1. Thinking Out Loud About Possibilities
Plenary Roundtable
Thinking Out Loud About Possibilities

2. How can we…
Improve our conferences?
Improve our project activities?
Improve mathematics education in our countries?

3. Common Issues/Questions Across Working Groups

4. About Teaching and Learning
Teachers/Teaching
Students/Learning
What is the knowledge base for teaching—what knowledge is entailed in teaching math?
What is good teaching? (Who should decide?)
What is the role of technology in teaching and teachers’ work?
What does it mean to know mathematics?
What is competence in mathematics?
How does technology enhance learning of mathematics?

5. More on Teaching and Learning
Collaboration leads to better teaching
We can teach big ideas of the discipline/We can teach qualitatively & quantitatively
Importance of seeing progress/reflective practice/self and collective efficacy beliefs
Learning/doing math is a social activity and collaboration leads to better learning
Perhaps we (or the school math systems we create) underestimate what students can do/learn
Importance of mathematical disposition/attitudes/beliefs

6. More on teaching and learning…
It’s all about making sense. Sense-making generates knowledge and application of knowledge leads to wisdom.
(Thanks Brad!)

7. Interesting Practices
For Teachers
For Students
Lesson Study
Good questioning techniques
Using errors and misconceptions as learning moments
Case Writing and Analyses
Autobiographical reflection and writing
Focused classroom observation & data collection
Rich Learning Tasks—evoke curiosity, challenge intuition, make sense of math and teaching math
Group work and other forms of student-student interaction
Dynamic software and other technology tools
Use of concrete materials & other representations
Problem posing/publishing student problems
Games and drama
Metacognitive reflection
Rich Learning Tasks—evoke curiosity, challenge intuition, make sense of math

8. Some Other Questions
What can be learned from study within and across cultures?
Why is the school curriculum the way it is? Does it have to be this way? Why?????!!!????? Why?????!!!?????
What is sacred and what isn’t about the current organization of school mathematics programs?
How does the curriculum relate to the history of ideas in mathematics within and across cultures?
What are the ethical issues in how we teach, learn, and use mathematics?

9. More Questions
How can we get individuals and societies to be more competent in knowing and doing mathematics? Why do we want/need to?
How should exam systems be organized?
Who/What creates obstacles to progress?
From where do we get our authority as math educators? How do we know that we know what we’re doing or talking about?

10. Concerning the Conference Theme
Supporting innovative practices may require (radical) restructuring, possibly revolutions of existing systems and institutions
There is often a gap between intellectual/ disciplinary paradigm shifts and enactment “on the ground.” The current reform has been with us for decades now. What is holding us back?

11. Is it… Fear of the unknown?
Reluctance to give up tradition and security that comes with it?
Inability to prioritize resources (human, financial, technical, etc.)?
Lack of competence to enact our ideas?
That we need to re-examine our values?

12. We do have choices.
We do make choices.
Our choices have consequences.

13. JOIN THE REVOLUTION OF THE POSSIBLE*
THINK OUT OF THE BOX
JOIN THE REVOLUTION OF THE POSSIBLE*
*apologies to Ed Silver and the QUASAR project