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Dissertation Defense: Mathematical Modeling
Transcript of Dissertation Defense: Mathematical Modeling
K through 12 teachers of mathematics
Claremont Graduate University
PhD in Education
Teachers’ Understanding of
and Concerns about
Mathematical Modeling in the Common Core
Nancy Butler Wolf
Variables entering regression equation:
#1: Understanding of Modeling
Contributed 20.05% of the Variance
Contributed 12.57% of the Variance
- 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
- 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
the preferential looking tasks
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
Levels of Use branching interview
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
(B = .884, p = .004, EXP(B) = 2.42)
(B = -.782, p = .049)
Contributed 7.60% of the Variance
Contributed 4.01% of the Variance
#5: Time Conflicts
Contributed 3.64% of the Variance
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
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
Major categories of teacher concern
Time to plan and prepare
Materials & resources
Training and professional development
Testing and assessment
Benefits of mathematical modeling
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