algebra project

In my assorted cleanings I have *not* successfully located my copy of the algebra project book, which I am confident would have my father grinning in his grave. So, I've googled instead. An amen moment from one of 'em: "one group might have got that answer using an approach that's not mathematically sound... we need to make students understand... the reason a rule work is because it's tried and true...and it works every time in that situation." And then, that it's the teacher's job to figure out when a student has applied their non-valid reasoning to get the right answer. Oh, *please,* can I hear an amen?
Note that she didn't say the student used an approach different from the one that the teacher presented, but one that was **not** **mathematically** **valid.**
Now... to have teachers who know the difference!!!!

My students believe sometimes that it's all a complete mystery -- the rules work when they work, but there are exceptions and really only those other people -- the elite Smart People Who Know Math -- who know when.