Why do we need to teach mathematics to under 16s?

Preparatory questions and links:

Focusing questions:
When we are talking about mathematics and the pre-high school curriculum, is it possible to do 'proper' mathematics?
What adjustments need to be made to take cognitive development into account?
What areas or topics within mathematics can usefully be explored for interest, without needing 'in-depth' proof or supporting concepts?
Is it ok to investigate topics and leave questions totally unanswered until much later, if at all? What impact could this have on the learner?
Is mathematics irrelevant for the majority of under 16s and does the core curriculum need to be changed to functional numeracy instead?

(Provided by @ColinTGraham)

Useful Links:

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Threaded discussion from Friday 28th January 2011 -
Threaded discussion from Monday 31st January 2011 -

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