Of course, with the current curriculum of the OP, all I have to do is explain my logic, even if faulty, and all is forgiven.
I think the point that is being missed is that you should be gaining an understanding rather than just memorizing a bunch of stuff that you can't really apply well. Assuming that is true, explaining your 'logic' should allow you to see your own error. Failing that, whoever you communicate your logic to should be more than happy to show your error. Certainly people don't all think things out the same way. There can be many ways to arrive at correct answers, though some may be more efficient. Hearing a student's explanation of their thinking can reveal potential thought pathways that may later get them in trouble. I don't have an opinion one way or another on Common Core. I do think the woman used a very poor example in what she did.
I've been too hard on myself for no reason.
Quite the contrary. I think students who explain their logic should be learning to self critique their thinking.
