Thought I'd steer clear of this heavy meta-science argument and respond instead to wseiber's:
Contrary to popular belief (at the base of many intelligence tests etc), there is no uniquely defined, "correct" way of continuing any finite number sequence.
My 9yo daughter would certainly concur with you there, wseiber. Here's a recent homework question she was given.
[Q1 and Q2 have pictures of shapes - you'll have to use your imagination]
Complete the following patterns:
1) circle, triangle, square, circle, triangle,...
(Her answer of square, circle, triangle,... was marked correct)
2) tall block, medium block, short block, tall block,...
(Her answer - medium block, short block etc - again correct)
3) 11, 21, 31,...
(Her answer? She spotted the similarity to Q1 and Q2 and gave what was to me a perfectly plausible and natural answer, i.e. 11,21,31,11,21,31,11,... Teacher, of course, marked it incorrect, and probably still has no idea where it came from, or how the questions led her "astray". I got quite a chuckle out of it - I just hope my daughter hasn't been assessed as innumerate!)
