> > On Jun 3, 2013, at 9:25 PM, Richard Strausz > <Richard.Strausz@farmington.k12.mi.us> wrote: > > > Bob, if you were leading such a workshop and > someone made that mistake how would you respond? > > > > Richard > > > You determine how she got there. Since I wasn't there > I can only guess her reasoning, but I would guess > that she already knew which was larger because of the > discussion at hand in the workshop. She then realized > from the arithmetic that r1/r2 gave the same result > in this case. Then came her ultimate mistake in > reasoning, that this singular arithmetic result > implies a general rule. It wasn't a mistake in the > algebra you know, it was a mistake in the reasoning > behind the algebra you know. > > First I would make sure that she understands that. > > Bob Hansen
My question is one of teaching judgment. I don't know if there is a 'right' answer, but I think I'd want to show her an example first that her answer was wrong before launching into the algebra. If we had time, it might lead to an interesting discussion on what conditions would cause her answer to be right.