I wanted to come back to talk a bit about my follow up to bucketing kid mistakes. I had my students write a detailed reflection of their exam. They had to identify which type of mistakes they had made the most frequently, to list the math concepts they had missed, and to thoroughly evaluate their study strategies in order to seek further improvement.
As the kids were looking carefully at their mistakes (I said I'd collect their reflections and compare it against their tests to make sure they were doing a thoughtful job), they changed some categorizations down from procedural to simply careless, if they are sure that they knew what to do but just didn't apply the skill carefully. They also noted to me if they had made various mistakes due to the same essential misunderstanding (ie. not looking to distribute the negative sign).
The kids' reflections that have been completed so far have been very impressively detailed and honest! In response, I corresponded with them in writing to add my assessment or recommendation for improvement during the second semester, and I am going to return the tests and their reflections next week to take home to review with their parents. In my comments to them, I wrote down things like if I think they should be checking their answers regularly against the back of the textbook, or if I think it was quite commendable that they persisted for a long time during the exam to try to get through even the hardest questions, regardless of whether they had finally succeeded. On my Grade 8 exam in particular, I commended the whole class for doing well and persisting when challenged on certain problems. For Grade 7, I noted to the kids that many of their exam scores did not accurately correspond to their normal performance, which showed me that they still have ways to go in working on their test-preparation strategies. (One of them, for example, did tons of practice problems but never checked her answers against the back of the book, so many of her practice problems were in fact incorrect when I looked at them! Another student signed up for some random math website and did random problems before the exam, instead of the problems I assigned for practice. While other students did 50 problems of the same type, and then ignored the 9 types of other problems that were going to be on the exam. These are all weird things that I am glad now I know they need to fix...)
Overall, I think this idea was a success! Instead of me saying to the kids that they are still making careless mistakes, they were pointing it out to me that they're not reading instructions, or not answering the questions fully, or making careless procedural errors -- all of which, they say, could have been avoided. I was very pleased because they were drawing the same conclusions that I wish they could have drawn, without my input.
I wouldn't do this level of reflection after every test, because it's lengthy and I don't want kids to start treating reflections as a "let's-just-get-through-this" thing of routine. But, I think I am going to stick to doing careful reflections twice a year to help them grow as students.
PS. On a totally different note, have you seen this? It's beautiful, and amazingly makes me feel (again) like the world is small. The guy who made this is my college friend's friend from high school!