Does the nature of mathematics change as students get older or is it only the teaching methods that change?
Preparatory questions and links:
Focusing questions:
When, or if, you think about mathematics, what do you actually imagine mathematics is?
At what age do you remember saying to yourself "Ah, that's what mathematics is!"?
What role does cognitive development play in how mathematics is viewed, learned or taught?
Do you actually change your teaching methods as students get older? If so, how? If not, why?
Can 6 year olds be taught 'mathematics' or do we need to think about helping them build their mathematics over the years?
Does the nature of mathematics change, especially since some state that over 50% of it has been invented since 1945?
Is it possible to teach without taking development into account - ie should the focus be solely or mostly on a continuous adaptation of methodology towards the learner?
Are there certain techniques or methods which are always successful and so should not be changed?

(Provided by @ColinTGraham)

Useful Links:
Blog post by Gary (@republicofmath) Teaching a range of mathematics: content and development
Blog post by Ryan (@suburbanlion) (d/dt) Nature of Math = 0?
By David Moursund What is Mathematics?
By NTCM What is Mathematics? (early years explained for parents)

Threaded discussion from Thursday 14th October 2010 -
Threaded discussion from Monday 18th October 2010 -

Links mentioned in the discussions, with contributor:

Resources (costing money!) mentioned in the discussions, with contributor:

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