Discomfort and Learning

People love patterns and categorizations. Students laugh when I say "this problem is exactly like the last one but completely different." A good example of overgeneralization is the equation of a straight line y = mx + b where m = slope and b = y-intercept.

Everything is cool and groovy with y = 2x + 5 (slope 2 and y-intercept 5)
or y = 4x+ 8 (slope 4 and y-intercept 8)

but what about y = x (where slope 1 is invisible as is y-intercept 0)?

This New York Times article "How Nonsense Sharpens the Intellect" has research and ideas about promoting learning and creative thinking through novelty and anomalies.