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Dissertation Defense: Mathematical Modeling

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Nancy Wolf

on 20 February 2016

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Transcript of Dissertation Defense: Mathematical Modeling

K through 12 teachers of mathematics
Claremont Graduate University
PhD in Education
June 2013

Teachers’ Understanding of
and Concerns about
Mathematical Modeling in the Common Core

Nancy Butler Wolf

Results: Understanding

Variables entering regression equation:
#1: Understanding of Modeling
Contributed 20.05% of the Variance
#2: Information
Contributed 12.57% of the Variance
Factor Analysis
- Most teachers understand modeling
- Most teachers express concerns about "self"
- Teachers are willing to change practice
- Teachers express consensus about needs for implementation
- Teachers have specific needs for professional development
Major findings
- Teachers believe the CCSS will result in increased understanding and achievement

- Teachers are willing to change practice and to incorporate mathematical modeling into practice

- Teachers (especially elementary teachers) need increased content knowledge in mathematics

Key Findings for Districts in Transition
Tell me and I will forget
© Emma Pelaprat-Mason

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© Emma Pelaprat-Mason
Research Questions:
Above chance
performance in
the preferential looking tasks
Above chance
performance in
the preferential looking tasks
"How can it be, then, that so much school reform has taken place over the last century, yet schooling appears to be pretty much the same as it has always been?" (Cuban, 1988, p. 341)

What is the extent of teachers' understanding of the concept of "mathematical modeling" as defined by the CCSS & NCTM?
What are teachers' major concerns and levels of concern regarding their implementation of and instruction in mathematical modeling?
What are the implications for professional development that would best address teachers' needs and concerns in their transition to mathematical modeling?
Common Core Survey Tool
Stages of Concern Survey
Eight standards for
Make sense of problems and
persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and
critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Understanding Mathematical Modeling
Open-ended questions
Levels of Use branching interview
364 Responses
16 Interviews
From 8 Southern California districts
Teachers who agreed they have a clear understanding of mathematical modeling:
69.7%, M = 2.95, SD = .714
Teachers who understand what is involved in implementing mathematical modeling:
66.2%, M = 2.78, SD = .660
Teachers who understand the term "mathematical modeling":
72.4%, M = 2.82, SD = .653
Logistic Regression: Understanding
Professional Development
(B = .884, p = .004, EXP(B) = 2.42)
(B = -.782, p = .049)
#3: Collaboration
Contributed 7.60% of the Variance
#4: Concerns
Contributed 4.01% of the Variance
#5: Time Conflicts
Contributed 3.64% of the Variance
#6: Anticipation
Contributed 3.00% of the Variance

Predicting Membership in groups (yes/no) Understanding of mathematical modeling
Stages of Concern Instrument
Stage of Concern: Multiple Regression & t test
Multiple regression to predict Stage of Concern based upon demographic variables: Age, gender, teaching experience, highest level of education.
Only one variable entered regression equation:
Gender (Beta = -1.33, t = -2.407, Sig t = .017)
t test for independent groups: Stage of Concern higher for men (M = 1.16, SD = .261) than women
(M = .67, SD = .073)
t = 2.481, p < .05, r = .15
Path Analysis
To investigate variables that contribute directly and indirectly to incorporation of mathematical modeling into teaching practice
Results of path analysis
Strongest predictors of teachers' incorporation of CCSSM:
Prepared to teach (Predictive effect - 28.3%)
Knowledge of CCSSM (Predictive effect - 24.6%)
Willingness to Change Practice
95.1% of teachers willing or eager to change practice
(N = 312, M = 3.14, SD = .537)
91.7% of teachers willing or eager to incorporate mathematical modeling into practice
(N = 332, M = 3.05, SD = .559)
Teachers' expressed needs
Factors teachers believe will assist implementation of CCSSM into classroom
Open-ended questions:
Major categories of teacher concern
Time to plan and prepare
Collaboration time
Materials & resources
Training and professional development
Testing and assessment
Open-ended questions:
Benefits of mathematical modeling
Real-life application
Improved critical thinking and reasoning
Depth of understanding
High interest & engagement

-Teacher concerns must be addressed for smooth transition
- Very limited research regarding CCSS transition
- Districts are in the throes of planning PD

Relevance of findings

-Generalization beyond California
- Relatively low response rate

- Study to see if/how needs, concerns, change as implementation of CCSS proceeds
- Study to determine whether teachers' optimism about CCSS and willingness to change practice change as implementation of CCSS proceeds
- study needs & concerns of teachers from other states
Suggestions for Future Research
- Teachers need time to plan and prepare for transition to CCSSM

- Teachers need time and direction in collaboration
and shared decision-making

- Teachers are concerned about the lack of materials and resources

- Teachers need a safe space during transition to practice and make mistakes

Key Findings for Districts in Transition:
Teachers' Concerns and Needs
- Teachers need time to read and discuss the CCSSM

- Teachers need grade-appropriate instruction in math content

- Teachers need to
mathematical modeling in action, and

mathematical modeling problems and activities, before they can
modeling to their students

- Teachers need time and support to practice new ways of thinking, teaching and learning before focus turns to assessment and test results

Implications for Professional Development

Show me and I may remember
Involve me and I will understand
Chinese Proverb
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