I'm going to play devil's advocate for a moment. I used to teach math and science (to high school students, so I understand that it's a slightly different situation.) I used to make them show or explain EVERYTHING, and the reason I started doing that was because of an extremely gifted young man who came through my class one year. He had a talent for Physics, and a lot of the problems came to him almost instinctively. About halfway through the year, though, his grade in the class started dropping. So I started paying closer attention to how he was doing his classwork. As it turned out, this incredibly smart kid was so good at this stuff, he wasn't taking the time to work through the steps - while he was getting the right answer, he didn't fully understand how he got it. It was no problem until the problems started getting a little harder. The class built on itself throughout the year, so not having a thorough understanding of the ins and outs of the problem started to hurt him after a while, when he could no longer breeze through the steps and come up with the answer in his head. So I started having him explain everything to me in minute detail - no more skipping steps. He HATED it at first. But now he is in college at Virginia Military Institute. He recently emailed me to thank me for "making my life miserable," as he put it, because being familiar with that fundamental (although tedious) thought process is making his math and engineering classes MUCH easier for him.
Anyway, my point is that although it seems like a waste, there is actually some logic behind forcing her to explain it. I'm sure it's frustrating for her, but hopefully it will help her in the long run.
I have to wholeheartedly agree.
My daughter (still) doesn't NEED to 'write it all out' to get the correct answers. Most of the time, that is.
But her accuracy sure shoots up appreciably when we force the issue, and having taught
college students, both science majors and not, I agree that while it might
seem like a waste to force kids to write things out...
there really isn't a substitute for learning the process. Dimensional analysis, for example, relies VERY heavily on being able to problem-solve by blindly applying
the process.With students that haven't been
forced at some point to write things out, their problem-solving ability just goes to heck in a handbasket. Because most of the principles applied in biology and chemistry, and even in basic physics? They are really pretty basic algebra, trig, and geometry.
I can do most of it in MY head, for sure. But then again, the process is completely automatic at this point given that I've been working with solution normality, pH, and unit conversions for over twenty years. I
still write it out-- why? Because that's part of being trained as a good scientist. You write
everything down.
I've never known anyone with an advanced degree in math or science that didn't eventually need to learn this. The later you learn it, the harder it is to swallow, too (because there is a real danger in thinking that smart = NOT writing it out. No. "Smart" = getting the right answer and knowing it's correct, or being able to analyze your work and know where you went wrong.)
Is this dependent upon the level at which you are learning? Well, sort of. I've observed that MOST of the time, even gifted students need to write out more than they THINK they do, particularly when using a foundation skill to acquire a new skill. (So, for example, my daughter can't multiply binomials in her head when she's using that skill to do geometry/trig-- she needs to revert to writing it out so that she doesn't make the EASY mistakes.)
Does my daughter insist that this is a waste of her energy? Of course. She also insists that including units with measurements is in the same category, because everyone KNOWS that an elephant can't weight 2400 GRAMS... and that she doesn't need to indicate that a value represents inertia, because she'll "remember" what that three digit value represents. At eleven, she's not always right about those things.
Now, as to 'explanation' of work, THAT I think is ridiculous, for just the reasons already elucidated above. Well-written, neatly conducted calculations should include units when they represent real world quantities, and if they do-- then they should quite literally be self-explanatory. Hmmmph.
Sorry-- but this one is a personal soapbox. I know where this (I can just do it in my head) train goes, and at the college level, it's far from pretty.
