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, as well as the first and second in the series.)
Classroom Situation: This second grade class is in-person two days a week, at-home two days a week, and online from home on Wednesdays. This one-hour session focused on Roll-a-Square, a game from Unit 3 which focuses on addition, subtraction and the number system.
We have heard from many that engaging students in math discussions has been one of the more challenging aspects of remote learning classrooms. As I have visited virtual classrooms, I have been particularly interested in seeing how teachers facilitate the math discussions embedded in Investigations lessons and gauging students’ engagement. During my visit to this second grade, I was intrigued by the way the teacher used the “Students Might Say” feature of the curriculum to anchor a discussion.
The session began with a whole-class introduction to Roll-a-Square. Students then played the game on their own, as the teacher circulated among breakout rooms. Then, the class came back together for a whole class discussion focused on the following problem, presented via Google slides:
Students shared equations that represented the situation and a few of their solutions. Then, the teacher presented the following images. In the curriculum unit these “Students Might Say” images provide examples — for the teacher — of how students might solve the problem and record their solutions.
After the class read each quote aloud, the teacher asked students to compare the two strategies. (Note: students’ names are pseudonyms.)
Carla: They both got the same answer which was 23.
Tia: They both started with 27 and added on to 50.
Henry: They both used equations.
Leo: They both added two tens and a three.
Alberto: Chen added on the three to get 30 and then he added the tens. Nadia added the tens first and then added the three at the end.
Yama: They both added tens and a three, but they did it in a different order.
I was struck by how quickly the students engaged with this question. I was also interested in the number of students that spoke and that no one repeated an observation that someone else had already shared. This indicated to me that, while there was no direct student-to-student discussion, students were listening to their classmates’ observations and comments and monitoring their contributions based on what others had already shared.
I was also impressed by students’ ability to engage with both the written expression of the solutions and the set of equations that represented those solutions. When I looked back at the range of observations that students shared I could see that they were hovering around a big idea for 2nd graders — Chen and Nadia used the same strategy to solve this missing addend problem. They counted on from one number, but in different ways.
The teacher then layered on another graphic from the curriculum unit, and asked the students to consider which number line represented which solution.
The end of the hour lesson was looming, so there was not enough time to fully explore the connections between the representations and the problem, but several students quickly pointed out that the top number line connected to Chen’s solution and the bottom to Nadia’s. The discussion ended with one student’s summation of the math idea connected to the two representations:
Alberto: Nadia did it first with the 10 + 10 but Chen did it with the 3 first. They did the same thing but in a different order.
During this 15-minute discussion, students’ engagement and participation was apparent and their ability to observe and reflect on solutions that were not their own was notable. I also thought about how this discussion offered students the opportunity to engage with some of the foundational ideas of Math Practice 3: Construct Viable Arguments and Critique the Reasoning of Others.
The teacher’s unique use of the Students Might Say and the graphics of the student work and number lines stood out for me. She effectively used these features – which are intended to inform her understanding of what the discussion might sound like and look like – to support and facilitate student thinking and sharing. The effectiveness of this instructional decision in terms of having students analyze the ideas and work of other students was remarkable. All of this seems particularly important given this discussion took place during remote learning. While using these features of the curriculum should not replace students sharing their own solutions and models and representations, there might be a variety of reasons, especially in online learning, when it is appropriate to make this choice. What struck me was how effective a choice it was.
As I reflect on my visit to this grade 2 classroom, and to other classrooms, I am aware of the creative and thoughtful ways teachers are using Investigations to structure math teaching and learning and to facilitate math conversations. The curriculum is a tool that supports them in making informed decisions about how they do so. While much of this year is so different from what we know as typical, one thing’s the same – students are learning and students are having meaningful conversations and doing meaningful work. This learning is not lost.
Note: This vignette was one example shared during our Burst series focused on how specific features of the Investigations 3 curriculum can be used to promote and support math conversations and discussions in remote learning situations. Watch Session 1: Promoting Student Talk Using the Students Might Say.
- Meaningful Math Talk — It’s Still Happening in the Remote Classroom - March 29, 2021
- Counting is More than 1, 2, 3: Engaging Adults in K-2 Mathematics - August 8, 2018
- “This is Only Getting Better!…And Harder!” - June 12, 2018