This summer I’ve been reading a few different books. One of them is Becoming the Math Teacher You Wish You’d Had. It’s part of a book study that started a few weeks ago. Kudos to Anthony for helping start the study. I’m slowly making my way through the book, following the tag and listening to people’s comments on Voxer. My highlighter has been busy. I appreciate all the different teachers that Tracy showcases. I’m currently in chapter four, which is related to making mistakes in the math classroom.

I believe making mistakes is part of the math learning process. I don’t think I’ve always communicated that enough. Some students that I see come into the classroom with an understanding that mistakes are evil. They’re not only evil, but I’ve seen them used to humiliate and discourage students and peers. I believe these types of behaviors tend to crop up when the culture of a classroom isn’t solid. Of course there are many other variables at play, but a classroom culture that doesn’t promote risk-taking isn’t reaching its potential.

Tracy showcases different teachers in chapter four. All the educators highlighted seem to be able to communicate why it’s important to look at mistakes as part of the math journey. This chapter is full of gems. A couple takeaways that I found are found below.

- The math teachers that are highlighted seem to understand that mistakes are opportunities. When they happen, teachers have a choice to make. Modeling and showing students different ways to react to mistakes is important. Students need to be able to understand and be accustomed to making mistakes in stride. This can be a challenge since some students stall or immediately stop when they run into a mistake. Mistakes shouldn’t be perceived as failure. If a student makes a mistake they need be able to have tools and strategies to move forward. They need to also find the underlying reason to why the mistake or misconception happened. Having a misconception investigation procedure in place for these instances is helpful.

- Using classroom language that creates safety is key. Teachers need to be able to have phrases in the bank that empower students to participate and take risks. I found that the teachers highlighted in the book often ask questions related to students explaining their reasoning. They also set up the classroom conversation so that students build upon each others’ responses. Students speak their mind about math in these classrooms. They’re not afraid to respectfully agree or disagree with their peers and explain their mathematically thinking.

- I noticed that the teachers played multiple roles during the observation. Teachers often gave students time to work with partners/groups to discuss their mathematical thinking. This time of group thinking and reporting happened throughout the lessons. Teachers often anticipated possible misconceptions and guided the classroom discussion through students’ thinking. The teachers asked probing questions that required students to give answers that displayed their mathematical thinking. Teachers didn’t indicate whether an answer was correct or incorrect. Instead, educators asked students to build upon each others’ answers and referred to them as the lesson progressed.

I can take a number of the strategies identified in the observations and apply them to my own setting. I see benefits in having a classroom conversations where students explain their math thinking. That productive dialogue isn’t possible unless the culture of the classroom is continually supported so that students feel willing to speak about their thinking. Students aren’t willing to take risks and explain their thinking to the class unless a positive culture exists. That type of classroom needs to have a strong foundation. That doesn’t take a day, or a week. Instead, this is something that is continually supported throughout the year. Next year I’m planning to have students use the NY/M tool again. I’d like to add additional pieces to this tool. I’m also planning on using more math dialogue in the classroom. I believe students, especially those at the elementary level, need practice in verbally explaining their mathematical thinking to others. That verbal explanation gives educators a glimpse into a student’s current understanding. I also believe that giving students more opportunities to speak with one another about their math thinking will help them develop better explanations when they’re asked to write down their math thinking.

I’m looking forward to starting chapter five on Monday.