Mistakes and Erasers

Today I was looking at my child's online math learning platform, and I stopped on some very pointed instructions made in a video lesson, "If you made a mistake, cross out the mistake, and write the correct answer next to it. Don't erase."
I've long struggled with finding ways to address my child's fear of imperfection, and my students', and my own. I have a policy in my classes that you should do your math homework in pencil and erase your mistakes. When I bring it up, I always reiterate, "Remember you will make mistakes. Not because of anything about you, just because you're human. Be prepared." I have the "write in pencil and erase errors" instructions on all exams. I'm wondering how much impact it has to make a switch to encouraging people to keep their mistakes visible rather than erase them.

I looked for some research specifically on the question of whether having students erase mistakes is helpful or not, and I came up with basically nothing. Lots of research about the value of de-shaming mistakes. Here is one particular article that sort of summarizes some of the research well, as well as a video of one 7th grade teacher's approach to helping her students learn from their mistakes.

One of the things that I've sort of quietly struggled with in the past, and I've not ever taken the time to make a decision, is how much I treat in-class quizzes and exams as finished pieces of work. I've always cringed at disorganized work and big messes on exam pages, and frankly have punished students for it. I have a concept category of "Organization" that I judge for every piece of work that is turned in. It's totally wrong to do this. When you're performing a type of math that you already know, then you can have the cognitive capacity to attend to the presentation of the work. But if you're working out your understanding, then it'll be messy, and there will be mistakes along the way. And I want to give credit to students who are working out their understanding on exams and quizzes. The neatness and organization shouldn't be assessed until 2nd-draft presentations. So, maybe what it should be is that students get two shots at an exam: an original, and a make-up. The make-up can be done on the students' own time, and they are asked to be very tidy and organized for that one.

Back on pencils and erasing: I did find this blog post, which contains the anecdote of a person receiving the gift of a pencil from their mentor, with the following wisdom of an eraser.

1. Erasers allow us to correct mistakes, and mistakes are correctable. Everyone makes mistakes. You have to erase them, and let go of the mistake.
2. Erasers give us the power to adjust, and our best work requires adjustments and updates. Your plans absolutely must be written down, and they need to be written in pencil. The world and your situations will change. The eraser will help you be more flexible and adaptable.
3. Erasers give us a safety net, and remind us that the pressure isn’t as great as we might think. Think about it, if you do a math assignment in pen, the pressure is on to get the answers right the first time. This is not an excuse for doing poor work, but having an eraser does take off some of the pressure.
4. Erasers invite us to edit, and results of a second (or third) draft are almost always better. If you don’t succeed (or succeed as completely as you hoped), the eraser lets you make edits and try again.
5. Erasers erase the past, and help us focus on what’s next. Yes, you must learn from the past, but you must be forward focused. The beauty of a great eraser, like the one on the pencil I’ve given you, is that it erases well enough that you CAN focus on what’s next.

While I appreciate the sentiment of this advice, I have to poke at some of its lessons. The biggest one is just generally the concept of erasing mistakes. I have made sooo many mistakes in my life, and I am a better person for them. I understand so much more because of them. If you ask me whether I regret having made the decision that put me into a really bad situation, almost every time I will answer with a no. I regret having had to live through certain situations, in the sense that I remember the pain of living through them, and often still feel the pain in the remembering; but I do not regret in the sense where I would choose something different if given a time machine. I was married at a very young age, and I got divorced at a similarly young age. The whole process of my divorce was incredibly painful for everyone involved. But there is no way in the world that I would give up everything that I had during that 10-year relationship for the sake of "erasing" that mistake. Actually, truth be told, I don't necessarily think it was a mistake for us to marry; but it would have been nice if we could have gone into it with more of an agreement that either or both of us might choose something different later (here's an example of where we might benefit from normalizing error). 

I love the notion of erasers giving you an invitation to edit, but I don't think that erasing is a great metaphor. For one thing, second and third and fifteenth drafts are never done on the same sheet as the first draft, so the eraser is irrelevant in this analogy! Most editing of physical documents happens on computers these days, and in fact it's helpful to have the original draft with all of the editing marks all over it, so you have the opportunity to puzzle through the edits and the comments.

I actually really like the metaphor of editing. When we edit, we take the time to look at the previous draft and make improvements. In the end, we throw away the old draft and only keep the new. But we don't forget that the old draft existed. When we have a final product, we remember how many drafts we went through, and we will remember a few of the specific edits we made. This feels right to me, in terms of how I edit my personal life and self. I have the me that is present, and I remember lots of what went into the making of me, including some of the specific changes that I've made along the way. But none of those past drafts of me are hanging around for others to see. They exist in my memory, and in the memories of others, but those old memories are of previous drafts. If anyone asks who I am now, the best way for them to find out is to get to know the me of now.

I think the points about having a safety net for experimentation and a tool for focusing on the future rather than dwelling on mistakes are fine, but I don't love erasing as a metaphor. Sometimes there is joy in all of the weird things that you did along the way of experimentation (Post-It notes, anyone? Silly Putty?). And again, focusing on the future does not require forgetting mistakes of the past; in fact it usually requires remembering mistakes of the past.

Going through this metaphor of erasers of life, I think I've decided that I'm not strongly in a camp of encouraging students to erase their mistakes or to keep them, but I do think we need to have better normalizing of the making of mistakes. We need to have a culture that values experimentation as a way of progression, or even just getting things wrong sometimes and being willing to correct errors. For my teaching, I think this means I'm going to change the way that I grade in-class work on neatness; maybe I'll only grade on neatness for less-frequent projects that are done at home.