearly ready to be used. It still needs a few small modifications, additions or refinements.
No changes will be needed to meet the immediate needs of the client, but this is not generalizable to new but similar situations.
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.

 11 student teams observed
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1.
2.
3.
Correlation of rankings of:
11 teams self-reporting ranking
11 observation score ranking
Aggregate score ranking
With the MEA Quality Score

 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

MEA Score vs. Self-Reported Team Rank
5
4
3
2
R
2
= 0.29
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12
Self-Reported Team Rank

 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

MEA Score vs. Observed Team Rank
5
4
3
2
R
2
= 0.31
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12
Observed Team Rank

 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

MEA Score vs. Aggregate Teaming Rank
5
4
3
R
2
= 0.63
2 m
1
0
0 1 2 3 4 5 6 7 8 9 10 11 12
Aggregate Team Effectiveness Rank

 Preliminary data suggests that
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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

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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
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4 case studies
Collective case study

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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

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STEM context MEAs in secondary classrooms
How do MEAs help students progress in the NCTM Standards?
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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?

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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?

Virtual Field Experiences
 Video conferencing between universities, professionals, and K-12 classrooms
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Emphasis on technological tools that enhance small-group and problembased learning (MEAs)
“Client” – Team interactions

 To contact me:
Tamara Moore tmoore@purdue.edu

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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.
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