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Design and share beautiful flyers just like this one!

Spread the word with an online flyer. They're easy to make and impossible to mess up :)

Chapter 7... Division Time!

I cannot believe we are already on Chapter 7! This has been a great week of blogging and video notes from everyone! Thank you so much for opening your practice while also helping me improve upon my own!

In a couple of weeks we will be asking for your feedback on this book study experience. We will love to hear about what you learned, what you liked, what could be improved upon and if you would like to see learning experiences like this in the future. Please be thinking about these questions as we finish our ending chapters!

My K-2 people, in this chapter I would love to hear/see the ways in which division begins to develop in the younger grades with sharing situations!

As we learn together, please understand that the material I post or share is not necessarily meant to be the "how to" guide of Number Talks, but more a topic of conversation we can all learn more from. Thank you to those brave enough to open and share your journeys with us, I truly appreciate it! If you would like to comment or pose questions on any of the material in the newsletter, please feel free to visit the appropriate platform and engage in conversations!

Have a Great Weekend!

~Kristin

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Design and share beautiful flyers just like this one! Spread the word with an online flyer. They're easy to make and impossible to mess up :) I cannot believe we are already on Chapter 7! This has been a great week of blogging and video notes from everyone!

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This is part of Crystal Morey's Getting Better Together series, Making Number Talks Matter Book Study. Crystal and all the Teaching Channel Laureates are going public with their practice and seeking support in getting better from colleagues and the Tch community.
So it happens. A student finally feels comfortable and safe enough in your classroom to share his thinking. However, when he does, it's a strategy laced with misconceptions. You're unsure of your next teacher move. If that student feels embarrassed after interacting with you, he may feel "math injured" and refuse to participate in the future. On the other hand, you want to make it clear that there's something you don't understand about his thinking.

You're in a predicament. You feel forced to respond because the other students clearly know something is incorrect in his logic. But you're sensitive to feelings and classroom culture. In these moments, the response by a teacher is critical for maintaining a sense of safety in the classroom.

Well, I faced that exact situation recently. Luckily, I had the chance to meet with Ruth Parker, co-author of Making Number Talks Matter, the text that's at the heart of a an online book study I'm co-leading with Laureate Kristin Gray as part of my Getting Better Together series. I shared with Ruth a video that I recorded of myself (see below) leading a subtraction number talk in which a student demonstrates deep misconceptions. We watched as the student shared his solution to the problem 10 1/2 - 3/4 (the 2:18 to 3:42 mark in the video).

Please enable Javascript to watch this video

Though the student got to the right solution, when I asked the question "why is ½ + ¼ = ¾?" he was unable to respond. So I asked him to come back later in the number talk if he wanted to explain his thinking.

As the student returned to the conversation (6:45 to 8:50), he shared several misconceptions. He began with ½ + ¼ is 2/6 (a common misconception) but followed with an additional misconception I was unprepared for: he determined that 2/6 should be reduced to 2/3. Finally, he proceeded to say that 2/3 is equivalent to 3/4.

These misconceptions unveiled numerous, deep misunderstandings. As the teacher, I didn't know where to start. I worried that the number of questions I would need to ask to help him identify why his strategy was inaccurate would overwhelm him.

As Ruth and I reflected, she gave me the critique and advice I desperately needed. She told me there was little I could do in that moment to help the student brush up against his own misunderstandings. What I could do was let the student know that I needed time to think about his strategy and get back to him at a later time. Honoring a student's participation in the Number Talk is absolutely critical.

Ruth reminded me that my job in the midst of a Number Talk is not to "fix" the student's thinking. So it was essential that I let the student off the hook. This is not to say that I won't meet with that student privately and use this formative data to guide that discussion. I will, and have.

This thought was reinforced by Lisa Olin's comment in our book study Teams group, where I posted the video for general feedback:

In the weeks since I met with Ruth, I've been getting back to students privately. When unable to do so, I've been using this data to drive future lessons to help overcome the misconceptions I witnessed. In addition, I've been carefully guarding how many questions a student is asked by peers. When an interesting strategy is shared, there are often four to six student questions. While one or two may be appropriate to clarify thinking, too many questions can cause a student to shut down and create a feeling of being picked on.

I'm tremendously thankful for my meeting with Ruth. Teaching a subject matter that has high stakes testing attached, I feel such pressure to perform. Call it perfectionism, a type A personality, or overachieving. Whatever the label, for me, the result is stress. I needed to be reminded that sometimes it's ok to let students sit with their misunderstandings until the time is right to address them. It's OK to get back to students later. In fact, by doing so, you maintain an environment where kids feel safe and comfortable and willing to share their thinking, which is what allows them to reveal their misconceptions to begin with.

By addressing them privately, they avoid being embarrassed in front of their peers. Most importantly, they're able to maintain a level of calm, which makes deep thinking and learning possible.
Crystal Morey is a middle school math teacher in Enumclaw, WA. She has served on the county's Common Core transition team and is a teacher leader on a statewide project with Washington State's Office of the Superintendent of Public Instruction, and the Mathematics Education Collaborative. Connect with Crystal on Twitter: @TheMathDancer.

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What's the best response when a student makes his thinking visible publicly, but his response is full of misconceptions? Laureate Crystal Morey gets guidance.

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In 6th grade I feel like I see students using the Start from the Left strategy the most along with Break One Addend Apart.  I feel like students don't usually use the Round and Adjust or the Take and Give. I believe this is due to the fact that when most students think of addition, they are thinking simply that and nothing else.  The two strategies that were just mentioned  usually involves subtracting of some kind.  Students with great number sense would use all of these strategies.

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I really loved reading through the examples, especially with fractions and decimals. I never learned these strategies as I went through school, and when parents complain about the "new" way we teach our kids it is because they also don't understand how to manipulate numbers around and only know the traditional algorithm. I think about fractions and automatically think back to all the "tricks" to get the answer. The example problems in this chapter were GREAT to look at!