The Value of Mistakes

There are many things that you do not learn in your credential program or through student teaching. If you're reading this, chances are that you're already creating a list in your head of different things that you wish you had known before you started. (Feel free to leave that list in the comments below!) For me, one of those things was how to start the school year. Sure, I was told not to smile until December, make sure I had plenty of structure, but also make the kids feel welcome and create a caring environment. Great! How?

Thinking back, I don't remember the first day of school when I was student teaching. It wasn't that long ago and I'm sure that I have notes about it somewhere, but that's not my class. Can I really start a very different group of students the same way? We did some ice breakers and other collaborative games, but I wanted something more meaningful than that, something that would stick with them - I'd wish for the rest of their lives, but settle for the rest of the school year. I decided to share a story with them about myself:

While I was working on my credential, or shortly after, I attended a math conference on campus. In one of the sessions, they provided us with a prompt. Teacher A is planning a field trip for X students. If a small bus costs R amount of money and fits Y students and a large bus costs S amount of money and fits Z students, what combination of small and large buses will be the least expensive for X students?

 We were told to work in pairs to solve the problem and were given 10-15 minutes. My partner and I decided to quickly talk through our ideas and then work independently - solving the problem on our own, and then defending our solution to each other. I quickly worked through it, started to explain it to her, and realized I was wrong. She explained her idea and we saw that her solution was also wrong. So we got back to work. Then I had it! I calculated the price per seat and determined the best combination. My partner did not agree with my idea at first, but explaining it I was able to convince her. The presenter came by, we explained it, and he said he liked it and asked if we would be willing to share it with the class. We had no problem with that and quickly agreed. He went on his way and we started discussing other things - like finding a job. It was only a few minutes before he returned to say, "By the way, your solution is incorrect, would you still be willing to share it with the class?"

In a few minutes, I was sharing my errant idea with the class and letting them all know the wrong way to solve it. Although we were the only pair to solve it this way, a few others said that it made sense to them. Then someone asked a question and was able to identify our error and point us in the right direction.

I shared this with my students for a few reasons. First, I wanted them to know that I make mistakes, too. (I try not to very often, but it does happen.) Second, I wanted them to see that because I was willing to share my ideas, even if they were incorrect, I was able to learn a correct solution and adjust my method so that I could reach that solution. Third, I thought that by sharing my mistakes, they might be more willing to share their mistakes. I want a classroom environment where my students are willing to share their ideas, even if they are "wrong" and think critically while problem solving. I do not want my students to equate "different" with "wrong".

There were some rewards for me from this - a few students took it to heart. I had a parent warn me at the beginning of the year that their child did not like sharing ideas and was uncomfortable making mistakes in front of the class. Shortly after I was able to tell this parent that the student was regularly sharing solutions and ideas with the class, even if they were incorrect. At the end of the school year, one of the students wrote that she was more comfortable with us knowing that it was a "class that made mistakes" and learned from them.

Even though it may have only made a difference for a few students, I will share this with my next class. I want my students comfortable with making mistakes and learning from them and sharing with their peers. We all make mistakes, why not encourage it before our students are conditioned against it?