Monthly Archives: July 2015

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.