1. Rachel Wing DiMatteo 1 Daniel Heck 2 Mark Driscoll 1 Johannah Nikula 1 Research-based Professional Development Materials Increase Geometric Thinking 1 Education Development Center, Newton, MA 2 Horizon Research, Inc., Chapel Hill, NC Research presented at 2007 NCTM Research Presession in Atlanta, GA

2.  Identify and describe productive ways of thinking in geometry, geometric habits of mind (G-HOMs)  Create professional development materials based on G-HOMs 40 hours  20 two-hour sessions Group-study materials Structured Exploration Process (Kelemanik et al. 1997) Stage 1: Doing mathematics Stage 2: Reflecting on the mathematics Stage 3: Collecting student work Stage 4: Analyzing student work Stage 5: Reflecting on students’ thinking G-HOMs framework is a lens for analysis Fostering Geometric Thinking in the Middle Grades (FGT) Research reported here is support by the National Science Foundation under Grant ESI-0353409

3. Research Questions How do professional development materials that target students’ geometric ways of thinking… Q1: increase teachers’ content knowledge? Q2: increase understanding of student thinking in geometry & measurement? Q3: affect instructional practice in geometry? Participants 33 facilitators randomly assigned to Treatment or Wait-listed Control 33 facilitators recruited 277 teachers Treatment  15 facilitators and 117 teachers Wait-listed Control  13 facilitators and 104 teachers FGT Field Test

4. Measures  Geometry Survey Pretest-Posttest: Multiple choice items Analyze transcribed lesson Timeline FGT Field Test Spring 2005 2005-2006 Spring 2006 2006-2007 TreatmentPretestFGTPosttest Wait-listed Control PretestPosttestFGT

5. Measures  Geometry Survey Pretest-Posttest: Multiple choice items Analyze transcribed lesson  Classroom Observations: 3-day observations, 5 teachers per condition Timeline FGT Field Test Spring 2005 2005-2006 Spring 2006 2006-2007 TreatmentPretestFGTPosttestObservations Wait-listed Control PretestObservationsPosttestFGT

6. Measures  Geometry Survey Pretest-Posttest: Multiple choice items Analyze transcribed lesson  Classroom Observations: 3-day observations, 5 teachers per condition  Embedded Assessment Timeline FGT Field Test Spring 2005 2005-2006 Spring 2006 2006-2007 TreatmentPretestFGTPosttestObservations Wait-listed Control PretestObservationsPosttestFGT

7. Geometry Survey Pretest-Posttest: Multiple choice items (31) Analyze transcribed lesson 1 st Research Question: …increase teachers’ content knowledge? Preliminary Findings

8. Geometry Survey Pretest-Posttest: Multiple choice items (31) Analyze transcribed lesson Variables of Interest Individual Level Group Level Posttest Score Condition Pretest Score Percent Minority Math Background Urban, Rural or Suburban Years Teaching Math Group Size Preliminary Findings

9. Geometry Survey Pretest-Posttest: Multiple choice items (31) Analyze transcribed lesson Hierarchical Linear Models  Did being in a group assigned to the Treatment condition affect teachers’ posttest scores? Preliminary Findings

11. Geometry Survey Pretest-Posttest: Multiple choice items (31) Analyze transcribed lesson Hierarchical Linear Models  Did being in a group assigned to the Treatment condition affect teachers’ posttest scores?  Did being in a group assigned to the Treatment condition affect teachers’ posttest performance on property, congruence & similarity, or measurement items? Preliminary Findings

12. Geometry Survey Pretest-Posttest: Multiple choice items (31) Analyze transcribed lesson 2 nd Research Question: …increase understanding of student thinking in geometry & measurement? Preliminary Findings

13. Geometry Survey Pretest-Posttest: Multiple choice items (31) Analyze transcribed lesson Transcript Question: What stood out for you in terms of the work the students and teachers were doing in this activity? Before FGT: “…the teacher was leading the students by the questions she was asking. I also liked the way the kids had a chance to think about the problem and come back to answer questions.” After FGT: “It was clear that they had worked on the volume of a rectangular prism and they had filled a rectangular prism with layers of cubes to find the volume of the prism. They actually took this thought and applied it to the cylinder…” Preliminary Findings

14. Geometry Survey Pretest-Posttest: Multiple choice items (31) Analyze transcribed lesson Transcript Question: What stood out for you in terms of the work the students and teachers were doing in this activity? Before FGT: “(The) teacher was not giving any answers, formulas or even strategies (and) was simply working through a discussion with the class to see how they solved it and what direction it went. Each class discussion could be totally different.” After FGT: “ --Analyzing cylinders and boxes --volume of prisms versus cylinders --understanding of height and radius --dimensions of shapes” Preliminary Findings

15. Geometry Survey Pretest-Posttest: Multiple choice items (31) Analyze transcribed lesson Treatment teachers attend more to students after FGT Treatment teachers attend more to students’ mathematics after FGT Preliminary Findings

16. Increase in geometric content knowledge, especially in the area of measurement Increase in attention to students and their mathematical thinking

17. Will be published by Heinemann in 2008 To find out more about the project: www.geometric-thinking.org Rachel Wing DiMatteo Education Development Center Newton, Massachusetts rwing@edc.org Fostering Geometric Thinking