> > On Jun 4, 2013, at 8:34 AM, Richard Strausz > <Richard.Strausz@farmington.k12.mi.us> wrote: > > > 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. > > Of course it is natural to start with a counter > example to show that her conclusion is wrong, she > probably wouldn't listen to anything else till you > do, but that doesn't show why it is wrong.
I agree totally.
> I know what you are thinking, like everyone else on that > site, "It's wrong because it doesn't work!" or "It's > wrong because she divided by r instead or r^2!".
I think you and I disagree about the intent of the blog post and most of the folks who commented. Dan Meyer himself referred to the counterexample as a good first step before the algebra is taught.
> > What you (and they) don't understand is that in the > context of teaching a student algebra, "wrong" > doesn't mean why the conclusion is wrong, it means > how did she wrongly get there? I don't care if her > conclusion is right or wrong. I care how she got to > it. She might be wrong even if her conclusion is > right. That is what needs to be addressed because > that is what algebra is. How to reason. > > Imagine this. You may just be the product of several > generations of teachers trying to teach algebra to so > many unprepared students that at this point you have > simply forgot how to teach algebra as well as the > point. I don't mean that disrespectfully.
I have forgotten a lot of things over the years, but not how to teach algebra - even though I'm not teaching it this year.