The University of Texas at Arlington Department of Mathematics

1. The University of Texas at ArlingtonDepartment of Mathematics GK-12 MAVS Program • Program Director: Dr. Minerva Cordero • Co-Principal Investigators: • Dr. TuncayAktosun • Dr. James Epperson • Dr. Theresa Jorgensen • Dr. Jianping Zhu • Program Coordinator: Ms. Cecelia Levings

2. Overview • Project title: Mathematically Aligned Vertical Strands connecting mathematics research and pedagogy for GK-12 Fellows and teachers (MAVS project) • Involves 8 fellows and 8 teachers • Funded by the NSF GK-12 program: $2.85 million from 2009 – 2014.

3. Overview One of the goals of the MAVS GK-12 Project at the University of Texas at Arlington is to create a seamless transition in mathematics that bridges the school curriculum to graduate level research.  Challenges: • Abstract nature of mathematics research • Understanding school curriculum and standard • Bringing fellows, teachers, research advisors, and GK-12 mentors together

4. Overview Our Strategies: • Vertical integration • Team structure that facilitates collaboration and coordination (mentoring triad and teaching quad) • Intensive summer program for fellows and teachers • MAVS Seminars that promote interactions and sharing of best practice • Innovative lesson plans and projects that brings graduate level research to school classrooms

5. ResearchMathematics Vertical Content Strands

6. Vertical team At the heart of the MAVS project are cohesive vertical teams of graduate students, K-12 teachers, and mathematicians.

7. Vertical Team

8. The GK-12 (MAVS) Fellows • All MAVS fellows are graduate students in the University of Texas at Arlington Department of Mathematics who have have begun independent research. • These students are pursuing either the Masters or Ph.D. track - it should be noted that independent research is a requirement of both degrees. • Eight graduate fellows per year are being supported.

9. 2010-2011 Fellows • GK-12 fellows working in mathematics research at UTA • Jason Bacon Algebra • Justin Blackwell Applied Mathematics • Angie Brown Geometry • Jason Gilgenbach Statistics • Antonio Lopez Applied Mathematics • Aubrey Rhoden Applied Mathematics • Catherine Rogers Applied Mathematics • Padmini Veerapen Algebra

10. The K-12 Mentor Teachers • Eight mentor teachers per year are participating in the MAVS project: four from Sam Houston High School (SHHS) and four from its feeder junior high schools. • Each mentor teacher is assigned as chief mentor teacher of one graduate fellow for the project year. • MAVS fellows spend their K-12 school contact hours in the classroom of their assigned mentor teacher.

11. 2009-2010 Mentor Teachers • Sam Houston High School Alicia Geppert Kimberly Helixon Gina Kaucher Thang Tran • Carter Junior High Daree Yancey • Hutcheson Junior High Ashlee Dephilippis • Workman Junior HighKelly Randell Christopher Boyd

12. GK-12 Team Structure • Teaching Quad – groups consisting of two MAVS fellows with a mentor junior high teacher and a mentor high school teacher • MentoringTriad—MAVS fellow, research advisor, and MAVS faculty mentor • The MAVS faculty mentor bridges the communication between the Teaching Quad Team and the Mentoring Triad and facilitates the communication with the district mathematics supervisors and school administrators.

13. GK-12 MAVS Teaching Quads & Research Triads

14. 2009-2010 Quads

15. Summer Program • Summer: Professional Development Institute (two weeks) • Fellows present research • Teachers discuss curriculum-scope and sequence • Together each fellow-teacher pair designs six research lessons

16. Summer PDI

17. MAVS Seminar • Throughout the school year, the GK-12 project PIs, fellows, teachers, and faculty meet for MAVS seminars. • The seminars are held weekly at the beginning of an academic year, then bi-weekly, and monthly in the later part of the academic year. • The MAVS seminar has two components: • A research component • A teaching component • The seminars are scheduled on a rotating basis among UT Arlington and the campuses of participating schools • Teaching Quads meet to collaborate, trouble shoot, and share best practices • Fellows present classroom lessons or research

18. MAVS Seminar • Each graduate fellow is required to present twice per year at this seminar. The first presentation will focus on the mathematical research they are conducting under the guidance of their research advisor. The second presentation will focus on their progress on implementing their research into their GK-12 activities and their experiences in the classroom. • The fellow’s research advisor will attend both of these presentations.

19. MAVS Seminar • Fellows, mentor teachers, and the project PIs all meet for informal discussions about challenges and issues in bringing graduate level research into middle and high school classrooms. • Discussions at these meetings also focus on how the mentoring relationships are developing, what is going well, what should be modified, how lessons were implemented in the schools and any evidence of students' success.

20. Fellows in the classroom…

21. Fellows in the classroom…

22. Research Projects Medical Imaging in the Ninth Grade By: Aubrey Rhoden (MAVS Fellow) and Kimberly Helixon (Mentor Teacher)

23. Research Projects Medical Imaging using Computed Tomography

24. Research Projects Collaboration The UNT Medical Center performed experiments on mice to determine the effect that inclusions such as blood clots would have upon the body’s temperature. The biomedical engineering department at UTA has also justified this method in a different case using optical tomography.

25. Research Projects With the Dirichlet boundary condition on Where w(x,y) is the temperature at location (x,y) ( the solution of the diffusion equation) p(x,y) is the perfusion coefficient at location (x,y) (also included in this coefficient is the thermal conductivity, specific heat, and density all of which are considered constant throughout the domain) f(x,y) is the heat source

26. Goals From The boundary of the forward Problem one can reconstruct the blood perfusion to determine where blood clots or strokes occurred.

27. Linear Approximation Given seven equations with finite domains the student is expected to graph these equations that represent a one dimensional slice of body tissue compared with the blood perfusion.

28. Point-Slope Formula Given this graph the students are expected to find the equations for line segments A, B, C and D. The students were also expected to Identify the domain and range of each segment.

29. Quadratic Approximation Importance concept introduced to the students: Piecewise linear functions can be used to approximate complex curves.

30. Quadratic Approximation Given seven equations with finite domains, students are asked to graph these quadratic equations that represent a one-dimensional slice of body tissue compared with the blood perfusion.

31. Compare the Results The students will compare and contrast the differences between linear and quadratic models with the same data points.

32. Conclusions Importance concept introduced to the students: The approximation can be improved by using more sophisticated piecewise functions.