Which works better - long-term projects and investigations or ones which can be completed in one or two lessons?
Preparatory questions and links:
Focusing questions:
How do long-term and short-term investigations or projects differ?
How should long-term investigations be introduced and maintained?
Are certain areas of the curriculum more conducive to investigations than others?
How does the content of the investigation impact on the length and method of exploration?
What do you see as the main purpose of inquiry-based projects, long or short, in mathematics? Does this have any bearing on the amount of time you spend on it during lessons?
Should the exploration be done during lessons, outside lessons or a mixture of both?
What criteria would you use to assess the effectiveness of the investigation - too long, too short, quality of outcomes, etc.?

(Provided by @ColinTGraham)

Useful Links:
By TES - links to resources for mathematics investigations
By Project Euler - list of problems which require more than just mathematical insight to solve.
By Richard Brown - investigations for primary age classes.
By NRICH - monthly maths problem
Blog post by Reidar Mosvold - Review of Math Investigations (Note this is a US elementary curriculum by TERC)

Threaded discussion from Thursday 11th November 2010 -
Threaded discussion from Monday 15th November 2010 -

Links mentioned in the discussions, with contributor:

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

Other links which may be useful