Transcript Slide 1

Problem Solving and Teamwork:
Engagement in Real World
Mathematics Problems
Tamara J. Moore
Purdue University
February 8, 2006
Background and Research Interests
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High School Mathematics Teacher
Mathematics in Context
Problem Solving
Engineering Classroom Research
What are Model-Eliciting Activities?
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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
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Require the design of a “novel”
procedure or model to solve a problem
for a real world client
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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?
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Iterative Design Process
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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?
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Connections with Other Fields
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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
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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
Lessons from SGMM
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How MEAs Have Helped
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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
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Require mathematical model development
Support development of teaming and communication
skills
Research Questions
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What relationship exists between
student team functioning and
performance on Model-Eliciting
Activities?
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What are the correlations between
Model-Eliciting Activity performance and
student team functioning?
Setting
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ENGR 106: Engineering Problem
Solving and Computer Tools
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First-year introductory course in
engineering
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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
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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
Teaming
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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
Purpose of the Study
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Investigate relationships between:
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student team functioning
team performance on ModelEliciting Activities
Interventions and Relationships
Team Functioning
MEA Performance
Observations
MEA Team
Response
Team Effectiveness
Scale
Is there a
connection?
MEA Reflection
Team
Function
Rating
Quality
Assurance
Guide
Response
Quality
Score
Team Effectiveness Scale
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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
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Interdependency, Potency, Goal Setting, and
Learning
Researcher Observations
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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?
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
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11 student teams observed
Correlation of rankings of:
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3.
11 teams self-reporting ranking
11 observation score ranking
Aggregate score ranking
With the MEA Quality Score
Preliminary Results
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MEA Quality Score vs.11 teams
self-reporting ranking
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Pearson – coefficient is -0.543
Not statistically significant at a 0.05
level (2-tailed correlation)
Moderate degree of correlation
Preliminary Results
MEA Quality Score
MEA Score vs. Self-Reported Team Rank
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4
R2 = 0.29
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2
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Self-Reported Team Rank
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Preliminary Results
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MEA Quality Score vs.11 teams
observed ranking
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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
MEA Quality Score
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R2 = 0.31
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Observed Team Rank
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Preliminary Results
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MEA Quality Score vs. Aggregate
Team score ranking
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Pearson – coefficient is -0.792
Statistically significant at a 0.01 level
(2-tailed correlation)
Marked degree of correlation
Preliminary Results
MEA Quality Score
MEA Score vs. Aggregate Teaming Rank
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R2 = 0.63
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m
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0
0
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Aggregate Team Effectiveness Rank
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12
Preliminary Findings
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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
Next Steps
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4 MEAs total – 100 teams per MEA
Use teaming instruments to assess team
functioning – create an aggregate score
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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
Significance of the Study
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Answers fundamental question:
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Leads to other research questions
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Does team functionality affect team performance?
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
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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
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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?
Possible Future Directions
Virtual Field Experiences
 Video conferencing between
universities, professionals, and K-12
classrooms
 Emphasis on technological tools that
enhance small-group and problembased learning (MEAs)
 “Client” – Team interactions
Questions?
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To contact me:
Tamara Moore
[email protected]
References
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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
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