1. A Working Symposium on Teaching and Learning Proof Across the Grades: Removing Uncertainty Despina Stylianou - City College, CUNY Patricio Herbst - University of Michigan Eric Knuth - University of Wisconsin Madison Keith Weber - Rutgers University Maria Blanton - University of Massachusetts Dartmouth

2. It is important for students to become “certain about their uncertainty” and for teachers to guide this awareness. How do we help them remove uncertainty?

3. September, 2004- NSF-funded conference on Teaching and Learning Proof Across the Grades October, 2007 - Follow-up NSF-funded conference on Research Paradigms in the Teaching and Learning of Proof Teaching and Learning Proof Across the Grades: A K-16 Perspective - Taylor & Francis, to appear Context:

4. Detailing connections between grade bands* in teaching and learning proof across the grades * e.g., elementary grades, middle school, high school, college Goal for Today:

5. What is students’ capacity for proving at your grade band? What forms of arguments can they construct? What forms of arguments do students need to understand prior to this grade band and how are these arguments (and their development in students' thinking) connected across grade bands? What experiences (curricular and instructional) do students need in order to construct these various forms of arguments at the respective grade bands? What knowledge do teachers need in order to support students’ understanding of proving (and what is being done to provide that knowledge base)? Questions for Small Groups:

6. 4 small groups - elementary (Maria), middle (Eric), high school (Pat), college (Despina) ~40 minutes for discussion of questions in small groups ~20 minutes share in combined small groups (elementary/middle; high school college) ~20 minutes whole group discussion Logistics: