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

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”

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

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

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

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)?

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?

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?

x as solution What solutions do we have?