Our staff has been thinking hard about how teachers are using Investigations 3 to teach math in all of the different scenarios they are faced with this year. We’ve been visiting the remote classrooms of teachers we’ve collaborated with previously, to learn from teachers and students who are teaching and learning math online, and to see how the rigor and coherence of the curriculum is supporting them in that work. This series of blogs will share some of what we are learning. (Read an introduction to this series of blogs.)
Classroom Situation: This session – the first of 1U3, How Many of Each? How Many in All? – took place in a “hybrid” first grade class with 22 students. Half of the class goes to school Mondays-Tuesdays, the other half on Thursdays-Fridays, and everyone is remote on Wednesdays aka “Zoomsdays.” Because students – all of whom are pseudonymed – are in school twice a week, the teacher can send home the physical materials (e.g., dice, game instructions, gameboards) they will need at home. This lesson was about an hour long and was modeled after the following plan:
I had a lot of questions as I joined my first elementary math class via Zoom—about the technology, about the virtual environment, and about what was reasonable to expect of first graders and their teachers. I wondered how visiting an online class would compare to an in-person observation. And I was curious about how (and how much of) the intended curriculum could and would be enacted remotely. An hour later, I had some answers. (And more questions.) The biggest lesson? In so many ways, it felt like a typical visit to an Investigations classroom. Read on to hear why.
Classroom Routine The class began, as many do, with a brief Classroom Routine. The teacher used the Teacher Presentation (built into Savvas Realize) to do Build It with the whole class. She shared her screen and encouraged students to “pin” it. Together, they identified and then represented the numbers 20, 15, and 10, with pennies on two ten frames. These first graders easily unmuted their microphones to speak, and then muted themselves again. The teacher moved the pennies as instructed by the students. The highlight? When Seth said, “One and a half [ten frames] is 15.” I was stunned. I’ve seen a lot of Build It and I’ve never heard a first grader talk about one and a half ten frames before. I’ve often said I never visit a classroom without learning and/or being surprised by something; this was no different.
Introducing Roll and Record The class then transitioned into the main focus of the math lesson. After reminding students that they had played Roll and Record with two 1-6 dot cubes earlier in the year, the teacher used the Teacher Presentation to introduce the new variation. She asked students to use their fingers to show what she’d rolled, and dragged cubes out to represent the problem.
“Take a minute and think about this problem. Your job is to add, to combine, to find the total of 5 and 3.” After a lengthy wait time, she returned to gallery mode, so she could see all of the students. She held up a whiteboard showing 5 + 3 = and 3 + 5 = and asked for strategies for solving this problem.
Kaya: I used my fingers. I got 8.
Teacher: How did you use your fingers?
Kaya: (holds up one hand) 5. 6, 7, 8 (raises 3 fingers, one at a time).
Teacher: Kaya counted on. Any different ways of thinking about the problem?
Tala: I noticed that there was a 5 and if you add one more to the 3 that makes it 4 and 4 and that’s 8.
Teacher: Any other ways of thinking about the problem?
Seth: The 3 in the 5 and the 3 in the green [make 6]… and then 2 more.
I was struck by the flexibility students showed in figuring out how to combine 5 and 3, and in their ability to explain their thinking. A straightforward problem like 5+3 can be an interesting and engaging problem, and discussing ways to solve it can uncover important mathematical ideas.
Preparing to Play The teacher explained that they would record the same way they had in the past, by writing the sum in the appropriate column on the gameboard.
She explained that students would play, independently, in a breakout room with others. She gave them a few minutes to find the materials that had been sent home: a 1-6 dot die, 1-6 number die, a copy of the gameboard, and some connecting cubes. Before sending students off to play, the teacher reminded children they could angle their camera once in the breakout, to share what they were doing on their desk or table.
Roll and Record in Breakouts At this point, the teacher put students into three breakout rooms, to play the game with actual materials. While they played individually, they also talked together about the problems they were solving, the strategies they were using, and what they were noticing as the numbers started to fill their gameboards. I joined the teacher’s breakout room. Some highlights:
A student shared that one of her dice had 7-12 and wondered if this was right. The teacher helped her get what she needed, but capitalized on the math opportunity by asking everyone, “Why won’t a 7-12 die work?”
- Kaya: Cuz if you roll 11 on that one and let’s say 3 on the other, there wouldn’t be enough space. There’s no 14 on the game sheet.
Someone wondered why the board starts with 2 instead of 1. The teacher put the question to the room.
- Matt: Only if you had one dice you could get 1. With two dice, you can’t get 1.
- Kaya: Cuz like if you have one die with a 1 on it then you can get 1 but if you have two you can only get 2, you can’t get 1. Say I get two 1s, then I rolled 2.
As time was running down, the teacher asked kids which columns they’d filled. When they called out many of the same numbers she asked, “Why are those numbers going to the top so quickly, I wonder?”
- Sachi: There’s only 1 way to build the 2. And only 1 way to build the 3. And there’s a couple of ways to build 6, 7, 8, 9, and 10.
- Kaya: On the ends there’s only a couple of ways to make the number. Like you can only make 12 with two 6’s.
The math of this game focuses on adding two numbers to 6, number-writing practice, and moving from counting all to counting on. These ideas were the focus of much of the discussion. But these thoughts about probability floored me. They brought to mind a quote from a recent blog from kidsquadrant.com — “Kids have great ideas, and they have great ideas much earlier than you’d think!” – and had me thinking about the importance of making room for such ideas and wonderings.
Wrap Up Class ended with a quick check in back in the whole group, as students transitioned to the next part of their day. The teacher commented on some strategies she had seen and mentioned how “we’re starting to look for counting on.” She explained that they’d be playing again — on Google Classroom or back in school – and would be learning and playing a new version of 5-in-a-Row when they were back in the classroom.
Reflections At the end of my first Zoom class, I was buzzing with thoughts and new questions.
- This felt like one of many visits I’ve made to first grade classrooms over the years. The teacher focused on mathematical ideas and on students’ thinking about them. Even in this virtual setting, students had amazing ideas and were happy to share, discuss, and build on them. Given the space and encouragement to wonder and ask questions, kids are interested in and engaged by going deep with even the “simplest” of ideas.
- Typical “issues” arose. Gathering the materials took some time; some kids had the wrong dice or didn’t have the gameboard. Problem-solving took care of those issues (e.g., kids drew the gameboard on their whiteboard or searched board game boxes at home for a die). And there was a classic first grade tangent about favorite games. “This [holding up a die] is from Clue! Do you play Clue? I love Clue!”
- It struck me how technologically fluent and flexible these 6- and 7-year-olds – and their teacher! – were in early December, even with only one online session a week since the beginning of the year. They muted and unmuted, “pinned” the teacher, and had ways to share their work in the breakouts. The technology never seemed to get in the way of the math thinking.
- As in the non-virtual classroom, the Teacher Presentation was a useful tool for doing a whole class activity and introducing a new variation of a game. It focused the class’s attention and provided common images and problems to discuss. Using it did limit the number of students the teacher could see and the onscreen recording she could do (though Savvas is at work on this as we speak!). Other low-tech tools were also powerful. The teacher used a small whiteboard, and students used their fingers to represent numbers, hand signals to agree/disagree, and connecting cubes to model problems.
- Even though the class spent an hour doing math, it took more time to get through less material. As written, this session calls for re-introducing and playing two games and a 15-minute discussion at the end. The decision to introduce just one of the games and delay the meatier discussion felt like the right adaptation for the time and situation. The game that wasn’t introduced will be. They will have the discussion they didn’t have, in a future session or across several. Because they are using a focused and coherent curriculum, they were talking about important math ideas that connect to work they have done and to work they will do. Thinking about how to structure and lay out the work, given the current situation, is something I am interested in thinking and learning more about. What makes sense to teach to the whole-class on Wednesdays? What makes more sense for the in-class days? For the at-home days? What ideas may not make sense to prioritize this year?
- My final thought is about the amazing work that teachers are doing. The world changed, on a dime, and many are needing to learn and use new tools, on the fly, with little training. The situation and expectations can change weekly. Despite all of this, the classes I am visiting are focused on making sense of math ideas; on listening to, discussing, and building on students’ ideas; and on empowering students to be thinkers and doers of math.