1. Carol Baldassari and Sabra Lee Program Evaluation and Research Group Lesley University Rosalie Torres Torres Consulting Group Qualitative Analysis of Changes in Teachers’ Knowledge, Beliefs and Classroom Practices

2. Focus on Mathematics NSF funded Math-Science Partnership  2 universities’ mathematics and mathematics education schools  5 school districts – grades 5-12  1 educational R&D organization Goal: Increase student understanding by deepening teachers’ knowledge of mathematics for teaching [KMT]

3. Basic Logic Model for MSP Programs Professional Development Teacher Learning Classroom Transfer Student Learning

4. Focus on Mathematics’ Theory of Change STUDENT UNDERSTANDING Student achievement  Student engagement, student research projects, “habits of mind”  Informed curricula decision-making and classroom planning, student task development, instructional approach  Development of mathematics community  Deepened knowledge of mathematics for teaching  TEACHER LEARNING Immersion in mathematics with colleagues and mathematicians

5. Research Questions What impact does FoM’s ‘immersive’ PD program have on teachers’ knowledge of mathematics? Do teachers transfer this knowledge to their classrooms? What contextual factors influenced changes in teachers’ knowledge and practice?

6. Why Use a Case Study Approach? Collected extensive data over time Focused on non-linear change Wanted to identify when, how numerous factors came into play and how related Wanted to identify specific experiences that affected each teacher’s shifting learning

7. Data Sources Data collected 2004-2007  Interviews with teachers, their principals, course instructors  Classroom observations  Observations of program components  Document reviews

8. Data Analysis Process Reviewed program’s theory of change Interview data used to generate codes Established inter-rater reliability Finalized set of codes Coded data chronologically by date collected Used qualitative research software (HyperResearch©)

9. Tracing Teacher Change…Visualization of Codes Professional Development Teacher Learning Classroom Transfer Student Learning Math background Ability to participate Leadership role Math community School context District context

10. Analytic Coding Scheme Initially used double coding strategy Realized the necessity of refining the coding process Searched for more systematic, meaningful way to account for relationships between and among original codes Used arrows to describe interconnections among codes Result: strings of codes

11. Tracing Teacher Change…Visualization of Codes Professional Development Teacher Learning Classroom Transfer Student Learning Math background Ability to participate Leadership role Math community School context District context

12. Codes PD->TL->CT->SL APability to participate MBmath background DC district context SC school context MCmath community LRleadership role MB PD LR SC Math background->professional development->leadership role->school context TL DC SC CT SL Teacher learning->district context->school context->classroom transfer->student learning

13. Coded Data Example TL DC SC CT SL One challenge is we have the new textbook Holt series and I just find that it is a different approach to math than Connected Math. Connected Math was more problem solving… The Holt [approach] is, here is the skill and we are going to drill it for a while … I find these kids struggle through the skill so it is helping them in a way that Connected Math couldn't but it still is not the perfect balance. My idea is to change the Holt approach…so we spend a couple of days on the skill and then 2 days from Connected Math that [they] apply to it. The application is where they need practice and you do not have it in this book… I feel that in order to use your math in the real world you need to start solving the problems or you'll ask, why am I doing that?

14. Code Frequency: 2 Teachers Re-coded all data using strings of codes Frequency of codes signified focal areas Frequencies of codes differed by teacher Teacher 1 Teacher 2 PD855 PDTL1333 PDTLCT720 MBPDTL226

15. Findings: Program’s Impact on Teachers Structure of PD Program Room arrangement: Set of tables accommodate ~4-6 teachers. Tasks: Teachers work on problem sets for 5-6 hours/day for 6 weeks. Teachers work individually and in groups. Resources: Colleagues; ’math counselors’ are available in study room for consultation. Interactive Lecture: Problems discussed ~ 3 days after teachers have worked on problem set. PD->TL-> CT Structure of Seth’s Mathematics Classroom Room arrangement: Some desks are paired together; others are set apart from one another. Task: Seth provides day’s problem set to students as they arrive. Students work individually or in groups on first, problem (review from previous day). As students work, Seth visits, looks at strategies; prods thinking; poses questions. One or more students put solutions on the board. All discuss demonstrated approach/solution; suggest alternate strategies/solutions Seth reinforces students’ use of precise mathematical language during discussion Seth and students identify/discuss critical aspects of problem, approach, solution. Students turn to ‘new’ problems.

16. Findings: What We Learned About Methodology Analytic coding process  Yielded deep understanding of [inter] relationships between all codes  Allowed us to see how and why teachers’ knowledge, beliefs and classroom instruction changed  Revealed relationships between teachers’ ability to participate, math background, school context, presence or absence of support and classroom transfer Affirmed and expanded FoM’s theory of change

17. Working Hypothesis This immersive, content-rich, and flexible program allowed teachers with a variety of mathematics backgrounds to be successful. Teachers’ experiences helped them develop confidence and authority, adapt the mathematics curriculum, and negotiate district and school challenges.

18. Carol Baldassari baldasar@lesley.edu baldasar@lesley.edu Sabra Lee slee@lesley.edu slee@lesley.edu Rosalie Torres rosalie@torrescons ultinggroup.com rosalie@torrescons ultinggroup.com Contact Information