Mathematical%20Problem%20Solving%20and%20Critical%20Thinking%20for%20Elementary%20School%20Teachers

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

• Richard OMalley, Mathematician
• Henry Kepner, Mathematics Educator
• Kelly Kaiser, Mathematics Educator
• Sharonda M. Harris, Teacher-in-Residence

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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

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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

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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

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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

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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

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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

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Student Presentations

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

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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

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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

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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 Secretarys Summit on Mathematics, U.S.
  Department of Education, February 6, 2003
  Washington, D.C.