1. Some thoughts from the conference
Facing the unknown or
Let’s talk about x
Some thoughts from the conference
Helen Chick

2. x as constant Debate about definitions
What are the constants in algebra education?
Debate about definitions
All students need at least some algebraic knowledge
Importance of “meaning” over “manipulation”

3. x as constant Importance of “algebraic expectation” and “symbol sense”
What are the constants in algebra education?
Importance of “algebraic expectation” and “symbol sense”
Algebra is abstract and symbolic
Children are capable of generalisation

4. x as variable Quality of research Quality of teaching
What are variables for conducting research; what varies in its quality?
Quality of research
Quality of teaching
Content covered and standards expected in different countries
Students’ ability to cope with abstraction

5. x as variable Amount of manipulation required by situations
What are variables for conducting research; what varies in its quality?
Amount of manipulation required by situations
Amount of manipulation required in syllabi
Relationship between research and practice

6. x as unknown What is the algebraic knowledge needed by which students?
What do we have to solve for?
What is the algebraic knowledge needed by which students?
What is the role and impact of technology?
What is the influence of culture (social or mathematical)?

7. x as unknown What manipulative and algorithmic skills are required?
What do we have to solve for?
What manipulative and algorithmic skills are required?
What notations and symbolism are appropriate?
What are the key ideas of algebraic structure? For whom?

8. x as unknown
What do we have to solve for?
How can we get good algebra teaching in all maths classrooms?
What tasks should we use?
What teaching strategies?
How can we make better connections between research and practice?

9. x as solution
What solutions do we have?