1. A NEW VISION FOR TEACHER PREPARATION IN MATHEMATICS AND SCIENCE Beyond Bridging This material is based upon work supported by the National Science Foundation under Grant No. DRL-1019860. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Chantel C. Blackburn Department of Mathematics University of Arizona February 22, 2011

2. Overview Introduction to Beyond Bridging Bridging models Going beyond the bridging models Math methods course

3. Beyond Bridging Intro $2.2 million NSF Research on Learning in Formal and Informal Settings (DRL) Grant Integrating university science and mathematics education coursework and practica expectations of elementary school classrooms serving diverse populations.

4. Bridging Models Placing PS teachers in K- 5 classrooms during field placements Teaching methods courses in K-5 schools Professional development for K-5 IS teachers to change the K- 5 classroom

5. Beyond Bridging Mentoring Inquiry science and problem solving-based mathematics instruction Involving IS teachers in building new K-5 teaching practices Collaborative learning spaces between different communities of practice K-5 Teachers & Administrators University Science & Mathematics Preservice Teacher Educators Field Placements & Field Based Methods Courses

6. Beyond Bridging Mentoring Inquiry science and problem solving-based mathematics instruction Involving IS teachers in building new K-5 teaching practices Collaborative learning spaces between different communities of practice K-5 Teachers & Administrators University Science & Mathematics Preservice Teacher Educators Co-education community / Third Space Scientists & Mathematicians

7. Beyond Bridging Building understanding of science and mathematics constructs Supporting PS teachers in succeeding in multiple communities Co-constructing new possibilities for learning to teach elementary science and mathematics K-5 Teachers & Administrators University Science & Mathematics Preservice Teacher Educators Co-education community / Third Space Scientists & Mathematicians

8. Math Methods Professional development with IS teachers (mentors and whole school) Paring PS teachers with mentors and buddies Sub and roving sub days

9. Math Methods Interviews PD with IS teachers on student strategies with addition/subtraction and multiplication/division problems Upper/Lower Elementary IS teachers in math methods Interviewing students

10. MM Instructors: Problem Structure MM Instructors: Problem Structure IS Teacher: How to Teach IS Teacher: How to Teach Multiplication: Total unknown Partitive Division: Number in each group unknown Measurement Division: Number of groups unknown Multiplication/Additio n: Total unknown Division/Subtraction: Total known Third Space: Multiplication/Division Problems

11. MM Instructors IS Teacher Equity. Excellence in mathematics education requires equity—high expectations and strong support for all students. Learning. Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. “I have this chart in my classroom for key words. It says total for addition or multiplication.” “My students would focus on the word times and then they would know what to do. They would multiply. They know that one word and then they could do it.” Third Space

12. Resources Carpenter, T., Fennema, E., Franke, M., Levi, L., & Empson, S. (1999). Addition and subtraction: Children's solution strategies. In T. Carpenter, E. Fennema, M. Franke, L. Levi, & S. Empson, Children's mathematics: Cognitively Guided Instruction (pp. 15-31). Portsmouth, New Hamshire: Heinemann. Lewis, A. B., & Mayer, R. E. (1987). Students ʼ miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology, 79(4), 363-371. doi: 10.1037/0022-0663.79.4.363. Moje, E. B., Collazo, T., Carrillo, R., & Marx, R. W. (2001). "Maestro, what is ‘quality’?”: Language, literacy, and discourse in project-based science. Journal of Research in Science Teaching, 38(4), 469-498. doi: 10.1002/tea.1014. Moje, E. B., Ciechanowski, K. M., Kramer, K., Ellis, L., Carrillo, R., & Collazo, T. (2004). Working toward third space in content area literacy: An examination of everyday funds of knowledge and discourse. Reading Research Quarterly, 39(1), 38-70. doi: 10.1598/RRQ.39.1.4. NCTM (2000) Principles and Standards of School Mathematics.