PCMI International Seminar: Bridging Policy and Practice in Mathematics Education Around the World, Summer, 2011
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 weeklong International Seminar, "Bridging Policy and Practice in Mathematics Education Around the World" was held as part of the 2011 PCMI Summer Session. This seminar focused on the teaching and learning of complex numbers 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 (Canada, Finland, Ghana, Honduras, Indonesia, Slovenia, South Korea, and the United States).
Discussions and presentations related to the general questions:
Where do complex numbers fit in your country's curriculum? Is there a role for complex numbers in the study of geometry with transformations?
In particular participants responded to the following:
- Complex numbers and their usage are taught in many countries in the solving of quadratic equations. Is this common in your country? If so, how and when does it occur? If not, when and how are solutions of quadratics handled?
- The study of complex numbers sometimes focuses on the arithmetic of complex numbers at the secondary level (high school). Is this common in your country? If not, when and how are the numbers introduced? What obstacles or misconceptions do students encounter when learning about complex numbers?
- How do prospective teachers encounter complex number in their teacher preparation programs? How extensively is it used and for what levels of teachers?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?
- What applications of complex numbers does your country teach (such as DeMoive's Theorem and polar coordinates)? How do these topics fit into a tertiary mathematics program at the introductory level?
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
- Reflections on the History of Complex Numbers
- Integrating Algebra and Geometry with Complex Numbers
- A Learning Progression for Complex Numbers
- Complex Numbers in Teacher Education: Connecting Mathematics and Pedagogy
2011 PCMI International Seminar Participant Directory (password protected)