Cameroon

France

Germany

Mexico

Pakistan

Poland

Singapore

Uganda

USA

PCMI International Seminar: Bridging Policy and Practice Summer, 2006

Missing from the current discourse on mathematics education is an insightful examination of educational systems around the world from the perspective of what actually works in teaching mathematics and preparing teachers to teach mathematics. Many traditions and practices in mathematics education in different countries have much to offer each other, and there are many current practices and visions of reform against which a particular country's concepts and policies must be critically examined.

PCMI has established the International Seminar on Mathematics Education as a fundamental component of its programming. Over the long term, the function of this Seminar is to design and implement a series of reflections on common problems, along with suggestions for policy and practice and innovative offerings that will be made available to the international community. The set of countries represented will be expanded over time, with continuing attention to diversity and variety in educational challenges.

The fifth week-long international workshop, "Bridging Policy and Practice: Mathematics Education Around the World" was held as part of the 2006 PCMI Summer Session. This seminar focused on mathematics teacher education with a strong emphasis on preparing teachers to promote mathematical problem solving, reasoning, and proof. The participants came as teams consisting of one mathematics education policy-maker and one practicing secondary mathematics teacher from each of nine countries (Cameroon, France, Germany, Mexico, Pakistan, Poland, Singapore, Uganda, and USA).

Presentations and discussions that took place in the work sessions related to:

• theoretical/conceptual frameworks for problem solving, research findings related to the teaching and learning problem solving and reasoning and proof, and the roles of problem solving and reasoning and proof in the secondary curriculum
• popular approaches to teaching "mathematical problem solving" and features of approaches to teaching "mathematics via problem solving"
• the roles of problem solving and reasoning and proof in teacher preparation programs, and strategies for preparing teachers to teach reasoning and proof and problem solving (or via a problem-solving approach)
• the mathematical content knowledge that supports effective teaching of problem solving and reasoning and proof

Specific questions that framed the activities of the work sessions were:

• How is problem solving integrated into the secondary mathematics curriculum and how are teachers prepared to teach problem solving?
• What mathematical content knowledge is necessary for secondary teachers to teach problem solving?
• Has the vision of problem solving changed over the years? If so, how has it changed?
• How are reasoning and proof integrated into the secondary curriculum and how are teachers prepared to teach reasoning and proof?
• What research findings or current practices would be helpful in teaching reasoning and proof?

The participants worked together to establish consensus on various issues that emerged in the course of the discussions, and formed working groups to further explore these issues. One product of these efforts is a document that presents the participants views and recommendations in relation to these topics.

Participants from previous seminars had the opportunity to review these documents and their comments contributed to the final version that is posted as the official record of the 2006 PCMI International Seminar. This document is available on the PCMI@MathForum website at http://mathforum.org/pcmi/PCMI2006IntSeminar.pdf

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