I had a thought about this - when my kids do worksheets they obviously write ON the worksheet and while I'm not a stickler for showing their work, I do encourage it to a point to avoid mistakes and make it easier to correct mistakes. But if someone is working with a hardcover text will they typically re-write the problem? Is this a positive or a negative? My kids are a little averse to writing so OTOH, I don't want to make math too onerous. OTOH, it might be good practice and also force them to really focus on the problem. As I think about this, I am realizing this is part of my problem with the online and worksheets approach. There's something about the presentation of the answer that seems not right to me.
Anyone have any thoughts?
By chance I was reading an article relating to this just last night:
http://www.artofproblemsolving.com/Resources/articles.php?page=mistakesI think best practice when using a textbook is not to write out the question, but just to write a reference to the question (e.g. page number, question number) and then set about answering it. I've heard it argued that writing out the question helps to fix it in the student's head, and perhaps for some it does, but it doesn't seem like a sensible thing to insist on everyone doing, to me.
I think it's important to be able to show your work, if asked - in "real life" mathematics often what matters most is not being able to get an answer, but being able to convince someone else that your answer is correct. However, I also think it's useful to be able to organise one's thoughts in one's head - sometimes people (this was me at one point) get so caught up on needing to show their working that they can't do anything beyond simple arithmetic without pen and paper, and that's limiting, too. Variety is the spice of life.
