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Oct. 1, 2009MERC Presentation1 Principal Investigator: Kurt Stemhagen, PhD Research Associate: Jason W. Smith, PhD Middle School Mathematics Teachers’ Beliefs and Practices A Final Report to the MERC Policy and Planning Council

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MERC Study Team Kurt Stemhagen Jason Smith VCU Michael Bolling Chesterfield Co. Schools Allison Whitley Colonial Heights Schools Karen Cribbs Jenny Jones Vandi Hodges Hanover Co. Schools Melinda Jenkins Henrico Co. Schools Cheryl Webb Yvonne Smith-Jones Yvonne Smith-Jones Hopewell Co. Schools Sandra Lynch Thomas Sulzer Powhatan Co. Schools Dawn Cobb Latoya Daniels Richmond Public Schools Richmond Public Schools Oct. 1, 2009MERC Presentation2

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Oct. 1, 2009MERC Presentation3 Purpose: to examine complexities in the relationships between 4 th -8 th grade math teachers’ beliefs and practices to improve professional development

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Oct. 1, 2009MERC Presentation4 Guiding Questions Do beliefs/practices tend to cluster together for certain groups of teachers? Does the web of beliefs model provide continuity between teacher beliefs and practices? Are there individuals for whom beliefs and practices still seem to be at odds? If so, why? Are there other influences that shape teacher practice? Is democratic mathematics education a tenable theoretical construct and, if so, how does it relate to other beliefs/practices? How can professional development for mathematics teachers be improved by the findings?

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Oct. 1, 2009MERC Presentation5 Conceptual Framework Earlier work on teacher beliefs-practices often found a lack of coherence between the two Leatham: Does a certain belief cohere w/ a certain practice? This is the wrong question to ask… Our conceptual model was inspired by Leatham’s challenge

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Conceptual Model Oct. 1, 2009MERC Presentation6

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Oct. 1, 2009MERC Presentation7 Instrument Development Incorporated existing instruments when possible and employed seven expert reviewers to hone instrument Piloted with 27 math teachers Used written comments, Chronbach’s Alpha, and factor analysis to fine-tune instrument

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Oct. 1, 2009MERC Presentation8 Instrument Construction— Reliability Belief Constructs Cronbach’s Alpha Math Teaching Efficacy.704 Absolutist Nature of Math.698 Constructivist Nature of Math.614 Transmitive Teaching.830 Constructivist Teaching.757 Democratic Teaching.837 Practice Constructs Cronbach’s Alpha Transmittal.680 Constructivist.600 Democratic.662

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Instrument Construction Factor Analysis Oct. 1, 2009MERC Presentation9

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Participation All seven MERC districts were represented 323 teachers responded to survey (+/- 42% response rate) Working dataset, n=249 Oct. 1, 2009MERC Presentation10

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Demographic Findings Content Area of Highest Degree Percentage (n=243) Education54.7* Teaching19.3 Mathematics10.0 Other15.2* Oct. 1, 2009MERC Presentation11 Grade TaughtPercentage (n=241) 4 th 34.9 5 th 27.4 6 th 12.9 7 th 12.0 8 th 12.9 * Percentages adjusted to reflect those who selected “other” and who clearly described an education degree.

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Demographic Findings # of College-Level Math Courses Taken Percentage (n=244) 0-211.9 3-543.9 6-819.3 9 or more25.0 Oct. 1, 2009MERC Presentation12 Highest Degree Attained Percentage (n=245) Bachelors44.9 Masters54.7 Doctorate 0.4

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Demographic Findings Experience (Years Taught) Percentage (n=244) 0-4 yrs.16.4 5-9 yrs.32.4 10-19 yrs.25.8 20 or more yrs.25.4 Oct. 1, 2009MERC Presentation13 Categorized as “Highly Qualified”? Percentage (n=240) Yes79.6 No17.1

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Demographic Findings Provisional License?Percentage (n=243) No91.4 Yes 8.6 Oct. 1, 2009MERC Presentation14 Completed Math Coach/Specialist Training? Percentage (n=243) No85.6 Yes14.0

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Demographic Findings Access to Math Coach/Specialist? Percentage (n=243) Yes82.3 No17.7 Oct. 1, 2009MERC Presentation15 Special Education Teacher? Percentage (n=244) No80.7 Yes—Primarily Inclusion 8.4 Yes—Primarily Self- Contained 8.8

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Correlations - Beliefs Oct. 1, 2009MERC Presentation16 Nature of Math (Absolutist) Nature of Math (Const.) Transmittal Pedagogy Constructivist Pedagogy Democratic Pedagogy Math Teaching Efficacy Nature of Math (Absolutist) *** -.297.000.663.000 -.238.000 Nature of Math (Constructivist) -.297.000 ***.-393.000.512.000.367.000.416.000 Transmittal Pedagogy.663.000 -.393.000 *** -.423.000 Constructivist Pedagogy -.238.000.512.000 -.423.000 ***.308.000.207.001 Democratic Pedagogy.367.000.308.000 *** Mathematics Teaching Efficacy.416.000.207.001 ***

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Correlations - Beliefs to Practices Oct. 1, 2009MERC Presentation17 Belief ConstructsTransmitive Practices Constructivist Practices Democratic Practices Absolutist Nature of Math.365.000 Const. Nature of Math -.172.008.360.000.300.000 Transmittal Pedagogy.352.000 Constructivist Pedagogy -.229.000.169.010.168.010 Math Teaching Efficacy.189.003

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Comparing Sub-Groups Oct. 1, 2009MERC Presentation18 ConstructSig.Cohen's D Absolutist Nature of Math.000-0.49 Transmittal Teaching.007-0.36 Constructivist Teaching.0020.35 Math Teaching Efficacy.001-0.31 Transmittal Teaching Practices.011-0.29 4 th -5 th grade teachers compared with 7 th -8 th grade teachers…

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Comparing Sub-Groups Oct. 1, 2009MERC Presentation19 ConstructSig.Cohen's D Constructivist Nature of Mathematics.0000.50 Transmittal Pedagogy.015-0.37 Constructivist Pedagogy.0010.39 Mathematics Teaching Efficacy.0030.38 Teachers who have undergone specialist training compared with those who have not…

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Perceptions of External Influences on Practice Oct. 1, 2009MERC Presentation20 External Influence Selection Frequency Most Frequent Ranking state/federal mandated student perf. standards (e.g., SOL, NCLB) 90%1 central-district office policy (pacing guides, etc.) 84%2 availability of resources (materials, money, etc.) 62%4 school administrators 60%3 professional development 58%4

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Oct. 1, 2009MERC Presentation21 Discussion Beliefs Matter… There are a number of significant relationships between teachers’ beliefs, other important beliefs, and their reported practices Philosophical beliefs, in particular tended to have significant relationships with both pedagogical beliefs and with practice Enacting transmittal beliefs appears less troublesome than enacting constructivist beliefs (const. philosophy was more likely to find its way into practice than were const. teaching beliefs)

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Discussion - Beliefs and Practices Oct. 1, 2009MERC Presentation22 Nature of Math Absolutist Transmittal Pedagogy Transmittal Teaching Practice r=.30 r=.66r=.35 Nature of Math Constructivist Pedagogy Constructivist Teaching Practice r=.36 r=.17 r=.51 Relationships between corresponding philosophies, pedagogy beliefs and practices…

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Discussion - Other Highlights Oct. 1, 2009MERC Presentation23 Significant differences in orientation/practice between: Upper elementary and upper middle school teachersUpper elementary and upper middle school teachers Those completing specialist training and those who have notThose completing specialist training and those who have not Democratic Mathematics Education: Very promising as pedagogical belief/orientationVery promising as pedagogical belief/orientation DME practice not entirely differentiated from Constructivist PracticeDME practice not entirely differentiated from Constructivist Practice

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Recommendations - Professional Development Improving practice requires adjusting beliefs Belief scaffolding involves cultivation of awareness of one’s beliefs and how they relate to each other There are social dimensions to belief scaffolding Oct. 1, 2009MERC Presentation24

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Professional Development Establish ongoing communities of inquiry These P.D. experiences should include opportunities to consider: what we think about mathematics (both its nature and how we feel about it) why we teach it ways to teach it well impediments to doing so ways to overcome these impediments Oct 1, 2009MERC Presentation25

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Future Research Fleshing out P.D. course of study Continue to use SEM to test conceptual model Employ cluster analysis to further identify types of teachers (to aid in differentiated P.D.) Further study of external influences Continued work on Democratic Math Ed. March 9, 2007MERC Presentation26

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Oct. 1, 2009MERC Presentation27 Principal Investigator: Kurt Stemhagen, PhD Research Associate: Jason W. Smith, PhD Middle School Mathematics Teachers’ Beliefs and Practices Questions and Answers…

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