MISSION: To bring together teams of two educators-a university mathematics educator or policy-maker and a secondary teacher-from a small number of nations representing a cross-section of the regions of the world to discuss major issues in mathematics education policy and practice. The seminar goals are to:

• promote open discussion of issues affecting the mathematics education policies and practices of each nation,
• identify common issues faced across national contexts,
• identify common sources of direction and support for efforts to address problems, and
• search for common solutions to related problems

Funded by the Wolfensohn Family Foundation, the Bristol-Myers Squibb Foundation, and the International Commission on Mathematical Instruction.

HISTORY
Summer 2001
Theme
To consider issues and challenges faced by mathematics educators from very different contexts and identify common strategies for, and approaches to, meeting those challenges. Of particular interest were challenges, strategies, and approaches regarding national standards, teacher education, content case studies, reform efforts, depth versus breadth in curriculum, mathematics education for all students, and the role and status of mathematics education as a profession.

Countries
Brazil, Egypt, France, India, Japan, Kenya, Sweden, and the United States

Emerging Issues/Central Themes
Teacher preparation emerged as a primary area of interest and concern across the countries and, as a result, became the theme for the subsequent seminar (2002).

The second theme related to the relationship between national curricula and teacher autonomy regarding classroom practice. A major issue with regard to this theme was that the standardizing effect of national curricula seemed to be mitigated by the varying ways in which teachers implemented the curriculum in their classrooms.

The third theme related to the highly influential nature of mathematics education reforms in the United States. Efforts to improve mathematics education in the US are applauded and used as models or guidelines by educators from other countries.

Regarding the fourth theme of tradition versus reform in mathematics education, participants from several countries noted that tradition related to historical approaches to learning certain procedures or concepts.

Countries varied widely on the mission and purpose of mathematics education in terms of access and equity for all students. The role of schools in society differed markedly across countries. In a significant number of countries, mathematics education combines a national system and a private tutoring system. The private system enables teachers to earn a living wage and enables students who can afford the expenses to receive a higher quality education than is available to most students.

Proceedings
The report, Mathematics Education Around the World: Bridging Policy and Practice Reflections from the 2001 Park City Mathematics Institute International Panel on Policy and Practice in Mathematics Education, can be access by following the link for the International Seminar via the PCMI home page (http://mathforum.org/pcmi/).

Summer 2002
Theme
To consider goals, content, and delivery of pre-service and in-service education for mathematics teachers, as well as the policies that govern these in each nation. To identify common issues faced across national contexts and identify pre-service and in-service programs and practices that work well in a particular nation, and may work well in others.

Countries
Brazil, Egypt, France, India, Japan, Kenya, Sweden, and the United States

Emerging Issues/Central Themes
Teacher preparation varies widely depending on the country, particularly with respect to criteria for entering candidates and the amount and level of preparation needed to complete the program.

In-service opportunities are typically uncoordinated and scattered, and usually not mandated. Even when they are required, in-service activities are not necessarily situated in a coherent program (Japan is a notable exception).

Several countries are trying to reform their teacher pre-service programs. One example is a program design that has a common sequence of courses for all students prior to specialization.

Teacher education programs respond differently to diverse cultures within a country. Some countries provide specific courses on these cultures and their way of life as part of the work toward certification. Others focus on assimilating everyone, regardless of culture, into the mainstream culture.

The use of instructional technology in mathematics is not well thought out or enacted in many areas. Gaps among policy, theory, and practice are common.

Proceedings
The report, Bridging Policy and Practice: A Focus on Teacher Preparation. Reflections from the 2002 Park City Mathematics Institute International Panel on Policy and Practice in Teacher Education, is also available via the International Link on the PCMI home page (http://mathforum.org/pcmi/).

Summer 2003
Theme
To examine the preparation and professional development of teachers with respect to both mathematical content knowledge and how to teach that content. To deepen the personal contact among policy makers and teachers from the selected countries representing diverse educational systems and cultures by sharing examples of "best practice" from pre-service and in-service programs.

Countries
Cameroon, Ecuador, Iran, Japan, Northern Ireland, Romania, New Zealand, and the United States

Emerging Issues/Central Themes
Support and help for beginning teachers is critical but is rarely provided in a systematic way in most of the countries.

Issues of communication, resources, and educational infrastructure are problematic in developing countries, directly impacting what it is even possible to do with teachers.

Grounding the conversation in examples was productive. It was particularly helpful to participate in a teaching laboratory observation.

Summer 2004
The International Seminar did not officially take place during the summer of 2004 because the Tenth International Congress on Mathematical Education (ICME) was held in Copenhagen, Denmark. All participants from the past three summers were invited to take part in two PCMI-related sessions that were held as part of ICME. In addition, the classroom teacher from Ecuador, Luis Fernandez, was attended the PCMI High School Teachers Program (HSTP) immediately following ICME. Mr. Fernandez took part in the HSTP courses, had informal discussions with the US participants, and made a formal presentation to the group on teaching in Ecuador. He also consulted with PCMI leaders on how to take what he learned at HSTP and adapt it in ways that would be most useful in his country.

Proceedings
The brief report on the PCMI sessions held during ICME is available via the International Link on the PCMI home page (http://mathforum.org/pcmi/)

Summer 2005
Theme
To consider the meaning of mathematical literacy in an international context and examine the connection between definitions of mathematical literacy and views on the mathematical knowledge needed by teachers in order to teach well. Participants also explored the ways in which teacher preparation programs in the seven countries approach the task of instilling the types of mathematical knowledge for teaching that support mathematical literacy among all students.

Countries
Chile, Germany, Iran, Russia, Singapore, Uganda, and the United States

Emerging Issues/Central Themes
We can learn a great deal by examining what works in other nations, but educators in each country must attend to issues of context (both in the originating country and the destination country) when trying to decide if a particular practice that works abroad will work at home. Simply adopting a practice because it had a desired outcome abroad may introduce a destabilizing element into the education system at home. Care must be taken to adapt exogenous practices to the local social, cultural, and economic context rather than impose such practices on systems and peoples to which those practices are ill-suited.

Regional conferences that are attended by mathematics teachers, mathematics teacher educators, and mathematicians can help to close gaps in communication and promote better alignment of secondary and tertiary mathematics education.

The training and working conditions for teachers in some countries place them at a significant disadvantage with regard to fulfilling national expectations for students' mathematical proficiency and increasingly globalized expectations for mathematical literacy. Providing teacher preparation experiences and working conditions that adhere to some internationally-proven standards could significantly improve the teaching and learning environments in many countries.

There are similarities and differences in the ways in which mathematical literacy is defined in different countries. In some cases, these definitions are borrowed from other countries. In other cases, they are indexed to the local/national economy. International assessments that attempt to measure mathematical literacy define it in a particular way and produce results that support and confirm the definition and measured outcomes in some countries and conflict with those in others. What would it mean to be mathematically literate from a multi-national point of view? What mathematics would such an individual know, and what mathematics-related activities would that individual be able to do?

Proceedings
The report, Bridging Policy and Practice: Statements on Adapting/Adopting Best Practices, Establishing Regional PCMI Seminars, International Recommendations for National Standards and Norms Concerning Teachers' Preparation and Working Conditions, and Mathematical Literacy for All Students is available via the International Link on the PCMI home page (http://mathforum.org/pcmi/)

Summer 2006
Theme
This seminar focused on mathematics teacher education with a strong emphasis on preparing teachers to promote mathematical problem solving, reasoning, and proof.

Countries
Cameroon, Germany, Mexico, Pakistan, Poland, Singapore, Uganda, and USA, along with a commentator/discussant from France and the from the USA.

Emerging Issues/Central Themes
There are similarities and differences in the ways in which problem solving is conceptualized and implemented in the primary and secondary mathematics curricula of different countries. In several of the participating countries, the standards for problem solving, reasoning, and proof contained in the National Council of Teachers of mathematics (NCTM, 1989, 2000) standards have influenced how these topics are defined and when they appear in the curriculum.

Most of the participating countries demonstrated diversity in their approach to these topics, both with respect to the school curriculum and to the teacher education and professional development programs. Variety ranged from little emphasis on reasoning and proof prior to secondary school Geometry to frequent problem-based learning in elementary school. Preparation for teachers ranged from little or no mention of these topics (except to the extent that they are already imbedded in the official curriculum) to intense focus in the teacher education program and frequent professional development opportunities in these areas.

Issues that influence whether mathematics teachers emphasize problem solving, reasoning, and proof in their classrooms include:

• teacher's level of mathematical knowledge, which must be high to support dynamic interpretation and flexible responses to students mathematical ideas.
• availability of materials for use in problem solving, as examples of the types of reasoning teachers should aim to promote, and as models of informal and formal proof that are appropriate for students at different grade levels.
• Infrastructure that supports high levels of peer interaction and teacher-student interaction, such as sufficient classroom space for setting small groups and class sizes that are small enough to allow for adequate monitoring and guidance.

Proceedings
The report, Bridging Policy and Practice in the Context of Reasoning and Proof Statements on: Problem-Solving in the School Mathematics Curriculum; Preparation of Teachers for Teaching Problem Solving, Reasoning and Proof; and Conditions for Teachers to Engage in Problem Solving and Reasoning in Their Classrooms is available via the International Link on the PCMI home page (http://mathforum.org/pcmi/)

Summer 2007
Theme
This seminar focused on mathematics teacher education with a strong emphasis on preparing teachers to promote mathematical problem solving, reasoning, and proof. Standards for reasoning, and proof vary across countries with a strong historical background to have reasoning and proof based in geometry.

Countries
Australia, Columbia, Mexico, Namibia, the Netherlands, Turkey, Vietnam and the United States of America.

Emerging Issues/Central Themes
There are similarities and differences in the ways in which reasoning and proof are implemented in the mathematics curricula of different countries. Among the considerations emerging were:

• The meaning of reasoning and proof
• When and how students learn the concepts and when the concepts become formalized
• The effect of technology on what and how reasoning and proof are taught
• The mathematical content and didactical knowledge teachers need to teach reasoning and proof
• Needed research from an international level on teaching reasoning and proof

Most of the participating countries demonstrated diversity in their approach to these topics, both with respect to the school curriculum and to the teacher education and professional development programs. Variety ranged from little emphasis on reasoning and proof prior to secondary school Geometry to frequent problem-based learning in elementary school. Preparation for teachers ranged from little or no mention of these topics (except to the extent that they are already imbedded in the official curriculum) to intense focus in the teacher education program and frequent professional development opportunities in these areas.

Briefs
Participants produced three short policy briefs that present their collective views on

• The Nature and Role of Reasoning and Proof,
• Conditions for the Effective Teaching and Learning of Reasoning and Proof, and
• Assessment of Reasoning and Proof.

These briefs are available at http://mathforum.org/pcmi/overview2007.html

PCMI@MathForum Home || International Seminar Home || IAS/PCMI Home

© 2001 - 2009 Park City Mathematics Institute IAS/Park City Mathematics Institute is an outreach program of the School of Mathematics at the Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540 Send questions or comments to: Suzanne Alejandre and Jim King