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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

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
  • Each MEA addresses multiple mathematics
    principles and standards

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

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

Research Questions
  • What relationship exists between student team
    functioning and performance on Model-Eliciting
  • What are the correlations between Model-Eliciting
    Activity performance and student team

  • 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

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

  • 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
  • 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 Effectiveness Scale
  • Student-reported questionnaire to measure team
  • 25-item Likert scale
  • Given immediately following MEA
  • Internal reliability measured
  • Cronbachs Alpha gt 0.95 (N 1400)
  • Subscales
  • Interdependency, Potency, Goal Setting, and

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 clients needs?
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

Preliminary Results
  • MEA Quality Score vs.11 teams self-reporting
  • Pearson coefficient is -0.543
  • Not statistically significant at a 0.05 level
    (2-tailed correlation)
  • Moderate degree of correlation

Preliminary Results
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
Preliminary Results
  • MEA Quality Score vs. Aggregate Team score
  • Pearson coefficient is -0.792
  • Statistically significant at a 0.01 level
    (2-tailed correlation)
  • Marked degree of correlation

Preliminary Results
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
  • 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
  • To what extent does the use of MEAs encourage
    female students (all students) to pursue STEM
  • 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

  • To contact me
  • Tamara Moore

  • 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.