**I=prt**

When I think back to a specific time I felt like a failure as a math teacher, a couple different things come up. Once, in what had to be my fourth or fifth year teaching, I was going over interest with my 7th (?) graders, and of course, was being observed by my Bank Street advisor at the time, and I confidently taught my students that interest = principle times rate times time (I even had it written on my slide) and even emphasized to them that it's principle not principal, which, of course, is wrong, and was the first thing my advisor pointed out in our debrief. I felt mortified.

**Integer Chips**

Another time, also around the same time, is when I was trying to move from direct teaching of integer operations to conceptual teaching, using red and black integer chips to model addition and subtraction number sentences. Growing up, I was taught the algorithms for these, and knew that when subtracting integers, you simply just "keep, change, change" or keep the sign of the first integer, change the subtraction operation to addition, and change the sign sign of the second integer. All of a sudden I was supposed to use these red and black chips, to model subtraction. Not wanting to introduce them to the tool before fully understanding it myself, I spent many a lunch period trying to make sense of the chips until one day, it all came together. Zero pairs! Yes, I can put in as many zero pairs as I need without changing the value of the number sentence, and then, once I have enough chips to subtract, I can then follow through with the subtraction. It was so clear! And it was kind of nice to see the algorithm in a whole new way. I think what stuck with me the most however, was an important reminder that sometimes, understanding something in math just takes time, and that is OK.

**This Year**

Although there are many more examples of mistakes/errors/failures I could mention throughout my teaching career, I would be lying if I said that they are all a thing of the past. I still make them, and will still make new ones in the future. Luckily, I can say will fair confidence that I solidly have middle school math down, and so not much surprises me in terms of content, but every once in a while, I will come across something I said, that mathematically turns out to be untrue. The nice part about that is then, I can proudly admit to my 6th, 7th, and 8th graders that I was wrong (if they haven't already caught me) and that mistakes happen and they are OK.

As for feeling like a failure, I can't think of one great teacher, who, doesn't think of themselves as a failure sometimes. How can we not? Even the best of us (I'm talking way better than me) still have bad lessons and bad days. I feel like a failure when I have tried everything I know to help a student make sense of something, and they still don't. I feel like a failure when it takes me more than a week to grade an assignment, because teaching five classes across three grades is a lot of prep and grading work. I feel like a failure when I know I wasn't able to give a lesson 100% because I didn't have the time to plan better.

But mistakes don't mean the end of something. Mistakes give us the opportunity to change our thinking. After all, if we all thought the same way and always got everything right, we might not be creative. We might not see different perspectives. We might not be afraid to try new things, out of fear of failure. To borrow a phrase from my favorite cartoon teacher & hero, Ms. Frizzle, mistakes give us the freedom to "take chances... and get messy" ;)

Mistakes are messy. Math is messy sometimes. And that's OK.

I've had mixed reactions when I've used manipulatives similar to the Integer Chips that you describe. For some students they were helpful, while others were more like you, havingalready mastered algorithms without the need for "tiles" or "chips."

ReplyDeleteMy school embraces manipulatives, and soon I'll be required to use them in my upcoming lessons, including integer lessons.

It's been a pleasure getting to read your posts during the 2017 Blogging Initiative. See you in 2018!

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