# Decisions, Decisions

This week our Math Rocks cohort met for the fourth time. We had two full days together in July, and we had our first after school session two weeks ago. One of our aims this year is to create a community of practice around an instructional routine, specifically the number talks routine. We spent a full day building a shared understanding of number talks back in July. You can read about that here. We also debriefed a bit about them during our session two weeks ago.

This week we put the spotlight on number talks again. We actually broke the group up by grade levels to focus our conversations. Regina led our K-2 teachers while I led our 3-5 teachers. The purpose of today’s session was to think about the decisions we have to make as teachers as we record students’ strategies. How do you accurately capture what a student is saying while at the same time creating a representation that everyone else in the class can analyze and potentially learn from?

We started the session with a little noticing and wondering about various representations of 65 – 32:

Very quickly someone brought up exactly what I was hoping for which is that some of the representations show similar strategies but in different ways. For example, the number line in the top left corner shows a strategy of counting back and so do the equations closer to the bottom right corner.

This discussion also led into another discussion about the constant difference strategy – what it is and how it works. It wasn’t exactly in my plans to go into detail about it this afternoon, but since my secondary goal for the day was to focus specifically on recording subtraction strategies, it seemed a worthwhile time investment.

After our discussions I shared the following two slides that I recreated from an amazing session I attended by Pam Harris back in May. (For the record, every session I attend with her is amazing.)

The first slide differentiates strategies from models. Basically, if you have students telling you their strategy is, “I did a number line,” and you’re cool with that, then you should read this slide closely:

The second slide differentiates tools for building relationships from tools for computation. This slide is crucial because it shows that while we want students to use tools like a hundred chart to learn about navigating numbers within 100, the goal is to eventually draw out worthwhile strategies, such as jumping forward and/or backward by 10s and then 1s.

The strategy on the right that shows 32 + 30 followed by 62 + 3 is totally the type of strategy students should eventually do symbolically after building relationships with a tool like the hundred chart.

After blowing their minds with those two slides, I led them in a number talk of 52 – 37. During my recording of their strategies, I stopped a lot to talk about why I chose to do what I did, to solicit their feedback, and even to make some changes on the fly based on our discussion.

For example, in the top right corner of the board I initially used equations to represent a compensation strategy. Someone asked if this could be modeled on a number line because she thought it might make more sense, so I did just that in the top left corner. By the time we were done they were like, “Oh, hey! That ends up looking like a strip diagram!”

It was amusing that the first strategies they shared involved constant difference. They were so excited about learning how the strategy worked that they wanted to give it a try. I didn’t want to quash their excitement by telling them that the strategy tends to work better, especially for students, when you adjust the second number to a multiple of ten. I wanted to stay focused on my goals for the day. We’ll discuss the strategy more in a future session.

(Unless you’re in Math Rocks and you’re reading this! In which case, see if you can figure out why that’s the case and share it at our next meeting.)

After some great discussion about recording a variety of strategies, we watched Kristin Gray in action leading a number talk of 61 – 27.

We talked about how she recorded the students’ strategies. We also talked about some really lovely teacher moves that I made sure to draw attention to.

We wrapped up our time together talking about what new ideas they learned that they wanted to try out with their students. I had asked one of the teachers to lead us in another number talk, but we ran out of time so I think I’m going to have her do that at the start of our next session together. Hopefully everyone will have had some intentional experiences with recording strategies between now and then to draw on during that number talk.

Oh, another thing we talked about at various points during the session was how to lead students in the direction of certain strategies. This gets into problem strings, which may or may not happen in number talks depending on whom you talk to. Regardless, here are some we came up with. Can you figure out what strategies they might be leading students to notice and think about?

# And Now For Something A Little Different

Providing PD to teachers is tricky business. Our district offers two weeks of jam packed professional development every summer. The catch is that it happens while teachers are off contract, so there’s no requirement to be there. In addition, teachers have so many options of courses to attend – literacy, math, science, social studies, technology, TAG – that it can be hard to fill seats in some sessions.

During the school year, we periodically offer PD during the school day. We usually only do this when we have special funding that allows us to cover the costs of subs for teachers who attend the PD. Otherwise, you might not get many teachers to attend. However, when we do have sub funds, we usually can only afford to pay for one sub per campus so we’re only able to bring in 34 of our 1,200 or so elementary teachers. It’s a drop in the bucket.

For the past two school years, we’ve offered after school PD sessions called Just In Time. As the name implies, they were offered just in time for the start of the next nine weeks grading period. The purpose of these sessions was to give teachers a preview of the upcoming units. Now that our units are a few years old, attendance has dwindled because they’re no longer very timely.

So this year we decided to try something new.

We threw out the Just In Time sessions and created new mini-courses to bring some of the amazing topics from summer PD into the school year and to give teachers more choice in their professional development offerings. Instead of choosing from the Kindergarten, grade 1, grade 2, grade 3, grade 4, or grade 5 Just In Time sessions for math, teachers now have 7 course topics available to them. Here’s a link to a document that details each of our courses.

The sessions are still after school for an hour and a half, which is a turn off for some, but I’m hopeful that many more teachers will be drawn to a topic they want to explore this school year. I specifically designed our courses to be experiences over time because I believe that one-off PD experiences have little lasting impact on teaching practice. However, attending 4 sessions spread out over several months where teachers have the opportunity to try out what they’re learning in between sessions feels like a better recipe for success.

We had the very first session of our very first course yesterday. (Huge thanks to our amazing instructional coaches who will be leading all of these PD sessions!) The 16 teachers who attended were engaged and eager to learn about number talks. Here’s hoping this is a sign of even more great learning to come this school year!

# Math Rocks Redux Part 2

At the end of July, @reginarocks and I kicked off our second Math Rocks cohort – a group of 30 or so elementary educators that meets for almost 30 hours across 7 months. Our first cohort, which ran last school year, was a success, but when it came time to plan for year 2, we definitely found ourselves wondering how we could provide an even better learning experience this year.

The other day I wrote about the tweaks we made to day 1 of Math Rocks. All in all, the tweaks were minor – you can read about that session here – but day 2 was completely overhauled! That’s what I’d like to write about today.

But first, let me bring you up to speed on some things that happened to influence my decisions about day 2. Last year, Regina and I delivered a lot of PD across a wide variety of topics and audiences  – diagnostic assessments with interventionists, fraction sense with grades 3-5 teachers, developing number concepts with grades K-2 teachers, weight and liquid volume measurement with grade 3 teachers, spiral review strategies for grades 3-5 – but the topic that seemed to resonate the most with our teachers was number talks. Across four half-day sessions, we ended up delivering an introduction to number talks to approximately 150 of our elementary teachers! I wrote about the experience here if you’d like to read about it.

Last year’s Math Rocks cohort also dove into number talks. As part of our work together we joined a book study of Making Number Talks Matter led by Kristin Gray and Crystal Morey. Our group loved it, but because the book study was mostly discussed online via Twitter and Teaching Channel forums, I realized later we didn’t do enough work in person to talk about and work through issues that came up to support our teachers as they took on this new practice.

Fast forward to Twitter Math Camp this summer, and I had the opportunity to take part in an incredible PD experience with David Wees, Jasper DeAntonio, and Katilin Ruggiero in their session titled “Rehearsing Instructional Routines Together.” You can access all of the slides and materials from the session on the Twitter Math Camp wiki here. Their session focused on teaching us the Contemplate then Calculate routine – which I now love! – but the structure of the PD itself is what captured my attention most. So much so that I borrowed liberally from their work when designing day 2 of Math Rocks!

Day 2 of Math Rocks followed this structure:

• Regina, Jan, and I each model a number talk
• Math Rocks participants unpack the components of a number talk
• Math Rocks participants plan their own number talk in pairs or trios
• Math Rocks participants rehearse their number talks for the group

All of this work drove us toward our two goals for the day:

1. Dive deeply into the number talks routine
2. Develop a community of practice that can more precisely talk about our teaching

The day started with Regina, Jan, and I each modeling a number talk. This was challenging to plan. One of the key pieces of David’s session at Twitter Math Camp was instructional routines. Contemplate then Calculate is a routine that is broken down into very discrete steps. In order to bring this to our teachers in my district, I had to think about what the steps of a number talk are supposed to be.

What ends up making this challenging is that what makes up a number talk is not universally agreed upon. A big point of contention has to do with how many problems you do in a number talk. Some people say number talks should focus on one problem and all the strategies used to solve that one problem, while others say a number talk can involve multiple problems to solve and discuss. Those that disagree say that having multiple problems is called a number string, not a number talk. Yay, semantics!

For the purposes of my work with my Math Rocks cohort, I opted to say a number talk can include more than one problem for the sheer fact that Sherry Parrish’s book Number Talks, which we have 6 copies of on all 34 of our elementary campuses, does present number talks as strings of problems. The sample number talks videos on the DVD all show teachers modeling strings, and all or nearly all of the sample pre-planned number talks that are shared in the book are strings as well. Knowing my teachers will be using Sherry Parrish’s book as a resource, I opted to define the routine as having multiple problems to solve, but I did not define how many problems.

When deciding what the components of our number talks instructional routine would be, I also consulted this document from Math Perspectives. Here’s how they delineate the routine:

Finally, I took all of that and simplified the number of steps to make the routine feel smooth and easy to follow. Here’s what I presented my teachers during day 2 of Math Rocks:

Making the Math Rocks folks sit through three number talks might sound like overkill, but it served two purposes. First, we wanted to model number talks across grades to demonstrate that this routine is appropriate across the elementary grades. The three number talks we modeled came from mathematics in Kindergarten, 2nd grade, and 4th grade.

Second, modeling so many number talks ensured we as a group had three shared experiences to draw upon when unpacking the routine later. We wanted the participants to really be able to unpack and analyze each of the components of the number talk, and in order to do that they needed to have seen each of the components enough times to have meaningful conversations about them.

After modeling the three number talks, we used the Ideas Carousel protocol to unpack the components of the number talks routine. (Just as a reminder, I borrowed liberally from David’s sessions. This protocol came from his session, too. )

Here’s how the protocol works. We made a poster for each of the components of the number talks routine, and participants chose a component to unpack. With their group, they recorded their understandings of the parts of that component, the rationale(s) for each of those parts, and any questions/wonderings they had.

Once the groups had a chance to dirty up their posters, they started rotating through the remaining posters. At each poster, they had to read the poster, check ideas that resonated with them, add new ideas, star ideas they wanted to discuss as a group, and circle the idea their group thought was most important on that poster.

After interacting with each poster, they took one last gallery walk through all of the posters before returning to their original poster. Once there, they read over their original comments and all of the extra things added by everyone else, and they marked anything that surprised them. Here are their completed posters:

Finally, as a group we talked through their wonderings, a-ha moments, and anything else that came up. It was such a rich conversation and demonstrated that we have a lot of interesting questions to explore this year. For example:

• How do you do number talks in an intervention group that meets for only 30 minutes daily and is composed of students who are reluctant to participate or try out different strategies?
• How do you modify number talks for emergent bilingual students? Sharing their strategies verbally may be too much of a challenge. What can we do to accommodate them?
• How do you know what to record when students are talking about their strategies? How do you get better at that?

This really gets at one of our goals for this day of learning – creating a community of practice that can more precisely talk about our teaching. I don’t have all the answers for them, and how much more interesting is it that we as a group get to explore and discover our own answers through our experiences this year? We get to decide what works (and doesn’t) for our students, and we have a group of people to do that important work with.

Now that we had accomplished our other goal for the day – diving deeply into the number talks routine – we gave the participants time to plan their own number talks. We grouped them by grade levels to plan, though we did have one team composed of a special education teachers and two interventionists.

Finally, we had time for some of them to rehearse their number talks in front of the rest of the group. I reiterated a key thing David Wees said in our Twitter Math Camp session: the purpose of this rehearsal is not to coach individual teachers to be better at number talks. Rather it’s to give us as a group an experience where we can talk about the act of teaching. I like the meaning behind it, but I also think it helps take the pressure off the teachers. It’s not about any one person at the front of the room, it’s about how it gives everyone an experience and ability to talk about the very messy work of teaching.

All in all it was a very intense and focused day, but I loved it! I think this was just the right experience to kick off our time together over the next 7 months. I look forward to the conversations and support we’ll be able to provide one another going forward. What I’d like to do during the school year is have different participants plan and rehearse number talks so we can continue talking about the routine. I also want to spend some time focusing on how we record students’ strategies so that everyone can feel more confident in this area so they can be more intentional about how they are representing students’ strategies for the rest of the class to benefit from.

Thank you to David, Jasper, and Kaitlin for providing an awesome experience that I was able to take back and adapt for my teachers! Special thanks to Jasper for his elevator speech that encouraged me to attend his session instead of the one I was originally planning to attend.

# Math Rocks Redux Part 1

This time last year, @reginarocks and I kicked off our inaugural Math Rocks cohort. We spent two awesome days of PD together with a group of 30 elementary teachers which you can read about here and here.

And this time this year, we kicked off our second Math Rocks cohort which you can read about in this very post!

For those who want to stick to the present and not go back into last year’s posts, Math Rocks is our district cohort for elementary teachers to grow as math teachers. Our two focus goals for the year are building relationships around mathematics and fostering curiosity about mathematics. The cohort meets for two full days in July followed up by 9 after school sessions, September through January, and a final half day session together in February. It’s intense, but so rewarding to get to work with teachers for such an extended amount of time!

I want to write a post about this year’s Math Rocks cohort to give you some insight into what stayed the same and what changed. Now that we’ve gone through this once, we knew there were some things we wanted to tweak. Without further ado…

One thing that stayed the same was kicking off Math Rocks with a little Estimation 180! The purpose behind this was twofold. First, we did it as a getting-to-know-you activity. Once everyone was ready, we had them mingle and make friends while answering questions like:

• What is an estimate that is too LOW?
• What is an estimate that is too HIGH?
• Where’s the math? and
• Which grade levels could do this activity?

Second, throughout day 1 we snuck in a couple of activities like Estimation 180 that were created by members of the Math Twitter Blog-o-Sphere (#MTBoS for short). Later in the day we introduced the cohort to the MTBoS, and it’s nice to be able to say, “Oh by the way, remember those Estimation 180 and Which One Doesn’t Belong? activities we did? Those are created by members of this community we’re introducing you to. Isn’t that awesome?!”

Last year we did a community circle after the Estimation 180 activity, but I scrapped it this year in order to streamline our day and add time for the biggest change to day 1, which I’ll talk about in a bit. Instead, we moved right into the ShadowCon15 talks from Tracy Zager and Kristin Gray that serve the purpose of setting up our two Math Rocks goals.

Just like last year, we had the participants reflect before Tracy’s video. They had to create three images that symbolized what math was like to them as a student. It’s fascinating (and concerning) to see how many images involve computation facts practice of some sort:

Even more fascinating (and sadly disturbing) was listening to participants’ horror stories about fact practice as a child. One person talked about the teacher hitting students on the back of the hand for getting problems wrong on timed tests. Another one said the teacher had everyone in class hiss at students who got problems wrong. Hiss! Can you believe that?!

We only made a slight change to this portion of the day. Last year we prefaced each video with a description we got from the ShadowCon site. This year I let the talks speak for themselves. It seemed more powerful to let Tracy and Kristin build their own arguments without priming the pump so much.

I mentioned earlier we left out the community circle in the morning to make room for the biggest change to day 1. Let me tell you about that. Introducing goal #2 leads us into one of the biggest components of Math Rocks, joining Twitter and creating a blog. In order to build relationships and foster curiosity, I want my teachers to experience being members of the MTBoS during their time in Math Rocks.

Last year I gave directions here and here on our Math Rocks blog. I shared the links to those two blog posts and set them loose to get started. To say we ran into problems is a vast understatement. I severely underestimated the support needed to get 30 teachers with widely varying comfort levels with technology connected to Twitter and blogging. No offense to them – they were great sports about it – but I definitely threw our first cohort in the deep end and I’m lucky (and thankful!) they all came back for day 2.

This year I slowed things down quite a bit, and together we walked through the process of creating a Twitter account and a blog. I ended up spending about an hour and fifteen minutes on each part. That’s how much I learned from last year’s experience! Slow and steady wins this race. For those who were comfortable getting started on their own, I gave them their tasks up front here and here so they didn’t have to sit and wait for the rest of us.

Oh, that reminds me of another behind-the-scenes change this year. Instead of using a blog to share missions, I decided to try Google Classroom. I made separate assignments of creating a Twitter account and creating a blog, and the documents I linked in the previous paragraph were linked to those assignments. I haven’t done much else with Google classroom yet, so I’m not sure if it’s going to be a better choice or not, but so far it’s working out okay.

Doing all of that pretty much took up the rest of day 1, with the exception of a little Which One Doesn’t Belong? to give us a break between introducing Twitter and blogging.

All in all, I’m happy we were able to keep so much of day 1 intact. I feel like the structure of it does a nice job of establishing our goals for the year and I’m happy I was able to find a way to get everyone connected to Twitter and blogging in a less stressful way.

Day 2, on the other hand, is completely different from last year, and I look forward to writing about that in my next post.

# 18 Amazing Things

This school year, my partner Regina and I facilitated an 8-month long cohort of math educators called Math Rocks. You can read about our first two days together in July here and here. I also wrote this post if you want a peek into our learning during the school year.

As our time together drew to a close, I asked each participant to write a blog post reflecting on Math Rocks. Today I went back through their reflections to pull out snippets to share to encourage other teachers in our district to apply for next year’s cohort. You can read more snippets from their reflections here.

Can I just tell you how amazing it is to read this? In my first few years of teaching, the path of my career and my understanding of math were steered in entirely new directions when I took part in an extended PD experience. I can’t express to you how much it means to me to be in a position now where I’m able to learn with and from teachers on their own journeys through teaching and math. I couldn’t be happier.