Principal Investigator: Kurt Stemhagen, PhD Research Associate: Jason W. Smith, PhD

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

2. 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 Hopewell Co. Schools Sandra Lynch Thomas Sulzer Powhatan Co. Schools Dawn Cobb Latoya Daniels Richmond Public Schools MERC Presentation

3. Purpose:to examine complexities in the relationships between 4th-8th grade math teachers’ beliefs and practices to improve professional development MERC Presentation

4. 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? MERC Presentation

5. 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 MERC Presentation

6. Conceptual Model MERC Presentation

7. 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 MERC Presentation

8. Instrument Construction—Reliability MERC Presentation

9. Instrument ConstructionFactor Analysis MERC Presentation

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

11. Demographic Findings • *Percentages adjusted to reflect those who selected “other” and who clearly described an education degree. MERC Presentation

12. Demographic Findings MERC Presentation

13. Demographic Findings MERC Presentation

14. Demographic Findings MERC Presentation

15. Demographic Findings MERC Presentation

16. Correlations - Beliefs MERC Presentation

17. Correlations - Beliefs to Practices MERC Presentation

18. Comparing Sub-Groups 4th-5th grade teachers compared with 7th-8th grade teachers… MERC Presentation

19. Comparing Sub-Groups Teachers who have undergone specialist training compared with those who have not… MERC Presentation

20. Perceptions of External Influences on Practice MERC Presentation

21. 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) MERC Presentation

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

23. Discussion - Other Highlights • Significant differences in orientation/practice between: • Upper elementary and upper middle school teachers • Those completing specialist training and those who have not • Democratic Mathematics Education: • Very promising as pedagogical belief/orientation • DME practice not entirely differentiated from Constructivist Practice MERC Presentation

24. 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 MERC Presentation

25. 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 MERC Presentation

26. 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. MERC Presentation

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