Go Big or Go Home: Math Rocks Day 2

This has been a busy week, but I can finally sit down to write about day 2 of our Math Rocks class. (In case you missed the post about day 1, here it is.)

One thing that has kept me busy is reading and responding to all of the blog posts that our group has generated this week. Here are a few you should check out if you have a few minutes:

  • Leilani wrote about how one simple sentence led to rich problem solving and discussion last year.
  • Kari shared a story that sounds like it’s straight out of a teacher nightmare, but it really happened to her!
  • Carrie’s post is short and sweet, but I love that she chose to write about Counting Circles in her very first blog post.
  • Brittany shared an honest and touching reflection of an experience in Math Rocks this week.

I’m so impressed by the stories, reflections, and ideas already being shared. It makes me so excited to see what else we have in store this year!

We started Day 2 with some math. This is actually a problem we posed at the end of Day 1, but we never had time to discuss it because setting up everyone’s WordPress and Twitter accounts took quite a while!


This problem actually came from Steve Leinwand’s keynote at Twitter Math Camp 2014. The numbers involved are small, but I chose this problem because the relational thinking involved would likely stretch many of the educators in our group. This is the problem Brittany refers to in her blog post.

After giving everyone 5-10 minutes to solve the problem, I had them go around their tables to share their current thinking. I let them know before they started working that it was okay if they hadn’t finished solved the problem yet. The purpose of the discussion was to give them a chance to share either their solution *or* their current thinking about the problem. Both are perfectly acceptable. I wanted to model this specifically because it’s a teaching move I would like for them to try out in their classrooms. I got the idea from this Teaching Channel video. You’re welcome to watch the whole thing – it’s about introducing fraction multiplication – or you can skip to the 3:30 mark.

After sharing, most everyone was ready to jump into creating a solution together. I had them share their agreed upon solution on a blank piece of paper. Then they had to take a picture of it and tweet it out to our hashtag for the course, #rrmathrocks. As they worked, I walked around and talked to them about how their solution had to be convincing because anyone on Twitter would be able to see it, so the solution has to stand on its own.

I did this intentionally because after they tweeted out their work, I shared with them how they could do something similar in their classrooms by participating in the Global Math Task Twitter Exchange. Each week a class signs up to pose a problem to their grade level hashtag. Other classes from around the world solve the problem and tweet out their solutions. It can be very motivating to students because you’ve provided them a global audience for talking about and doing math. I wrote a post related to this a few weeks ago.

We didn’t talk about their solutions…yet. I have plans for them down the road.

After everyone tweeted out their solutions, we revisited our norms:

  • Share and take turns
  • Give each other time to think
  • Be open minded
  • Share far and wide
  • Be respectful of each other
  • Take risks
  • Always do your best

I’m especially proud of how much they’ve embraced being open minded and taking risks already.

We quickly moved on to reviewing first drafts of our new district common assessments. Our department has to write them, but we try to involve teachers as much as possible in the review process in order to get feedback and to be as transparent as possible. We want to assure teachers our goal is not to trick them or their students.

Since we had a group of educators from grades K-5, and our assessments are for grades 3-5, we paired up the primary teachers with intermediate teachers. The intermediate teachers were responsible for ensuring the primary teachers understood the standard correlated with each question.

Some wonderful discussions ensued. I talked to a few teachers about a question that they felt was one step too difficult for the students. They convinced me to make a change to the question so that it will be clearer from students’ work and answers whether students can truly do what the correlated standard says they should be able to do. Another group had questions about multiplication algorithms. We had a great conversation about the distributive property and the area model, and how these two things can support students up into middle and high school.

After they were done reviewing assessment items, we came back together to discuss ambitious math instruction. I love the phrase “ambitious math instruction.” I didn’t coin it of course. This came from Teacher Education By Design, a project out of the College of Education at the University of Washington. It’s one of my favorite places on the internet.

You should probably check out their page on ambitious math instruction for yourself, but here’s a snippet:

Developing a vision of ambitious teaching and putting it into practice is complex work. The instructional activities, tools, and resources offered by this project are designed to support teachers to learn about and take up practices of ambitious teaching and engage children in rich mathematics. The routine structure of the activities bounds the range of complexity teachers might encounter while creating space for them to learn about the principles, practices, and mathematics knowledge needed for teaching while engaging in the practice of teaching.

What I really like about this is the use of routine activities as a way to allow teachers to try out new ideas and practices within clear boundaries. They go on to share their core practices of ambitious teaching in mathematics:CorePractices

In Texas we have mathematical process standards that tell us what students should be doing to acquire and demonstrate understanding of mathematics. Now I have a set of practices I can share of what teachers can do to support their students in learning and using these processes.

We gave each table one of the core practices and asked them to create a semi-Frayer model that showed why the practice is important, example(s) of the practice, non-example(s) of the practice, and an illustration of the practice. Again, we had them take a quick photo and tweet them out to #rrmathrocks. This time we did pull their tweets up on the big screen and use them to talk through each practice.

Teacher Education By Design currently has 5 instructional activities on their site with more to come. Regina and I chose to share two of them – Quick Images and Choral Counting. Many of our teachers are already familiar with Quick Images, which is exactly what I wanted. Since they are already familiar with the routine, it meant they could focus on looking for the core practices in the videos we watched rather than trying to balance that with learning a new classroom routine. Choral counting was new for many of them, so we shared that activity second.

Before getting into either routine, I wanted to stop and think a bit about number sense. We did the Number Sense Trajectory Cut-N-Sort from Graham Fletcher.

As expected, there was a lot of interesting conversation about which concepts come first and why. I had wanted them to make posters and draw a quick sketch next to each concept, but we were pressed for time so I just had them do the matching and ordering. When they were done, I handed out the complete trajectory so they could self-check and discuss with the other members of their group. Because we ended up going through this activity more quickly than I had planned, I’m going to look for other ways to revisit the components of number sense at a later date. It’s a really rich topic, and I want to ensure our group has a good grasp of all it entails.

We finally went into the Quick Images activity. Regina modeled the activity with the group and did a little debrief before we watched two videos of Quick Images in action in a Kinder and 5th grade classroom. I think this routine is often considered a primary grades activity, so I purposefully showed both ends of the elementary spectrum to give them an idea of how robust it really is. When we discussed the videos, we specifically asked for examples of the core practices in action, and we talked about what math concepts can be explored through this activity.

I had wanted to end this activity by having everyone plan a sequence of 2-3 Quick Images that they could do in their classrooms at the start of school, but we were still trying to make up for some lost time. I’m sad that it didn’t happen because I wanted them to experience what it’s like to think through the planning of this activity. However, since this wasn’t a brand new activity for most of them, I felt like it was okay to let that go for now. Maybe we’ll revisit it in the future.

We then moved into Choral Counting. I led a count with them where we started at 80 and counted by 2s all the way up to 132. In the middle of the count, I stopped everyone and asked what the next number would be, and I asked how the person knew. In our debrief afterward, I admitted that I wasn’t intentional enough about where I chose to stop. I asked the group where I should have stopped, and they agreed that 98 or 100 would have been a better place to stop because students often have difficulty counting across landmarks.

I also asked whether we would say 216 if we continued the count. One person said yes, because all of the numbers are even and so is 216. I did my best to act like the surprised teacher: “Whoa! You just said all of these numbers are even. How in the world could you make that claim so quickly? There are 27 numbers up here!” She shared that the ones digit in each column was an even number. I told them it’s important to keep an ear out for grand claims like this. It’s easy to just accept the statement that all of these numbers are even, but to the untrained elementary school eye, that is not necessarily obvious nor do they necessarily understand why or how it’s true.

We watched a video of a 3rd grade class doing this activity, and again we debriefed with a focus on the core practices. I was so impressed with how intently they watched all the videos and all of the teacher moves they noticed. From conversations I had during the rest of the day, it sounds like some of them are inspired to be more intentional in their planning and carrying out of these types of activities.

Now that we had made up for lost time, I was able to have them practice recording some counts. One of the powerful pieces of choral counting is that how the count is recorded impacts the patterns students notice and the conversation that ensues. I had each person choose a count appropriate for their grade level and record it three different ways. This reinforced what some of them already noticed before about how intentional planning can make these activities that much more powerful.

At this point we were starting to run out of time, so all we were able to do with the remaining time is introduce the book Intentional Talk. We’re not going to read the whole book during this course. It offers so much, but I’d rather be selective and practice a few key strategies out of the book. We’re going to start with chapters 1 and 2 and add another one down the road if time permits. I really want to ensure everyone has the chance to process and practice the concepts from chapter 2 before trying to add more to their plate. If you’re wondering why, check out these posts I wrote about the first two chapters of Intentional Talk here and here.

After reading the first few pages of chapter 1, everyone tweeted out a key point that stood out to them.

IntentTalk1 IntentTalk2 IntentTalk3 IntentTalk4

We wrapped up our intense and amazing two days of learning by telling them about Math Rocks Mission #3. The gist of it is that they have to set goals for themselves and their students. They also have to anticipate the obstacles that might get in the way of meeting their goals. I’ve listed all of the Math Rocks blogs on the sidebar of the Math Rocks site. If you get a chance, you should take a look at their goal-setting posts. I’ve enjoyed reading about how excited they are for the upcoming school year as well as their thoughtfulness regarding their goals and potential obstacles. Not everyone has written yet, so you might wait until Tuesday which is their soft deadline because that’s when I launch Mission #4! We’ll be launching a mission per week up until school starts.

If you’ve made it this far, thank you for reading about our first two days together! It truly has been a privilege to spend 12 hours with this talented group of educators. I can’t believe this is just the beginning. We have 9 after-school sessions together throughout the school year and one half day session to wrap everything up in February. I’m looking forward to it!

Go Big or Go Home: Math Rocks Day 1

My brain is full! I just finished two amazing days of PD with about 30 educators in my district. I promised I’d blog about it, and I need to because I just have so much going on in my head right now. Like I said, my brain is full!

This school year, I’m leading an advanced course with elementary teachers in my district. I didn’t really have any guidance beyond that, so it was left to me and my co-worker Regina to set some goals and make a plan. All we started with was a name: Math Rocks. And that’s only because our district already offers an advanced course called Reading Rocks.

Back in May, Regina and I put together an application and asked teachers to apply for this course that has never existed before. Amazingly enough, about 36 people took the time to apply. We read through their applications and selected 24 educators to be in our inaugural class. What I like about it is that we have a wide variety of folks – general education teachers K-5, a few instructional coaches, a TAG teacher, and a few interventionists. And within that group we have dual language teachers and inclusion teachers. They are so diverse; I’m excited about the varied perspectives they’ll bring to our work.

We kicked off the course yesterday and today. We’ll continue our work online for the next month before school starts. Once the school year begins, we’ll meet every other Thursday after school throughout the fall semester. We’ll continue into the spring semester with a final meeting in early February. It’s going to be awesome!

But let’s get back to the first two days. This is the most we’ll ever be together in one place: 12 intense hours across two days.

We opened the first day with a little estimation from Andrew Stadel’s Estimation 180. We of course did the task that started it all: How tall is Mr. Stadel?

After everyone made their estimates, we had them take a walk. Every time we asked a new question they had to find a new partner and introduce themselves. We went through the usual Estimation 180 questions:

  • What is an estimate that is too LOW?
  • What is an estimate that is too HIGH?
  • What is your estimate?

We also added some questions of our own:

  • Where’s the math?
  • Which grade levels could do this activity?
  • Which process standards did you use?

Take A Walk

This was a great way to get everyone up and moving at 8:30 in the morning, but it also started something they weren’t going to be aware of immediately. One thing I did very intentionally throughout the two days was embed FREE resources from my online PLC, the Math Twitter Blogosphere (MTBoS). Unbeknownst to everyone, one of my primary goals for the course is to connect them with this inspiring community. And what better way to entice them than by taking these two days to show off some of the rich resources this community creates and shares freely?

Community Circle

After our getting-to-know-you activity, we moved into a community circle. Regina set the tone by talking about why our district is excited about and invested in this course. Then everyone went around to introduce themselves to the group and talk a bit about why they chose to apply for the course. Their reasons varied, but there were some overriding themes. For many of us in the group, math is not a subject we loved as a kid. In fact, several folks went so far as to say they hated it growing up. On the bright side, these same folks want their students to have better experiences with math than they did. Everyone agreed that math is a rich subject, and they want their students to experience and appreciate that richness.

Their stories during the community circle provided a nice segue into our next activity. We asked the participants to reflect on their own experiences learning math. They had to choose three images that came to mind that symbolize what math was like to them as a student and sketch them on a blank sheet of paper. When everyone was finished, we did a gallery walk.

IMG_9587 IMG_9586 IMG_9585 IMG_9584 IMG_9583 IMG_9582 IMG_9581 IMG_9580 IMG_9579

There were a few recurring themes here as well. Many pictures showed formulas with variables. People said that they remembered being told to use these formulas because they would “work” but they never understood what they meant or why they were using them. Many pictures also showed numerous worksheets, indicating that math was more about quantity of problems than quality of reasoning or understanding. For those that said they disliked math as a child, we talked about when that started happening, and the group was split over it being Algebra or Geometry.

By the way, I’m sharing a lot of the negative experiences, mostly because I felt like I was hearing those most, but I do have to say that there were some voices of folks who did like math as a kid or they grew to like it as they got into higher grades. So negative stories were definitely not universal, which was encouraging.

After debriefing these experiences, we watched Tracy Zager’s talk from Shadow Con 2015. This was basically a small teacher-led mini-conference in the “shadow” of NCTM Boston (hence the name). All of the talks given at Shadow Con are available on the website, along with a facilitator’s guide if you’re interested in utilizing any of the videos in your own PD. Two of the videos really struck a chord with me and ended up becoming the inspiration for our two course goals.

Tracy’s video is called Breaking the Cycle. Here’s a short synopsis. I could write a whole blog post about this video and my thoughts on it, but really you should take 15 minutes and watch it for yourself. It’s powerful stuff.

The majority of elementary school teachers had negative experiences as math students, and many continue to dislike or avoid mathematics as adults. We’ll look at how we can better understand and support our colleagues, so they can reframe their personal relationships with math and teach better than they were taught.

We watched the video, debriefed, and then I shared our first goal for Math Rocks: Relationships.


We want our participants to focus on building relationships this year with:

  • their teammates,
  • their administrators,
  • me and Regina,
  • with their students, and
  • with other educators.

We also want them to build their relationship and their students’ relationships with mathematics.

To help them start working on this goal, we took Tracy’s call to action from the end of the video. Each participant chose a word from a word cloud that shows how mathematician’s describe math. Over the course of the next month, as they attend PD and prepare for the start of the school year, their mission is to plan for math instruction with that word as an inspiration and guide. We’ll revisit how this went when we meet back in September.


And then it was time for lunch. Whew! We crammed a lot in that morning.

After lunch we did a little math courtesy of Mary Bourrassa’s Which One Doesn’t Belong? If you’re unfamiliar with this site, students are presented an image of four things. They have to answer one question, “Which one doesn’t belong?” The fun part is that you can justify a reason why each one doesn’t belong. Here’s the one we did as a group:

Everyone had to pick one picture that doesn’t belong and go stand in a corner with other people who chose the same picture. Once they were grouped, they discussed with one another to see if their justifications were the same, and then we shared out as a group. Here are some of their reasonings:

  • The quarters don’t belong because they equal a whole dollar. The value of each of the other three pictures equals part of a dollar (4 cents, 5 cents, 40 cents).
  • The quarters don’t belong because the word you say for their value (one dollar, one hundred cents) doesn’t start with “f” like in the other three pictures (four, five, and forty cents).
  • The pennies don’t belong because they are not the same color as the other coins.
  • The pennies don’t belong because they are the only coin where the heads face right instead of left.
  • The nickel doesn’t belong because there is only one.
  • The dimes don’t belong because they are the only one where the tails side is showing.
  • The dimes don’t belong because the value of a dime has a 0 in the ones place. All the other coins have some number of ones in the ones place (5 ones in 25, 1 one in 1, 5 ones in 5).

Like Estimation 180, this activity was included intentionally because this is yet another FREE resource created by the MTBoS (pronounced “mit-boss”). It’s actually inspired by another FREE resource created by someone in the MTBoS, the Building Better Shapes Book by Christopher Danielson.

After talking about money, we prepared to watch Kristin Gray’s talk from Shadow Con. Hers is called Be Genuinely Curious, and you should take a few minutes to watch it for yourself:

When students enter our classroom, we ask them to be genuinely curious about the material they are learning each day: curious about numbers and their properties, about mathematical relationships, about why various patterns emerge, but do we, as teachers, bring that same curiosity to our classes? Through our own curiosities, we can gain a deeper understanding of our content and learn to follow the lead of our students in building productive, engaging and safe mathematical learning experiences. As teachers, if we are as genuinely curious about our work each day as we hope the students are about theirs, awesome things happen!

Again, we watched the video, debriefed, and then I shared our second goal for Math Rocks: Curiosity.


We want participants to use their time in this course to get curious about mathematics, about teaching, and about their students. We also want them to find ways to spark their students’ curiosity about mathematics.

When you’re curious about something, you need resources to help you resolve your curiosities. I didn’t want the folks in this course to feel like we were going to leave them hanging. That’s when I formally introduced the MTBoS.


I told them the story of how I joined the MTBoS back in August 2012. (On a side note, it’s hard to believe I’m approaching my third anniversary of being part of this amazing community of educators!) This is a community that prides itself on freely sharing and supporting one another. If the educators in Math Rocks really want to take their math teaching to the next level, getting connected to a network like the MTBoS is the way to go.

One of the amazing things the MTBoS has done to help new members join and get started is to create Explore MTBoS. Periodically, the group kicks off an initiative to help new members start blogs and Twitter accounts. Unfortunately, there isn’t an initiative starting up right when Math Rocks is starting, so I started one up myself. I created a blog where I tailored the existing missions from Explore MTBoS to guide our group as they become members of this online PLC. We did the first two missions to wrap up the first day of Math Rocks. Each person had to make a blog and create a Twitter account.

I’ll admit, I was super stoked about this, but I’ll be honest that I threw more than a few people way out of their comfort zone that afternoon. Despite that, they still made their accounts, wrote their first blog posts, and sent out their first tweets. I am so proud of them for taking these steps, and I am eager to see where it leads from here.

That wraps up Day 1, our first 6 hours together. I’ll share Day 2 in another post.

Intentional Talk Book Study, Chapter 2

I don’t know that I would ever recommend reading Intentional Talk cover to cover. I know that’s exactly what I’m doing this summer, but I can see why it might backfire with regards to changing teacher practice. Across 6 chapters, roughly 112 pages, the book goes in depth into 6 different ways to plan for and structure classroom conversation. The material is so rich, I can see teachers feeling overwhelmed attempting to put all of it into practice in a meaningful way.

In fact, that happened this past year at an elementary school in my district. The faculty did a book study of Intentional Talk, but by the end of the year there was little evidence that teachers were leading varied and intentional discussions. They liked what they read, sure, but trying to plan for and implement all these discussion types got pushed to the side because of numerous other demands on their time. They suffered from the problem of biting off more than they could chew.

This is a defeatist way to start a post, but the reason I’m leading with these thoughts is because I’ve been thinking about how to share this book with teachers and begin to help them successfully incorporate these ideas into their practice. My answer is to start with chapter 2.

Chapter 1 is excellent, don’t get me wrong. It provides rationale for why well-planned discussions are important, but honestly that chapter is only a must read for someone who craves background information or a reason to pursue this work. If you’re reading the book, you’ve probably already decided you want to learn more about facilitating classroom conversations. You aren’t looking for convincing. In that case, you probably want to jump right in and learn something new. So my advice is to skip chapter 1 (for now, at least) and move straight to chapter 2.

And then stop.

Seriously. Quit reading the book.

Take the time to apply what you learn in this one chapter. Believe me, there’s plenty to sustain you for a while! Take time to establish your classroom norms. They are critically important to creating the safe, respectful environment your students need before you start tackling the other discussion types. Take time to teach students the talk moves. Students need practice in learning what to say and how to say it. Let them practice. Let yourself practice! The talk moves are probably going to be new to you, too. Practice using them until you feel comfortable with them. That will take the pressure off when you do finally decide to tackle one of the targeted discussion types.

How long should you wait before picking the book up again? I have no idea. But chances are you’ll know when you’re ready. It might take a couple weeks, a month, or it might take a full semester, but at some point you’re going to notice that your students have gotten really good at sharing and discussing their strategies for solving problems. You’re going to realize that you know the talk moves like the back of your hand. That will be the time to branch out and ask yourself the question, “What other kinds of conversations could we be having?”

At this point, I might recommend reading pages 1-5 in chapter 1 to reconnect with the book and the principles that guide it. When you’re done, consult the table at the bottom of page 3 that provides a brief summary of the goals of each discussion type. Read through those and think about which type might support your students where they are currently in their math learning. After you choose one of the targeted discussion types, read the corresponding chapter and then stop. Quit reading the book again, and take the time to practice the new discussion type while continuing to do open strategy sharing.

Assuming you’re like most teachers, you’re going to teach more than one school year. There’s no reason you have to learn and master all these discussion types in one school year. The most important thing you can do is start by creating a classroom culture where students’ ideas are valued by you and their peers. Where students feel safe taking risks in sharing their ideas because they know everyone in the class is there to support each other in making sense of mathematics. Chapter 2 will help you with this goal. The rest of the book is great, but it can wait. No rush.

Intentional Talk Book Study, Chapter 1

“Math discussions aren’t just about show-and-tell: stand up, sit down, clap, clap, clap.”

Designing and implementing quality mathematical discussions takes effort. It’s not as easy as just having students get up and share their answers to a problem. But don’t let that turn you away from working to improve your practice! This is just chapter 1, after all, and there’s still so much to read and learn. In this chapter the authors lay out four principles that should guide our classroom discussions:

  1. Each discussion should have a goal. This means thinking in advance what it is mathematically you want students to get out of the discussion.
  2. Be explicit! Students likely don’t come to you with the skills needed to participate in classroom discussions. The teacher’s role is to help the students learn what they should be sharing and how they should be sharing it.
  3. Students should be talking and responding to one another. It’s easy in a classroom “discussion” for all comments from students to be directed at you, the teacher. Instead the discussion should be a conversation amongst all the students around a particular mathematical idea.
  4. Students must believe that they can make sense of math, and their ideas are valuable, even when they aren’t fully correct. There’s a lot of learning to be found in mistakes, and we need to value those as much as correct answers. Getting students to share means they have to be willing to take risks, and as teachers our job is to make our students feel safe to do so.

In addition to presenting these guiding principles, this chapter also differentiates two types of classroom discussion: open strategy sharing and targeted discussion. Open strategy sharing is what many teachers already do to some degree in their classrooms. This is when you let students share their answers and solutions to a problem. The goal is to get a variety of responses out in the open. 

However, sometimes you have a particular mathematical goal you want to focus on, such as having the students justify why a particular strategy works. That’s when you would use a targeted discussion instead. These types of classroom discussion are much more nuanced and planning for each one is different. This is why open strategy sharing only has one chapter in the book while 5 chapters are focused on the different types of targeted discussion:

  • Compare and Connect – comparing similarities and differences among strategies
  • Why? Let’s Justify – justifying why a certain strategy works
  • What’s Best and Why? – determining the best (most efficient) strategy in a particular situation
  • Define and Clarify – defining and discussing how to use models, tools, notation, etc. appropriately
  • Troubleshoot and Revise – determining which strategy produces a correct solution or figuring out what went wrong with a particular strategy

The chapter includes three vignettes to help illustrate the differences between open strategy sharing and targeted discussion. I love how the authors insert comments about the intentional decision-making the teacher did throughout each conversation. It shows early on in the book that the teacher isn’t being herded into some lock-step approach. Rather, at every moment you have the power to guide and steer the conversation based on the needs of your students.

One thing that really stood out to me that I didn’t catch the first time I read this chapter is that it’s okay to stop a conversation and come back to it later. I know as a teacher I often let conversations run so long that I wouldn’t get to other things I had planned. In my mind the conversation was so great, it was okay that we were cutting into our next subject by 10-15 minutes. I think this speaks to how I wasn’t planning my discussions in advance. I just let them happen and let them run their course for as long as they were interesting. As the vignettes in this chapter show, however, important mathematical topics can be discussed over several class periods instead of trying to cram it all in to one sitting.

The other thing that stood out to me was how these discussions have the power to give a voice to all our students, not just the high achievers or the outspoken ones. Creating a sense of community where all ideas are valued and respected allows all children the opportunity to be heard and to demonstrate what they understand about math. As the authors say in the book, there are many different ways to be smart in mathematics:

  • making connections across ideas
  • representing problems
  • working with models
  • figuring out faulty solutions
  • finding patterns
  • making conjectures
  • persisting with challenging problems
  • working through errors
  • searching for efficient solutions

How much more exciting to look for and honor these skills in our students rather than seeking out just correct answers! Just think of what valuing these skills tells students about what it means to learn and do mathematics.

Intentional Talk: A Casual, Summer-Long Book Study

I started reading Intentional Talk way back in December. I loved what I was reading, but with many other demands on my time, I was only able to read a chapter here and there before leaving it by the wayside altogether.

Fast forward to now and what do I stumble upon? Some fabulous folks on Twitter are doing a book study throughout the summer, reading just one chapter per week. I can totally handle that! You probably can too! Here’s a flyer with all the details:

If you’re unfamiliar with the slow chat format, basically it means there is no set time to chat. Rather, during the week questions will be posted using the #intenttalk hashtag and you can read and respond whenever it fits your schedule. How convenient is that?

I will point out that the chat did start last week. So depending on when you get your copy of the book, you might have to play a bit of catch up, but don’t worry, you’re not that far behind. Here’s a schedule to show you how the reading is broken up week by week. Take note of the moderator next week for chapter 3, none other than Elham Kazemi, one of the authors of the book! How often do you get to take part in a book study where the author participates? This is awesome!

If you’ve gotten to this point and you’re thinking to yourself, I don’t even know what this book is about. Why should I even bother reading it? Good question!

In the book’s Foreward by Megan Franke, she lists numerous reasons why classroom conversations are crucial for mathematical learning:

  • Students achieve mathematically when they explain the details of their mathematical ideas, when they engage with the details of other’s mathematical ideas, and when others engage with their own mathematical ideas.
  • Engaging in mathematical conversations in productive ways can help students see themselves as smart and competent in mathematics.
  • Students learn to listen to others, ask insightful and respectful questions, and reflect on their own understandings.

Be prepared. This is challenging work, but it is also greatly rewarding work that is worth our time and effort. The authors lay out the vision, but they also provide support through vignettes from primary and intermediate classrooms, guiding principles to help you make decisions, and planning tools to help you get started. And with a community of folks participating on Twitter, you’ll have lots of support to ask questions and share ideas. I hope to see you throughout the summer!

November in June

Today marks the first day of CAMT 2015 (The Conference for the Advancement of Mathematics Teaching). If you’ve never heard of CAMT, then it means you probably don’t live in Texas. We’re such a large state, we have our own NCTM-like conference every summer.

The keynote I attended this morning – there were two going on simultaneously – was given by a guy named Alan November. I had never heard of him before today, but I’m happy I know who he is now.

His speech had two primary themes and both resonated with me. The first is that we should focus on moving beyond the classroom walls towards building networks. He gave the example of a first grade teacher named Ms. Cassidy. She not only has a blog, but she also has a Twitter account. Using social media, her class has connected with other classes from around the globe, and they share their learning with one another. 

One of the ways they do this is through  Math Talk Grade 1 (#mtgr1). Problems are posed to the hashtag, and the students tweet out their solutions through the teacher’s account. In some ways this isn’t special at all. Everyday in classrooms across the country teachers pose problems and students solve them. The difference? An audience! Students are able to see how students from all over the world solved the exact same problem! How cool do you think it is for a class of 7-year-olds to browse through answers from students in Canada? How much cooler is it for them to discover they have a different, possibly better, answer than a student in Italy?

Does this spark your curiosity? Want to try this out for yourself? You’re in luck! You can join the Global Math Task Twitter Exchange taking place during the 2015-16 school year. They’re looking for folks in grades K-12, so if you teach one of those grades, sign up on the Google doc linked on the site and enjoy! If you’re in grades K-5, tweet out to #ElemMathChat from time to time to raise awareness of this exciting opportunity.

The other theme from this morning’s keynote was the importance of students’ voices. It basically comes down to this, teachers, as experts in their field, know too much to fully understand the perspective of students learning the content for the first time. This is known as the curse of knowledge. But students? They can totally relate to one another since they’re all in about the same place educationally. And it just so happens that kids like to talk to one another.

How does this relate to education? One way is by having students create videos for each other explaining concepts, strategies, ideas, etc. Alan gave the example of a class where students were given the choice of creating a tutorial video for homework or the students could do a typical homework worksheet with 10 or so problems.

He shared the story of one student who chose to create a video which turned out to be only about 3 minutes long. When asked how long it took to make the video, the student said 3 hours! The student knew the regular homework assignment would have only taken 10-15 minutes to complete. Her reasoning for doing the video? Homework doesn’t help anybody. The teacher already knows the answers. She made the video instead because it would help her friends.

Alan also shared part of a keynote speech given by Shilpa Yarlagadda. She realized she only had access to her teachers during the school day. At night her resources were her boring textbook or videos made by adults who drone on and on for 10-15 minutes. Her solution? Create her own videos and share them on YouTube. What makes her work special is that in addition to sharing content, she was able to use stories to make it relatable to other kids.

It turns out there are lots and lots of student-created videos out there. One place to find them is Mathtrain.TV. Now, just because students are making their own videos, don’t think that the teacher can just sit back and do nothing. In fact, the role of the teacher becomes Editor-in-Chief. Unsurprisingly, kids make mistakes in their videos all the time, and without guidance their movies can frankly suck. Just because they can relate to their peers doesn’t mean they know how to produce engaging, accurate videos. They need the support of their teachers to point out mistakes and help them learn how to revise their work, similar to how teachers already support students when writing stories.

As a blogger and tweeter for nearly three years, I see the advantages social media and networking have had for me professionally, and I’m excited that more and more school districts are opening up these tools to students and teachers to use in their learning and work. They provide authentic audiences and leverage the ability of students to relate to one another on their own level.

Wrapping Up a Year of Math Intervention PD

Earlier this school year, I blogged about an exciting opportunity I had to offer PD to all 107 of our district’s interventionists spread across the entire school year. I anticipated blogging about the experience during the year, but life got in the way. Here we are at the end of the school year and I am about to offer my final PD of the year tomorrow morning.

At first I wasn’t sure what I would do with them tomorrow. The way the schedule worked, I haven’t had a session with them since February. And with it being the end of the school year, I wasn’t sure what theyd be interested in hearing about. More than anything, they’re probably counting down the days to summer like their students are!

I thought a lot about it yesterday and today, and I came up with a plan that I think does a great job of honoring the work we’ve done together this year, brings us full circle to where we began, and even hints at directions for next year. As with anything I plan, it won’t go perfectly tomorrow, so I want to capture my ideas tonight of how I’m imagining and hoping it will go.

I’m basically going to give the same session 3 times in a row for an hour and a half each. That’s the only way we can cycle through all of the interventionists and provide PD on math, ELA, and a third rotating topic. The trouble is that the first group in the morning is invariably late. The starting time is 8am, but I doubt I’ll have everyone until 8:15. The session post-lunch is just as bad. The only group that will maximize the hour and a half is my middle group from 10:10 to 11:40.

I have too much to cover, so I am planning to start with an activity that I can do with whomever is in the room when the session starts. I’m going to ask the folks in the room to brainstorm at their table all the different ways they can make 120 using base ten blocks. If you miss the activity, it’s okay because you might catch the sharing portion. Even if you miss that, you’ll actually see various representations in the reading we’ll move into after this activity.

All year long, the interventionists have been doing a book study of Kathy Richardson’s How Children Learn Number Concepts. It’s been a great book study because I didn’t require any reading outside of the sessions. Knowing how busy the interventionists are, I know many of them wouldn’t do the reading. Instead, I let them do all the reading during our sessions. Did it take a lot of time? Yes. However, it meant every single one of them got the chance to read and discuss the book. And this is a book you don’t want to miss!

Unfortunately because some of the planned sessions were axed from the calendar, we only got to fully read 4 of the 6 chapters. We don’t have time to read chapters 5 and 6, but I am having them read the introductions to each chapter which is 9 or so pages each. Chapter 5 is about understanding place value (hundreds, tens, and ones) as well as addition and subtraction. A key idea from this chapter is that students must understand how to decompose and compose numbers flexibly, which will serve the students when they add and subtract multi-digit numbers. The example from the chapter is composing 120 in a variety of ways using base ten blocks, just like in our opening activity.


  As people finish reading, I want them to solve 397 + 205 in two different ways. We’ll chat about the reading for a few minutes to reinforce the importance of unitizing, and then we’ll do a brief number talk of the addition problem. I specifically want them to connect their strategies to the concepts in the reading.

Then we’re going to jump over to watching some videos of students solving 1,000 – 998 from the Math Reasoning Inventory website. The first two videos show students who quickly recognize that the difference is 2. The third video shows Ana, a student who uses her finger to draw and solve the problem on the desk using the standard algorithm. After comparing and constrating the students, I want to show them two more videos of Ana solving 99 + 17 and estimating 18 x 21. In every video, Ana gets the question correct, but she relies completely on writing the standard algorithm with her finger. She does not evaluate the problems or demonstrate any number sense.

I specifically want to focus on Ana because I want to talk about how an emphasis on skill-building over sense-making with intervention students can result in students like her who can get correct answers, but they only have a strong grasp of procedures, not necessarily mathematics. I want to ask them how they think Ana is going to perform when she moves up into middle and high school math. Is there a point at which her procedural skills aren’t going to be enough?

After this we’ll move into the pre-activity for the next chapter in Kathy RIchardson’s book. I’m giving the teacher’s this problem along with three sample solutions.

“There are three fish in an aquarium. The middle-sized fish eats 2 times what the first fish eats, and the big fish eats 3 times what the first or little fish eats. If the first fish eats 3 pieces of food, how many pieces of food would the other two fish eat?”

One of the solutions correctly shows how much food the other two fish will get, while two of the solutions show misunderstandings about the multiplicative relationships in the problem. I’m not going to call anybody out here, but I do want the teachers to sort of self-check before they read whether they are able to recognize the multiplicative relationships in the problem.

This problem is talked about in chapter 6 of Kathy RIchardson’s book, which is about understanding multiplication and division. I liked this problem a lot because she shared how questions like this were given to students, and the results showed that 45% of the second graders in the study were able to think multiplicatively, but only 49% of the 5th graders were able to do so with ease. This implies that despite three years of learning about multiplication in grades 3-5, the students in 5th grade did not demonstrate any greater understanding of multiplicative thinking than students in 2nd grade who have had little to no formal study of multiplication or division.

I love this chapter because it demonstrates how all of the work students should have done learning how to unitize tens and hundreds lays the foundation for unitizing in multiplication and division. Students must be able to think of counting groups of things and thinking of each group as a unit. She gives the following example to demonstrate the subtle shift in thinking students need to make to move from additive to multiplicative thinking:

Rick: I figured out 8 + 8, and that was 16. Then I added 8 + 8 again.
Emily: I had two 8s and that was 16, and two more 8s make another 16. That means four 8s makes 32.

From here we’ll briefly talk about the results from a survey given to over 1,000 teachers who were asked the following two questions:

  1. What reading skills do you most often teach to skilled readers?
  2. What reading skills do you most often teach to less skilled readers?

The results are, sadly, not surprising to me, but having the data helps drive home the point that we have to be mindful of what we’re teaching to differnent populations of students. You can read more about this survey and see graphs of the results here.

At this point, I want to share our district math goals, which I shared during our first PD session back in September:

The K-12 RRISD mathematics standards articulate five general goals for all students:

  • That they learn to value mathematics,
  • That they become confident in their ability to do mathematics,
  • They they become mathematical problem solvers,
  • They they learn to communicate mathematically, and
  • That they learn to reason mathematically.

Just because a student is struggling in math and put in an intervention program does not mean that we should ignore these goals. If anything , we should strive that much harder to reach them with these students! Based on their struggles, these students are already at risk of not valuing mathematics and not being confident in their abilities. We should build up their skills, yes, but we should also help them find ways to value math, to learn how to use it for work and play.

To this end, I’m using a few imbalance puzzles I got from Sue VanHattums’ wonderful book Playing With Math, (they are originally from this blog post).

I’m giving the interventionists two to solve, though if they can figure out one, that might be all we have time for. I’m not advocating they give these to their kids, but I want them to experience something that requires some problem solving, but it’s also fun and gets you communicating with your peers. I want them to experience something that might inspire them to create some new interactions with their students that work toward our district goals.

I want them to feel like they are walking away with something they can actually use with their students, so I’m introducing them to open middle problems. I was already a fan of the website, but it was Michael Fenton’s recent Global Math Department session that put them back on my radar in a big way. If you’re unfamiliar with the open middle problem type, basically it’s a problem that has a lot of solution paths, though not necessarily multiple solutions. Here’s an example of one from the website:

This problem has one correct answer, but students can attempt to find it in a variety of ways. I’ll share a few more examples with them so they get a feel for why these can be powerful problem types to include at times in their work with their intervention students.

I’m going to wrap up the session by showing Megan Taylors Ignite Talk about replacing “teacher-proof” curricula with “curriculum-proof” teachers. I just saw this for the first time recently, and it resonated with me with regards to intervention. So often I hear the cry for “teacher-proof” curriculum materials for RtI that can be used with fidelity and “get results.” While I see why this appeals to some people, I don’t think it’s the right way to go. 

When it comes to response to intervention, the key idea to me is that the interventionists should be constantly responding to their students’ needs. This means having a skillset that allows you to adapt and customize as needed to help the children grow mathematically, not to follow some prescription as though we’re trying to cure a cold. My goal this year has been to help build that skillset in the interventionists so they feel empowered to do that with their students, and I want to end our yearlong PD journey on that note so they can venture into their summer feeling like they are confident and ready to take on the challenges of next school year.