[quote=Cola] I know its a pain but I do not get the you shouldn't have to show your work take on math. It sure helps you move ahead when you jump into a “rigorous” stage of math work, especially at a younger ages.
I very well could be wrong but it seems to be clicking for my ds who has always been a math kid and totally hated showing his work on the easy stuff.
You are right - I agree that "show your work" is a good concept. The problem arises when it's coupled with math that's too easy, and the requirement many are describing here to use painfully convoluted methods to get to simple places. So on simple problems where DS can simply "see" the answer, "show your work means "go back after the fact and artificially insert a long, circuitous pile of steps you didn't actually use to satisfy an arbitrary process". Time to do math problem: 5 seconds. Time to write out invented process: 15 minutes. Time to provided written explanation in complete sentences: 30 minutes.
What I would like to see is if a teacher wants work shown, they need to ask a question that requires actual work to get to the answer (and that doesn't mean just add more digits to the question!).
In contrast to these problems at school, at home DS has not balked at all on his weekly AoPS problem that must be submitted as a full-detail "proof", with complete sentences. These are complex problems, and he enjoys writing them up (caveat: I scribe for him) in the form of "how would I show my friend T how to do this problem?" I think it's marvellous that AoPS requires them to learn how to provide coherent explanations of how they solve problems, and he is learning a ton from having to do this.
