**Results**

click

click

K through 12 teachers of mathematics

Participants

Interviews

**Claremont Graduate University**

PhD in Education

June 2013

PhD in Education

June 2013

**Teachers’ Understanding of**

and Concerns about

Mathematical Modeling in the Common Core

Nancy Butler Wolf

and Concerns about

Mathematical Modeling in the Common Core

Nancy Butler Wolf

1

2

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

Recommendations:

Key Findings for Districts in Transition

Tell me and I will forget

14

© Emma Pelaprat-Mason

Aparicio, M. T. S. (2004).

Results from an experimental study about reinforcements employed in training. Early Chid Development and Care, 174(2), 193-198. doi : 10.1080/0300443032000153525

Baldwin, D.A. (1993)

.

Infants' ability to consult the speaker for clues to word reference. Journal of Child Language, 20, 395-418.

Charles-Luce, J., & Luce, P. A. (1990).

Similarity neighborhoods of words in young children’s lexicons. Journal of Child Language, 17(1), 205-215. doi : 10.1017/S030500009000013180

Fenson, L., Dale, P. S., Reznick, J. S., Bates, E., Thal, D. J., & Hartung, J. P. et al (1993).

MacArthur Communicative Development Inventories: User’s guide and technical manual. San Diego, CA: Singular Publishing Group.

References

**Background**

**Conclusion**

**Discussion**

Gurteen, P. M., Horne, P. J., & Erjavec, M. (2011).

Rapid word learning in 13- and 17-month-olds in a naturalistic two-word procedure : Looking versus reaching measures. Journal of Experimental Child Psychology, 109, 201-217. doi : 10.1016/j.jecp.2010.12.001

Hollich, G., Hirsch-Pasek, K., & Golinkoff, R. M. (2000).

Breaking the language barrier: An emergentist coalition model for the origins of word learning. Monographs of the Society for Research in Child Development, 65 (3, Serial No. 262)

Schafer, G., & Plunkett, K. (1998).

Rapid word learning by 15-month-olds under tightly controlled conditions. Child Development, 69, 309-320. doi: 10.1111/j.1467-8624.1998.tb06190.x

Smith, M. L., & Yu, C. (2008).

Infants rapidly learn word-referent mappings via cross-situational statistics. Cognition, 106, 1558-1568.

Woodward, A. L., Markman, E. M., & Fitzsimmons, C. M. (1994).

Rapid word learning in 13-and 18-month-olds. Developmental Psychology, 30(4), 553-566.

Questionnaire

© Emma Pelaprat-Mason

15

Research Questions:

Above chance

(50%)

performance in

the preferential looking tasks

Above chance

(50%)

performance in

the preferential looking tasks

**Methods**

"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

mathematical

practice

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

Demographics

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)

Gender

(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

Percent

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

Limitations

- 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

see

mathematical modeling in action, and

do

mathematical modeling problems and activities, before they can

teach

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