There was a lively back-and-forth on the BoingBoing forum about whether anyone should care about what a celebrity thinks and whether or not New Math is bad.
As people discussed how awful the school system is, someone brought up the compulsion to "show your work" that is built into math. Then someone else asked whether "show your work" is actually a bad thing. Sure, kids don't like it, but it's good for them, right?
My reaction to "show your work" is revulsion, but I have to admit that the "show your work" people have a pretty good point. One mentioned that while she could do everything in her head in Grades 5 and 6, it was important to get in the habit of being careful then for later school. Another said that teachers are there to evaluate whether students know what they are doing, not whether they happened to get the right answer to some questions - they can't do that without knowing what steps the students took. Another person said that no matter what you are doing in any field it is worthwhile to be able to explain your methods.
So there you have it, really kids should show their work because there are lots of benefits and the only drawback seems to be that kids don't like being told to do things.
That's not easy for me to say, though, because "show your work" will always remind of me of a system that failed me as a child. It's one thing among many that taught me that the point of school and of work and of pretty nearly everything else you do is to just do what you are told to make other people check off whatever box you want them to check off.
To be clear, I never needed to show my work for my own sake. It's not a habit I learned in Grade 5 that suited me in Grade 12. Grade 12 was just as much of a breeze as Grade 5 was. My marks in highschool math courses are indicators of how much I liked the teachers of those courses. This was confirmed when I went to first year university and my average went up 15 percent over highschool. When my teachers told me I needed to learn to show my work because I'd need to later they had not idea who I was. When they said I needed to do my homework and study for tests to develop the skills of doing homework and studying, they were just dead wrong.
And sometimes I feel I can't blame them for being wrong. I was an outlier. I don't know how many children like me passed through their classes over the years, but if I was in the upper echelon of the top math program in the country - one of the top math programs in the world - and walking out of exams after forty minutes because I was done and keeping an average in the high 90s then it's safe to say I might have been the only example that any of those teachers saw that was quite like me. If not, they maybe saw one or two others. How could they extrapolate that I was the exception to their rule? What could they even have done with me if they had known?
A few teachers over the years tried to do things to keep my interest but their challenges were easy for me and in the end they left me alone. In many cases I was probably better at math than my teachers were anyway.
"Show your work" meant "do busy work because I don't have any idea what to do with you." That probably prepared me for the real world more than anything else I did at school. Knowing how to force yourself to sit down and do whatever stupid thing someone with authority over you says you should do is pretty much the essence of getting by in the workplace. There was a good dose of learning how to be liked but not well liked as well. In a way, school did all that it could for me.
But really, if I had wanted to show the work I was actually doing, it probably would have looked like this:
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