1. A reflective project for pre- service teachers in university mathematics courses Dr. Angie Hodge North Dakota State University

2. My role in teacher prep Joint appointment Mathematics (55%) Teacher education (45%) Teach mathematics courses Teach secondary methods courses Serve as a liaison between departments

3. Background Pre-service secondary mathematics teachers (PSMTs) complete a significant portion of their coursework in mathematics departments.

4. Background The Committee on Undergraduate Program in Mathematics (CUPM, 2004) recommends that 9-12 teachers: Learn to make appropriate connections between the advanced mathematics they are learning and the secondary mathematics they will be teaching. They should be helped to reach this understanding in courses throughout the curriculum and through a senior-level experience that makes these connections explicit. (p. 52)

5. Background Pre-service secondary mathematics teachers (PSMTs) do not always see these connections (Staples & Hodge). There is a need to help PSMTs make connections between their coursework and their future teaching.

6. Role of university geometry What are some ways you believe university geometry courses can/could contribute to PSMTs’ future classroom teaching?

7. Purpose To understand how the structure and content of a university geometry course can help PSMTs in connection to their future classroom teaching.

8. Axiomatic Geometry 3 credit, upper-division course PSMT requirement Math/Stat elective Mixture of non-Euclidean and Euclidean geometry

9. Axiomatic Geometry 14 students enrolled in the course 14 students participated in the study 9 of these were PSMTs At least 1 PSMT in each group

10. Class structure Limited lecture Focus on group work Group and individual assessments

11. Final project I included a final project to help understand how the students thought the structure and content of the course was benefical for them in their future careers. Focus here is on PSMTs.

12. Final Project (PSMTs) Presentations and summaries of how the class would help PSMTs in future careers. How does the structure of the course help pre- service teachers? How could the topics in this course help someone teach geometry at the middle or high school level? Why is this course required of pre-service teachers as part of their undergraduate degree?

13. Final project Duration: 45 minute presentations. Form: Students’ choice. Requirement: Handout for others.

14. Final project Specific topics as well as structure of the class were to be included to make points. Encouraged to examine NCTM standards and/or high school textbooks to justify claims.

15. Results related to structure Group work Teaching opportunities Obtaining a sense of what it “feels like” to partake in group work Saw a balance of independent/group learning in action Non-traditional format Provided a model for PSMTs to use in their classrooms

16. Results related to structure Learning from mistakes. Ability to re-do homework problems. Repetition of homework/proof concepts. Proving exactly one.

17. Results related to material Deeper Understanding Enabled them to provide a better explanation of material. Brought to light concepts that are taken for granted in Euclidean Geometry Parallel lines General skills (proof construction) practiced throughout course

18. Relevance to teaching degree Provided a good foundation of geometry Provided the why’s and how’s Provided bridge between math and education

19. Implications We should consider ways to provide PSMTs opportunities to reflect on how their coursework relates to their future teaching.

20. Future directions Follow up with PSMTs in the classrooms. Compare/contrast with other schools. Compare/contrast with other courses.

21. Questions? Angela.Hodge@ndsu.edu