x^3 = 1*x*x*x
Well, when you put it like this, the conclusion feels irresistible!
But it also feels like an artificial move. Not something the student would come up with, unless they already understand it.
I would probably go with:
x^3 / x = x^2
x^2 / x = x^1
x^1 / x = …complete the pattern, then contemplate on what “x^1 / x” is
I do exactly what you describe with my students, but sadly with extremely limited results.
Well, when you put it like this, the conclusion feels irresistible!
But it also feels like an artificial move. Not something the student would come up with, unless they already understand it.
I would probably go with:
x^3 / x = x^2
x^2 / x = x^1
x^1 / x = …complete the pattern, then contemplate on what “x^1 / x” is
I do exactly what you describe with my students, but sadly with extremely limited results.