PCMI International Seminar: Bridging Policy and Practice in Mathematics Education Around the World, Summer, 2010
Different traditions and practices in mathematics education across the world offer valuable ways of thinking about what it means to teach and to learn mathematics. In particular, many current practices and pieces of research can be examined against other countries' norms and policies as well as from the perspective and experience of different cultures, political systems, and economies. These reflections may inform not only individual countries' mathematics education programs but may serve to bring the international community closer to some common understandings.
Since 2001, the International Seminar on Mathematics Education has brought together a small group of international participants, selected for their key roles in policy and practice in mathematics education in their own countries. The primary goal of the Seminar is to establish an ongoing dialogue that examines, in practical and grounded terms, the interplay of policy and practice in diverse systems of primary and secondary mathematics education. Participants in the Seminar design and implement a series of reflections on common problems, along with suggestions for policy and practice and innovative offerings to share with the international community. The set of countries represented in the Seminar changes over time, with continuing attention to diversity and variety in educational challenges.
The eighth weeklong International Seminar, "Bridging Policy and Practice in Mathematics Education Around the World" was held as part of the 2010 PCMI Summer Session. This seminar focused on the teaching and learning of recursion and mathematical induction and implications for teacher preparation and development. The invited team participants consisted of one mathematics education/policy-maker and one practicing secondary mathematics teacher from each of eight countries (Cambodia, Canada, Denmark, Ghana, Israel, Peru, South Korea, and the United States).
Discussions and presentations related to the general questions:
Where does recursion fit into your country's curriculum? What is the role of technology in teaching and applying recursive techniques?
In particular participants responded to the following:
- Recursion is a common tool used in work with spreadsheets and especially with arithmetic and geometric progressions. Is this common in your country? If so, how and when does it occur? If not, when and how are arithmetic and geometric progressions introduced?
- Recursion is sometimes used as an introduction to mathematical induction at the secondary level (high school). Is this common in your country? If so, how and when does it occur? If not, when and how is each topic introduced?
- How does recursion fit with geometry/algebra in your country? If it does not, do you expect that it would at some point in the future?
- How do prospective teachers encounter recursion in their teacher preparation programs? How extensively is it used and for what levels of teachers?
The participants worked together to establish consensus on various issues that emerged in the course of the discussions and, in working groups, produced three short policy briefs that present their collective views on
- Multiple Perspectives on the Nature of Recursion and Proof by Mathematical Induction
- Why Are Recursion and Proof by Mathematical Induction Important Mathematical Tools
- Developing Reasoning with Recursion and Mathematical Induction in School Mathematics?
2010 PCMI International Seminar Participant Directory (password protected)