Why is it that the phrase “*solving *the Rubik’s cube” has such a different meaning to me than it does to others? For a long time I was quite puzzled by people who made the implausible claim that they had “solved” the Rubik’s cube. And then I had a sudden insight: they were using the word in a way that was very different from the way I use it.

To me, you can’t claim to have *solved *the Rubik’s cube unless you have invented (*on your own*) an algorithm that will turn any randomly arranged Rubik’s cube into the correct configuration. But apparently many people have a far lower bar. They interpret “solving” to be the process of *using *a known algorithm in order to turn a cube into the correct configuration.

I think of this as the difference between genuine problem-solving and going through an exercise. For example, *using* the quadratic formula is not problem-solving. Independently *deriving* the quadratic formula, or manipulating a non-obvious equation or word problem into a form in which the quadratic formula can be used,* *would be examples of problem-solving.

Categories: Math, Teaching & Learning