Monday, August 27, 2018

Keeping Class Agreements Alive

I've started reading Not Light, But Fire: How to Lead Meaningful Race Conversations in the Classroom, by Matthew Kay, and it is a joy. I'm only on Chapter 3, but it's already got me thinking about starting the year in a classroom by purposefully planning for race conversations from Day 1.

Although Kay's book is written from the perspective of a high school teacher, so far I find it very applicable to my work as an elementary educator. It's gotten me interested in talking, writing, thinking, and tweeting about how one could tweak his ideas in elementary school. This is the first of a few blog posts where I'll write about community-building as I've done in it my classroom over the years.

(Because I'm also thinking a lot about facilitating adult learning, I found as I wrote this that I also kept adding notes about how I'd done similar things in groups of adults learning together. That seems important, too.)

These posts are not overtly about race, but Kay makes the (not surprising but perhaps sometimes overlooked) argument for why you must build community in your classroom in order to have race conversations. He is clear that his ways of building community are not the only, or best, ways. So these posts will detail some ways that have worked well for me in elementary classes that talk about race.

Months ago, Kristin Gray was asking about how teachers keep classroom norms alive in the classroom past the first week or two of school, and I've been wanting to write about that too. So this first post is about Class Agreements and how I make our list of agreements a living document throughout the year.

Class Agreements: What are they? 

First of all, a note about what Class Agreements are NOT. Class Agreements are not a list of rules. As I tell students (and adults when I work with them in groups), rules are things we have to do. Agreements are things we are all going to try our best to do. We are all going to make mistakes, because they are hard things to do. None of us will follow the Agreements all the time. But we will try. (Thanks to Tina Blythe for teaching me this distinction.)

Now: What do you call them? I used to call them "Class Promises," but it feels strange to say we promise to do something that we have just said we won't always do. "Norms" feels a little businesslike to me, but other people like it. One class I worked with last year wanted to call them "Vows," like a wedding, which seemed intense, but that was their decision. In general I like the term "Class Agreements" because we all agree on them, but it doesn't matter too much what you call them.

How do you create them?

I begin in September by having students talk, write, and draw about their Hopes and Dreams for the year. We then talk about how we need to act and treat each other in order to make our Hopes and Dreams come true.

This is a well-known process created by Responsive Classroom, which you can read about here, but it's not easy. In particular, coming up with and finalizing the list of our Class Agreements is an arduous process, and I don't think I'm a particularly skilled facilitator of this part. But, in the end, we come up with a list we can all agree to.

Usually I try to keep the list of Class Agreements to four or maybe five items. One year's list was:
  1. Treat others the way you want to be treated.
  2. Be peaceful and respectful and talk out problems.
  3. Try to be positive and think good thoughts.
  4. Try your hardest and stay focused.
These are not my ideas -- they come from the students, and are probably not worded how I would word them if I wrote them. I try to make sure they come up with one about how to resolve conflicts, one about treating each other well, and one about working hard. There's often one about taking care of our learning environment as well.

After we create the Agreements and everyone signs them (agreeing to try to meet them), the Agreements don't just hang on the wall and get forgotten. I've done different things with them over the years, but here are a few.

Refer to the Agreements in Morning or Afternoon Circle

One easy way to keep the Class Agreements alive is to include them in Morning or Afternoon Circle in some way. I've often had students look at the Agreements in the morning and choose one they really wanted to focus on that day. They silently put up their fingers to show which one they've chosen (three fingers for Agreement #3, etc.). This just takes a couple seconds, but it keeps the Agreements in our minds. In Afternoon Circle, students can briefly share a way they or someone else followed the Agreements that day.

(I'd like to note that we did this in a class for adults I took this year with Gene Thompson-Grove: revisited our norms and thought about which ones we needed to focus on ourselves and which ones we would like the group to attend to.)

Times of Crisis: Class Meetings

Once, at a moment of crisis, when something went badly wrong in our class community and we called a class meeting, my co-teacher Annie Shah took the Class Agreements off the wall and put them on the floor in the middle of our circle to ground our discussion. She reminded the students how important they were and why we had written them, and then we talked about which ones we needed to do a better job with. This act of physically centering our community around the Agreements was a powerful reminder of the list as a living document, not an ancient artifact of the first weeks of school.

Use Class Agreements for Written Reflections

Finally, Class Agreements are powerful tools for written reflections. Students can reflect at the end of a unit, term, week, month, or year and write about ways they have embodied one or more of the Agreements. I also use them on reflection sheets that students complete when they've done something they shouldn't (usually involving hurting someone else physically or emotionally). These reflection sheets include a list of the Agreements and ask the student to circle which one they did not follow, then write about what happened and how they can fix the problem they caused.

(Written reflections on the norms are also something I've done as an adult student. In Tina Blythe's semester-long class, we did regular reflections about the norms we had created, sometimes verbally, sometimes in writing. Mid-way through the term, we folded a piece of paper into four squares and wrote about one of the following in each square: a norm we had done well with personally, a norm we needed to do better with personally, a norm the group had done well with, and a norm the group needed to do better with. This was useful feedback for the instructor.)

A Note About Compliance

I loved this post from @Jess5th about shifting the narrative away from compliance on the first day of school. She engaged her students in conversations about when it's important to follow the rules and when it's important to break the rules. I have never had that conversation so early in the year, but I think it's an important idea, so don't miss her post.

In my next post on building community, I'll write about a routine I learned in a mindfulness class called Appreciations. 

Thursday, June 7, 2018

Rule #1: Provide Think Time

Our second graders are on a field trip. It is quite a good field trip, novel and engaging, making them excited to be writers. But I am paying attention to who participates and why.

The second grade is a diverse group in the true sense of the word: racially, socio-economically, and in terms of learning profiles. Of the 22 students, about 8 to 10 participate often and actively during traditional, teacher-led lessons at school. These 10 tend to be whiter and come from more economically-advantaged families (although not exclusively, of course). 

The field trip is no exception. The man leading the class is energetic, hearty, and jovial. He asks fast questions and wants fast answers. He calls on the first hand up. 

“Where does our story take place? Who should be the main character? What does he look like? What is his name?” The questions come fast and furious, and only a few hands keep up. I am paying close attention to the race, gender, and learning profile of those who are getting called on. White boys are speaking most. White girls are second.

The man leading us is definitely in a hurry. “You’ve gotta have an idea right in your head when I call on you!” he says urgently, after calling on a few kids who didn’t have an answer at the tip of their tongues. 

Some students who try to have fast answers have their responses dismissed.

“Who should be the main character?” he asks.
“You!” says Wilfred, a student for whom English is a second language and who is clearly enamored of our host.
“Me? No!” the host replies.
“Oh. No,” Wilfred says, shaking his head as if the wrong words had just popped out. “I forgot.”

“What will happen next in our story?” our host asks.
“The dog smelled its own butt!” Jaquan says. Jaquan has some holes in his formal education and often needs extra time to process directions and content. 
“No, that’s too gross,” our host replies, and so neither Jaquan nor Wilfred’s ideas make it into our class story. 

“What is the doghouse made of?” is the host’s next question.
“Wood!” Teddy calls out. Teddy is a white boy who can do well in school but is often disengaged. He hasn't been speaking on this field trip until this moment.
“Raise your hand,” the host admonishes. Someone else raises their hand and says “wood,” which he accepts.

These three boys make attempts to participate in the fast-paced lesson. Who hasn’t even raised a hand? A few other quiet boys, and a bunch of the girls. The girls who haven’t raised their hands are primarily girls of color, girls for whom English is their Second Language, or girls with learning disabilities.

I start to feel urgent about the unequal participation, so I talk in whispers to students sitting near me. I repeat the host’s questions, asking them what they can come up with. By the time they think of something, he’s already two or three questions ahead of what we have been working on.

At some point, the other teacher on the field trip also wants to increase participation. She does it by saying, “Abby, we haven’t heard from you. Abby, Evita, do you have any ideas?” But they can’t, or won’t, come up with something when put on the spot like that, with no think time. 

Later, I sit with Roberto as he works on his own story. I ask him what he wants to name one of his characters. I then sit and count the seconds silently as he thinks. Twelve seconds later, he tells me a name. Twelve seconds. At the pace of our host, we would have answered three more questions by the time twelve seconds had passed.

I used to teach in ways that are somewhat reminiscent of how this host runs the field trip (although I hope never quite so fast-paced). Over the years, I’ve learned strategies to increase and equalize participation and access to the conversation. There are very simple routines I use when I teach that provide enough think time for everyone, communicate my expectation that everyone think and prepare to share their thinking, and minimize the domination of the quick, loud voices — voices which are often male, usually native English speakers, nearly always traditionally successful students, and, in a racially diverse school, often white.

Here are some of these simple routines I employ on a daily basis, in large and small groups.

Provide Think Time

The single most common strategy I use to ensure that everyone has time to process a question or direction is to provide Think Time. I explicitly teach what Think Time means and how students should use their Think Time, using anchor charts like this (which I completely stole from Kassia Wedekind and Christy Thompson).

This means that we all get comfortable with long silences of 30-60 seconds, sometimes longer. I usually ask students to indicate where they are in their thinking with their fingers.

“When you have one answer [or idea], put your thumb up in front of your chest. When you have another strategy [or idea], put up a finger.” This lets me know when they’ve had enough Think Time. I make sure everyone has at least one thumb up before I start asking for responses. (This thumb strategy is borrowed from Sherry Parrish and her Number Talks books.)

Choral response

I used to think that having a class respond chorally was old-fashioned and a bad idea. How do you know if students got the right or wrong answer if they all respond together? Won’t they just copy each other and recite mindlessly rather than thinking the question through? I have since learned that there are times when choral responses are preferable to individual ones, especially when paired with Think Time.

If I have asked a question that has a short, factual answer (such as What kind of syllable is this? or What goes with 10 to make 15?), I ask students to think quickly (for just a few seconds), indicate with a thumb when they have their answer ready, and then recite it all together.

“How many syllables are in this word?” I may ask. “Think it. Show me a thumb when you know.” Pause. “Now say it.”

The point of small questions like these is usually to keep students mentally engaged as the lesson moves on to something deeper and more important, or to provide short practice with a basic skill. By providing Think Time and then asking for a choral response, I make sure everyone is caught up and “minds on,” and everyone gets a chance to share their thinking. If they are wrong, they’ll hear that most people said something else and they’ll adjust their thinking. If I hear that a few people are wrong or there is disagreement, I’ll stop and we’ll discuss it.

Think, Pair, Share

There’s no need to write much here since this is a common enough practice, but I’ll mention how important it is to teach a clear structure for this routine and to practice that routine. I use this anchor and I actually have younger students touch their ears or mouths to show who is going to speak and listen first. I count backwards from 5 to 0 to give them time to find a partner, and when I get to one I always say, “Stand up if you don’t have a partner” so solo kids can find each other. We also talk about and practice how to look around the room to make sure everyone has a partner and how to include someone or change partners when it makes sense. We usually precede a Turn and Talk with Think Time.

Student-led discussions

… are not topics for this blog post, as the participation techniques I’ve laid out here are primarily for teacher-led lessons (the kind that was modeled during our field trip and which surely have a place in schools). But they bear mentioning as I have found them to be very effective tools for increasing participation (verbal and mental) among all students. I’ve written a bit about Hands Down Conversations here and you can find more on Kassia Wedekind and Christy Thompson’s blog devoted to the topic.
These structures are so simple and so tiny, yet they define most lessons I lead and they increase access to the conversation tenfold. Boiled down to two words, they can be summarized as Think Time. Well, Think Time and respectful silence so that others can think too. No one has their best ideas instantaneously, and our expectation should always be that students go deeper and think well rather than quickly. If I could give one gift to all teachers and field trip leaders, it would be the gift of Think Time.

Friday, May 25, 2018

Going Back Home

Today I visited the place where I became a teacher.

I haven't been inside that building in 9 years. But for the eight years before that, I went there nearly every day. I sat on the front steps calling people I loved on Sept. 11, 2001. I cried in the bathroom stalls and out on the back steps after hard days as a new teacher (and a not-so-new teacher, too). I had some of my most joyful teaching moments there, with first graders who grew a garden and read stories and explored pattern blocks together, and second graders who wrote poetry and discovered their neighborhoods and did yoga together. There I learned so much about good teaching, from some of the wisest educators I know, about relationships, about justice, about why we teach and how to teach and our responsibility to kids and families.

These halls I haven't walked for 9 years are so familiar to me. The metal grate in the middle of the hallway floor. The sliding closet doors, askew in their tracks. The apple tree outside, whose apples we used to press for cider in the fall. The door handles, the bulletin boards, the fraying blinds that hang over the bookshelves in the hallway so little hands won't disorganize the leveled books.

My school no longer lives there. A new school has called that building home since my school moved into a bigger building a mile down the road. I walked through the hallways as children arrived with their book bags and lunch boxes, hanging their things on the hooks I used to label carefully each September. I could feel the ghosts in those hallways, spirits who inhabit my memory so vividly. Ghosts of the teachers I laughed and cried with. Ghosts of the children who shared my days and, mentally, my nights, with whom I struggled daily as we learned and worked together. Ghosts even of teachers I didn't know well, but whose work shaped lives in ways I know are still remembered, and ghosts of the ideals we lived in that school, the ways we wanted to teach our students to live and think and be.

I am surely a bit melodramatic about the good old days we had there. So many of them were hard days, but now I know that that was probably the best place I will ever work. We were a community that was committed together to a common good -- though a common good that was not easily agreed upon, and often arrived at with great struggle.

Schools are places where adults' and children's joys and struggles are lived. Walking down the hallway, I thought about schools that are closed in the name of saving money and increasing "achievement." I thought how lucky my school had been because instead of being closed down, we had been relocated and merged with another school. Even though those moves changed our school irrevocably, the loss wasn't as great as the losses of communities whose schools are shuttered. 

Eve Ewing writes about the damage to a community that accompanies school closings. This line of Ewing's runs through my mind today: "[T]he decision to shuffle students from one building to another in the name of numbers is shameful. The decision to do so is based on the premise that children, teachers, and schools are indistinguishable widgets, to be distributed as efficiently as possible across the landscape. But the fact is that schools are ecosystems, each with its own history, culture, and intricately woven set of social relationships. Schools are community anchors. They are not interchangeable, nor are they disposable. Schools are home." 

Going back to my old school was as poignant and wistful as if I had gone back to the house where I lived for 18 years as a child. I understood vividly in that moment how true Ewing's words are, and what a loss it is for a community when a school is closed. "Schools are home."

Wednesday, May 23, 2018


In recent months, I have occasionally seen one second grader, Wilfred, engaged in passionate mathematical discovery. At other times, I have seen him head down during math, tears dripping. In fact, he's cried during math a handful of times that I can think of. It rips me up inside each time.

This week, we've been working on two-part problems that involve adding two quantities, then figuring out how much more you need to get to 100. He has been dejected, overwhelmed, and tearful.

Today, though, he worked with his teacher and had more success. I walked in and could hear his teacher saying, "See, Wilfred, you CAN do it! Do you see that you can do it?"

I walked him to the bus this afternoon.

"I heard you worked really hard and figured out some hard problems today!" I said as we made our way down the stairs.

"Yeah," he replied with a small smile.

"You know," I said carefully. "That's how math usually is. Usually, you can't just look at a problem and know the answer. You have to think about it and work hard to figure it out, maybe try some different ways, before you know the answer."

"Yeah," he said.

Then, after a pause: "But not for all kids. Some kids just know the answer right away."

There it was. The thought I'd been fearing.

"Only if what they're doing is familiar," I said, reaching for a word we've used often this year instead of saying something is "easy" (thanks to Tracy Zager for that suggestion). "If they've practiced that kind of math a bunch before, they might know the answer right away. But only if they've had a lot of practice."

"No," he said dejectedly, refusing to give in to my arguments because of what he had seen with his own eyes. "Some of the kids in our class haven't had practice. But they still know the answer right away."

I stopped, crouched down on the hot blacktop, and looked him right in the face.

"The only reason kids know the answer right away is if they have had a lot of practice," I insisted. "They might not have had practice in school. Some kids have had more practice with math before they got to school, or when they're not at school. But NOBODY knows the answer right away unless it's familiar to them because they've practiced it. NOBODY is born just knowing the answer in math. Do you hear me?"

"Yeah," he answered, half resigned, half hopeful.

This is what some kids think, folks. They see other kids who know the answer right away, and they think: you're supposed to do that. If you can't do that, you can't do math. And now it's the end of May, and school is almost over, and that's what Wilfred thinks. He thinks he isn't good at math because he doesn't know the answer right away.

I go back in my memory to the mental image I have of Wilfred during one of our inclusion math lessons, when he was making arrays of cubes with 4 in each row. He was ecstatic when he told me that 72 was twelve groups of four and six more groups of four, and he was over the moon when I talked him through the multiplication equations that would show his discovery. There was no quick "knowing the answer" -- it was an hour of completely student-led exploration and discovery, driven by his own questions. It was one of the highlights of my year, and, I hope, of his. I'm holding out hope for more of those mathematical moments for Wilfred.

Edited to add: 

There has been a great conversation, partly in the comments and partly on Twitter. 

My takeaway from the conversation is this: The way you handle a moment like this, as a teacher, depends so much on what you know about the student, your relationship with the student, and probably your own experiences as a learner. Read the comments and tweets below for more.

Wednesday, February 14, 2018

Who Talks? "Numberless" Graphs in Grade 2

A class of second graders is having their first Hands Down Conversation (HDC). They are discussing what happens when you add 10 to a number, and what will happen if we count by 10 but start at 8. I'm sitting outside their circle, taking notes on everything they say. This is how the conversation ends.

David: It would be 0, 4,5, 8, then it would be 18, 8 at the end, 28, 8 at the end, 38, 8 at the end, 48, 8 at the end, 58, 8 at the end, and it would keep going.

Eddie: I get what you’re saying, that there would be an 8 at the end of everything, but we kind of know that already.

David: Not everybody.

Theo: Not everybody knows that. Babies don’t know that. (He giggles).

There is a low hiss of voices around the circle. Some students don't like this way of talking.

I call a timeout to reflect on how our first hands down conversation has gone.

This class is not an easy one to facilitate. There are 22 students. 14 are boys. 8 are girls. More than half have an abundance of energy which makes it hard for them to sit still. Of those 14 boys, a majority (about 8) are quick-thinking, verbal, and impulsive, which means they often call out answers or comments before everyone has had time to think. Without careful management, this means that other students are completely excluded from the conversation.

(This is our hands down conversation anchor chart. It comes straight from the work of Kassia Wedekind and Christy Thompson, who have been working together on facilitating hands down conversations in literacy and math.)

The second week

After the second HDC, I list the names of the students who spoke on the board. We count how many spoke (7 of the 22 in the class). What do you notice? I ask. No one notices gender, so I ask how many boys spoke (5) and how many girls (2). We talk about some of the reasons so few children spoke. The same people talked over and over again. Some people tried to speak but their voices were quiet and they were drowned out by louder voices.

The third week

Before our next hands-down conversation, we work on a list of ideas for hearing more voices. Their ideas are spectacular.

Gender comes up a number of times. Girls suggest that boys should listen more and wait longer before speaking more than once. Each time the girls or I mention "boys," there is a murmur across the rug. The boys don't like it. I make a split-second decision not to write "boys" on our chart. The truth is that there is one girl who also spoke often and assertively, drowning out other voices, so this is not just a boy problem.

But I do tell them that men often talk more than women. I tell them that when grown-ups have meetings, the men talk more than the women, even when there are fewer men in the group. I say, "boys and men have to practice listening more and speaking less."

The next day, we have another hands down conversation. First we re-read our chart. We talk about what to do if two people speak at the same time (one person can say "go ahead" to the other). I ask the most talkative and impulsive boy to sit outside the circle with the teacher and a class list, and keep track of who speaks and how many times. That way he has an important job and won't overpower others so much. And I ask a quiet girl who rarely speaks to launch the conversation.

They do better. More students speak. More girls speak. And more boys speak than the week before. Some boys still talk a lot. But I can see others working really hard to make space for more voices. Some speak only once or twice. One stops himself a number of times and offers the floor to other kids. One girl tries asking another girl, "Would you like to speak?" At the end of the conversation we tally up the data: how many students spoke: 11. 7 boys and 4 girls.

This week

Before our next hands down conversation, I wanted to show them the data of how their conversations had gone over the past two weeks. I wanted to present the data to them visually so they could make sense of it, see the positive trend of more participation, then hopefully increase that participation. I decided to do so with a variation of numberless graphs, a routine Kassia and Brian Bushart (among others) have been working on. My graphs aren't numberless, but they have few numbers, few words, and I shared them from simplest to most complex.

After I projected each graph, I simply asked "What do you understand?" and "What do you wonder?" They discussed the graphs for more than 30 minutes. The turn and talks were loud and animated. Best of all, nearly everyone spoke in the large group, even students who rarely participate or who, when they do speak, are often confused.

Here is the first graph:

And here are their observations:

Here is the second graph.

And their observations:

Finally, the third graph.

Their observations:

Some of my favorite observations:
  • The girls and boys combined to make everyone.
  • The blue bars show who spoke on Week 1
  • The reds are taller than the blues (because Week 1, only a few boys and girls talked)
  • Girls still talked less than boys Week 2
  • The reds are the same on slide 2 and slide 1 (because the total number of students stays the same!)
  • The green is bigger than the blue (because more people talked Week 2 than the first week)

How many kids spoke anyway?

We didn't talk much about the actual numbers of students who spoke, but we did spend some time discussing whether there are 7 or 8 girls in the class. Besides the kids who just looked around the rug and counted, there was some discussion of how you could use a graph with only a few numbers on it to figure out how many each bar represented. One student described how he imagined these numbers in between the 6 and the 12.


I know most adults who look at these graphs will be interested in talking about the dynamics of our hands-down conversations. What do these data mean? How can we change them? How did the class talk about these questions and decide to move forward?

But what I loved about today's conversation what how easily the second graders stuck to low-inference observations. Only once did someone make a suggestion to the class, and it was after the comment that "the red has to be bigger than the blue." We talked about when that might not be true: when would the red and blue (or green) be equal? Only if every single student participated in the hands-down conversation.

Looking at data this way, and starting with what we understand, opened the door for everyone to participate. It was the perfect low-floor, high-ceiling task. Jayvaughn, a student who raises his hand to participate all the time but who is often confused and hard to follow, observed that "the reds are taller than the blues." And in fact (as I told the class), this is how grown-ups make sense of graphs like these. We look for trends overall. Figuring out exactly how many girls spoke or how many boys are in the class is less important than the trends, than observations like the fact that each time the reds were taller than the blues. After Jayvaughn made that observation, I asked if someone else could explain what his observation meant in terms of real life. Tyrell explained that this was the case because "week 1, only a few boys and girls talked."

I could go on and on about each of their observations and why I like them all so much, but I'll stop myself here. What I most was reminded of was how much depth and understanding can come out of just talking about what we see. This is why we spend so much time noticing and wondering (in math and in all subjects). When we slow down and just observe, we make the most sense for ourselves.

A Note on Gender Identity (added 2/24/18)

One thing I thought about but didn't include in this post originally was the gender binary implied in this whole data analysis. This is a class where everyone identifies, so far, as either being a girl or a boy -- but this analysis I encouraged them to do did not question that gender binary in any way. I am not sure how to hone my students' ability to pay attention to the gender dynamics of who speaks in class without reinforcing the gender binary, but I'm sure there are good ways. I'd love suggestions.

Saturday, January 6, 2018

Counting Collections: One Nearly-Perfect Answer to Inclusion

I have a new job this year, and with a new job comes a lot of learning -- which is fun and hard.

The biggest challenge I face is that I am tasked with creating inclusion opportunities for several students who are in a substantially separate classroom for students with Autism Spectrum Disorder. Although I have taught students with autism before, I have never worked with students who have this level of disability. I have been making a LOT of mistakes and, most of the time, learning from those mistakes.

Sometimes I bring a few of the students from the ASD classroom upstairs to the second grade general education classroom. This is hard, though, because it is a small, crowded, relatively noisy room. I feel a little claustrophobic and distracted with the extras kiddos in there, so I can only imagine how they feel.

Other times I bring between 4 and 10 students from both classrooms (the ASD room and the general ed room) into the Learning Center, where we either do the same lesson they are doing in the classroom, or a variation on it, or a variety of centers.

But the best part of my week is the 50 minutes on Mondays when I bring four students from the second grade general education class downstairs to the ASD classroom. They pair up with four students with autism for Counting Collections.

I bring different students down most weeks, so that everyone has a chance to go, but some students go more often than others -- because I want them to build off what they did the week before, because I think they need the counting practice, or because they are really, really good at being partners with their special education peers.

(A note on language: I wish that we had names for our classrooms that were, say, animal names, instead of calling them "second grade general ed" and "the ASD classroom," but we don't. Soon I'll introduce you to a few of the students and call them by name because it is both unwieldy and somewhat distasteful to call them the "general ed students" and the "special ed students.")

A few weeks ago, I paired Ricky up with Elena to be counting partners. Ricky is a second grader with ASD. He is working on matching quantities to numerals and counting quantities under 30. He is a quiet guy, but he does communicate verbally and understands a lot of what is said to him. Elena is in the general education second grade class. I had noticed her having some hesitation when counting under 100 (pausing at a new decade, for example), and she needed practice with making groups of ten and understanding place value.

Ricky and Elena chose a collection of links. There were 46 links in the collection. The first time I checked in with them, they were lining up the links and counting by ones. I saw Elena doing most of the counting, so I asked her to stop and let Ricky count, telling her she could help him if he got stuck or made a mistake. He paused for several seconds at each new decade after 20 and sometimes needed help remembering what came next as he counted.

The first time they counted, they got 39 links. I commented on how they had organized the links, and asked them to recount so I could see how they counted. This time they got 46.

"How can you be sure it's 46 and not 39?" I asked. They both looked at me for awhile. Then Elena started to count again. She counted one link twice and got 47.

"Is there a way you could organize them so they would be easier to count accurately?" I asked.

I have a variety of tools they can use for organizing: ten frames, cups, and plates. They chose cups, and started to put two links in each cup.

When I came back, they had 2 in each cup and had put the cups into groups of 4 cups (8 links), with one group of 3 cups (6 links).

"It's 46," Elena said.

"Did Ricky help count?" I asked.

"Sometimes," she answered.

"Show me how you figured out it's 46," I said.

She counted them by ones. She got to 30, then counted one more group of 8 (by ones), miscounted, and got 39. "So 30 plus 8 is 39?" I asked.

She thought for a few seconds and said, "No! It's 38." She recounted them to be sure, then continued on to 46.

I suggested they label each group with the total they had after counting that group. Elena re-counted and I asked Ricky to make the labels. He used a hundreds chart to find the numbers to write. He could find numbers like 38 and 46 but didn't know how to write them on his own. He wrote carefully, clearly, and proudly.

By that point, time was up. Between Elena and Ricky and the other pairs working that day, we had a variety of grouping strategies. Several had grouped by tens, and one pair had made groups of four. Here are a few photos of their work.

I decided the next week to share some of this work with the whole group. One of my goals was to encourage students who had not grouped by tens to think about the advantages of doing so.

The next week, I started class by saying I wanted to tell them a story. I had a slideshow of Ricky and Elena's process, and how they had gone from counting all in one big line to grouping in cups and labeling their groups. At the end I included a few other pictures, including the recording sheet showing the groups of ten. Many of the same students were back again (like Elena, who I partnered with Ricky again), but a few were different. Some students were interested in my "story" and the pictures. Others didn't seem to be paying much attention.

I asked which way of counting they thought would be more efficient and accurate: counting by 2s, 4s, or 10s. A few said they thought ten was quickest and therefore they were less likely to make mistakes. Seeing the recording sheet also gave them, I hoped, ideas for how to record their counting.

I showed them the collections of objects they could choose to count and the visual directions (below), reminded them of the options for recording sheets, and sent them off with the partners to start. (Thanks to Chelsea Schneider for ideas for recording sheets, and to Pierre Tranchemontagn for the photo of a simple recording strategy for my visual.) That day, a few teachers from another district were visiting, so I benefited from their extra eyes and ears -- they got to see things going on that I missed.

Elena and Ricky chose to count links again (they like them!), and they had a bigger collection. Here is how they grouped them:


And here is Elena's recording of her counting:

Ricky was less involved this time -- he kept hiding links and playing with them, while Elena patiently (or sometimes not-so-patiently) coaxed him back into counting.

After counting, I asked Elena how she would group her collection next time. She said she would try by 4s. So she's not sold on 10s yet.

Lily had come from the general education class as well that day, and she worked with Nick. Lily and Nick get along really well and love working together. Lily suggested they count their collection by twos. Nick didn't know how to count by twos. I came upon them to find her teaching him to count by twos using a hundreds chart. He circled the numbers as they counted together. I didn't watch them for long, but our visitors commented that they could see Lily deepening her understanding of skip counting as she explained it to Nick.

One more piece of work from that day (or it may have been the next week, I'm not sure). This shows the potential of Counting Collections to push students wherever they are in their understanding of number and operations.

What I've noticed and learned:

1. Choice

It is good to offer a lot of choices. I try to bring some familiar and some new objects to count each week. I have larger collections and smaller ones. There are three recording sheets to choose from (the two linked above, plus a sheet with 3 ten frames on it). Partners don't have to choose the same recording sheet. I suggest that the pairs decide together what they would like to count, or I encourage the student with autism to make the choice. They struggle more with attending and being engaged, so I want them to choose an object to count that they enjoy.

2. Collection size

One of my questions when I started Counting Collections with heterogeneous pairs was what size the collections should be. Most of the students with autism are working on counting up to 30 or just above 30. Most of the other students would do well to count larger collections, up to 100 or above 100. I asked on Twitter for advice, and the consensus was to ask each pair to count two collections, a smaller one and a larger one. In practice, I have found that some pairs don't get to two collections in one period, but if they count a collection between 40-60, it seems to be a good challenge for both members of the pair (as in the case of Elena and Ricky).

On one branch of that Twitter thread, Kristin Gray and I discussed recording, and agreed that if students counted more than one collection, they could choose just one to record on paper, and attempt to explain the larger collection verbally if it was a challenge.

In reality, I need an even more flexible definition of recording. On the first day Elena and Ricky worked together, Ricky's recording was figuring out how to write the numbers for each group as they counted. On another day, he was able to show how they counted a much smaller group on paper (pardon the water spill):

One student in the class communicates using a communication device, mostly one word at a time. For him, recording means finding the total on a hundreds chart. With a significant amount of help, he can draw a small collection on paper. Figuring out the best way to make Counting Collections work for him is a challenge I am still working on.

3. Everyone is learning.

My primary goal for this time is that both members of each pair are learning. I have worried from time to time that the students with autism might not get much out of the work if their partners do too much for them. But I have seen partners working together well -- helping each other count, sorting and organizing together, working together to record. With some suggestions from me, they often both have a challenge that pushes their thinking.

Our visitors were most impressed at how much the general education students were learning. One assumption about heterogeneous pairs like this is that the general education students will help the special education students and not be challenged themselves. (I hear this thought often as my school discusses increasing the amount of inclusion we will do in the future.) Because of the low-floor, high-ceiling nature of the task and the many choices involved, most of the time this does not seem to be a problem. One student deepens her understanding of counting by twos, another gains fluency with counting, others build their understanding of our system of tens, and another works on multiplication. It is really exciting to watch.

4. Don't micromanage.

The first week or two, I was obsessed with making sure everyone was productive at all times. I couldn't engage in deep listening or conferring because I was trying to get Chima to stop rolling shapes across the table and dropping them on the floor, or I wanted to be sure everyone was accurately recording their counts on paper. I rushed from pair to pair and never stayed in one place for long.

I soon realized I was spending my time talking about following directions and not math. I stopped trying to make sure everyone was moving forward all the time. Instead, I confer with pairs about their counting (Kassia Omohundro Wedekind has shared some great resources on conferring during Counting Collections) and let go of needing everyone to be productive at all moments. It turns out many of the students are working and thinking whether I'm on top of them or not. And if others aren't, I'm okay with that. It's more important that I have real conversations about the math.

5. Let partners do the work

Related to the last take-away is that fact that the heterogeneous partners can do a lot to keep each other moving. Sometimes they go in unexpected directions. Sometimes one of the pair ends up doing most of the work. But often they nudge and support each other beautifully. This frees me up to do the kind of conferring I want to do.
The last time I led this group, I tried Choral Counting with them. I'm eager to gradually add that in as part of our routine and see where it takes us. Then I'll be thinking of what other low-floor, high-ceiling tasks can meet all of these learners where they are. Send me your ideas!