1. Mathematical Problem Solving and Critical Thinking for Elementary School Teachers
NSF Site Visit
June 8, 2005

2. Team Members Richard O’Malley, Mathematician
Henry Kepner, Mathematics Educator
Kelly Kaiser, Mathematics Educator
Sharonda M. Harris, Teacher-in-Residence

3. Mission of the Milwaukee Mathematics Partnership
The overall mission of the MMP is to substantially improve mathematics achievement for Milwaukee Public School students. With this in mind, one goal of the MMP is to build and sustain the capacity of teachers, from initial preparation through induction to understand mathematics deeply and to use that knowledge to improve student learning

4. Goals of the Course
To build a strong foundation for the teaching and communication of mathematical concepts by hands-on-development of critical thinking skills via problem solving experiences
To provide a guided opportunity for the implementation of problem-solving instruction in a classroom

5. Goals of the Course
To emphasize the process as well as the product of doing mathematics
To foster collaboration and other forms of constructivist learning
To express mathematical ideas using clear concise language

6. Student Expectations
Students are encouraged to become better problem-solvers by experimenting with problems of various types
Students are required to maintain a journal with entries for each class and problem projects
Students are required to actively participate in daily classroom discussions
Students are required to present and facilitate two problems during the course

7. Key Features
Create a coherent learning sequence across mathematics content and methods courses
Integrate content and pedagogy grounded in practice
Align teaching teams of mathematics faculty and staff, mathematics educators, and PK-12 teachers

8. Student Journals Three Major Components
1. Work which was done before class connected to solving the assigned problems
2. Summary of class activities/discussion related to assigned problems
3. Student Reflection
Generalizations
Formulated conjectures
Student Growth evidence in the journals

9. Student Presentations
Choosing engaging problems
Directing the discussion
Deeper understanding of the problem
Knowing/understanding alternate solutions, questions that might surface and misunderstandings

10. Value of Partnership Design team collaboration
-Ownership of the course
-Developing trust and respect
High-Quality Learning Opportunities
Class format encourages student
enthusiasm and participation

11. Challenges to Partnership
Time
-Planning and revisions
-Course Format
Developing activities that will challenge students
Collecting data and sample problems that will be useful for future instructors of the course

12. What Mathematical Knowledge is Needed for Teaching Mathematics?
Teaching requires justifying, explaining, analyzing errors, generalizing, and defining. It requires knowing ideas and procedures in detail, and knowing them well enough to represent and explain them skillfully in more than one way. This is mathematics. The failure to appreciate that this is substantial mathematical work does teachers-and the improvement of teaching-a disservice.
Ball, D.L. (2003). What mathematical knowledge is needed for teaching mathematics? Prepared for the Secretary’s Summit on Mathematics, U.S. Department of Education, February 6, 2003; Washington, D.C.