The Power of Mistakes in Math

I am reading this amazing book by Jo Boaler called Mathematical Mindsets.
In it she references Carol Dweck's research on growth mindset and takes it a step further to make some needed connections to math teaching and learning in the United States and Great Britain. She discusses some work by psychologist Jason Moser. He studied the neural mechanisms that operate in people's brains when they make mistakes. He stated that there are two possible responses in the brain when we make a mistake. The first is called an ERN response which is an increased electrical activity when the brain has conflict between a correct response and an error. This brain activity occurs whether or not a person knows they have made a mistake. The second response, called a Pe, is a brain signal when we know we've made a mistake. It happens when we know we've made the mistake and we pay attention to the error. Moser's study is interesting because it shows that we don't even have to be aware that we've made a mistake for brain sparks to occur. Moser concluded two interesting things. First, they found that students' brains reacted with greater ERN and Pe responses when they made mistakes than when their answers were correct. Second, they found that brain activity was greater following a mistake for students who had a growth mindset compared to those with a more fixed mindset. Those people with growth mindsets had a greater awareness of their errors were more likely to go back and correct errors. So, there was a greater chance with these people that more brain sparks were likely to occur.

All this brain research is interesting, but what can we do in our classrooms to change the way children feel about making mistakes? Historically, math has always been so focused on getting the correct answer that it is hard to change our way of thinking about wrong answers. We really need to do things in our classroom to change that message.  There's a great idea in the book about a teacher who starts math class by asking students to crumble up a piece of paper. Then students throw it at the board thinking about the feeling they had when they have made mistakes in math.  Then students get their papers back, smooth them out and trace all the crumple lines with markers. The teacher explains that the crumple lines all represent brain growth that we experience when we make mistakes. Then the students keep these papers in a math folder or notebook.
Another idea referenced in the book is something called "My favorite mistake." When students are solving problems in math, choose a wrong answer that has a lot of right things in it, but there's just one little conceptual mistake. Share that with the class and focus on all the right things in the answer. Then focus on the mistake and how students can learn from it.  There's a great video from the Learning Channel called "My Favorite No" where an middle school math teacher does something like this. Doing things like this can start to change our students' thinking about mistakes.
I hope that these two ideas are things that you might be able to use with your own students.  Stay tuned- I will share a lot more ideas and insights from this amazing book.

Number Talk Accountability

You know how it is- you are doing an amazing number talk with your students. They are sharing all sorts of interesting mental math ways to solve the problems and you think, "This is good!" Then you realize that you only have maybe half of your students (and somedays that is a high estimate) really engaged in the process. The rest, and in my case, it is usually my lower kiddos are really not engaged or paying attention to the strategies. Either they are lost because the strategies are beyond their realm of thinking at the time or they just are not engaged.  What can you really do and still maintain the structure and purpose of the number talk?
One quick fix is to prepare a set of double sided cards. You choose the colors- mine are blue and green. I used leftover cardstock and I cut 3 x 5 inch cards out of the cardstock and glued them together so I have blue on one side and green on the other. Then, I laminated them. At the start of the number talk, I give the cards to the students. I explain that they start with the cards in their laps. When they know the answer, they place the card on their desk- they can choose which side is up. If it's blue, that means they have an answer, but they don't want to share. If the card is green, they have an answer and they are willing to share their strategy. This is a quick way to make students accountable, and it makes it easy for you to choose someone to share.
Another way to make students accountable is to ask them at the end of the number talk to use finger signals to indicate the most efficient strategy. After students have shared their strategies (and you've numbered them) ask students to choose which strategy they think is most efficient. By doing this you can informally see where the students are in their thinking and can plan accordingly with additional number talks.
A third way to provide some accountability is to hold small-group number talks throughout the week. You can easily add a quick number talk to your small group math instruction. And, holding the number talk in a small group allows you to really hone in on particular skills that certain students need.
Class anchor charts explaining different strategies is another great way to hold students accountable. When you make the strategies visible in the classroom, it provides a great reference for the students and holds them accountable because the information is right there on the wall!
Another way to hold students accountable for the strategies they are learning in number talks is by asking them to solve an exit ticket problem. Give students an index card or half-sheet of paper. Pose a problem that will require them to use the strategies you've been working on. Ask students to use one side of the paper to solve the computation using a strategy that was shared during number talks. On the other side of the paper, they can solve it with their choice of strategy.  Doing this give you a quick look at individuals and their understandings and misconceptions. It also helps you choose the next direction you want to go with further number talks.  But, don't use these as a grade- simply use the information gathered to guide your instruction.

Engage New York Training

I am starting a new job in a few days. I will be the K-6 instructional coach for math in my district. I will wear a lot of hats, but one of my favorite will be to plan professional development for the different schools. This is one of the things I am most excited about because I will have some say in the topics of professional development and I know what I don't like about PD and I can try to provide better training for teachers! One of the biggest pet peeves I have is when we start a program and the district just gives us the materials and expects us to figure it our ourselves. This happened two years ago when we were given the Eureka math materials. We were told that this wasn't our adopted curriculum but we should use it. But, they didn't give us any training on it AT ALL! Anyone who has used the materials knows that it is not the most user friendly program ever written. It is very wordy and hard to sift through all the script-like lessons to get to the meat of the lesson. And, when you are given the materials a couple of weeks before school starts there's really no time to investigate the Eureka websites and find all the resources that are there that help explain the program. So, for the last couple of years teachers have been wading through it-teaching it the best they can. But this past year when I had 3 new teachers on my team- all unfamiliar with the ENY/Eureka materials I truly realized how much we needed some professional development! And, fortunately, I am just the math coach for the job! I went on a quest for information- I visited the Eureka website and watched hours and hours of videos and sifted through a lot of information. I've created, what I think, is a pretty good professional development training on how to plan for a ENY/Eureka lesson. I know sharing the PowerPoint is not the same as being in a training, but if you're struggling with how to sift through all the words and script of the lesson, I think this might help a little. Check out the slides and then, if you're interested, click on the link. How to Plan a ENY/Eureka Lesson