Problem Solving and Teamwork: Engagement in Real World Mathematics Problems Tamara J. Moore Purdue University February 8, 2006.

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

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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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2

3

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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

Questions?

To contact me:

Tamara Moore

[email protected]

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 teachers. In Handbook of research design in mathematics and science education (pp. 591-645). Mahwah, NJ: Lawrence Erlbaum.

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Zawojewski, J., Bowman, K., Diefes-Dux, H.A. (Eds.). (In preparation) Mathematical Modeling in Engineering Educating Designing Experiences for All Students.