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We visit a 2nd grade classroom to observe a math session focused on subtracting with the Decomposition Strategy:
Throughout the video, students build the meaning of subtraction through using manipulatives, conversation, and reasoning. Rather than applying a fixed procedure, students move forward, each from their own starting point.
Supporting Differentiated Instruction in a classroom like this, where all students participate, is not easy. That’s why the logbook time in the last 15 minutes is a key moment: it allows the teacher to provide more individualized support.
But there are more moments too! In the first part of the article, we’ll analyze what happens and what resources the teacher uses to respond to differences in the classroom. And in the second part, we’ll broaden the lens and reflect on Differentiated Instruction in general, presenting the different resources offered by the Innovamat program.
Let’s go!
Contents
Analyzing a math session: Differentiated Instruction practices
Differentiated Instruction is not a single moment, but a series of small decisions that build throughout the session. Next, we analyze a class to identify where and how these moments show up:
The session begins with the teacher handing out manipulatives, the base-10 blocks they will use today. Next, she suggests solving the subtraction problems on the board.
The process is the same for everyone: first, they represent the starting amount and then take away the indicated amount. Here, the manipulatives play a key role, since they reduce the level of abstraction in a complex situation and allow each student to move forward at their own pace.
As usual, not all students understand what is happening right away. To support this process, the teacher invites some students to explain how they solved the subtraction problem, repeating their explanations, helping everyone understand the key ideas so no one falls behind. She also always keeps the manipulatives nearby when someone needs them.
The logbook time, at the end of the session, becomes an especially important space. While students practice and consolidate in their logbooks what they built during class, the teacher walks around and provides more individualized support. In this moment, we observe two especially important moments:
- On one hand, she stops with a student who is having more difficulty and establishes a guided conversation with him. Through dialogue and questions, she supports him in understanding the steps of the strategy. But she doesn’t stop there. Once he gets an answer, she invites him to check it using manipulatives, promoting critical thinking and reinforcing the reasoning and proof process.
- On the other hand, she also supports a student who has already solved all the subtraction problems and can go beyond. With him, the teacher holds a math conversation that allows her to assess his thinking: how he thought, what strategies he used, and what level of understanding he is at, and then adjust the next challenges.
Differentiated instruction and the factors that shape it
Differentiated Instruction is a multifactor phenomenon that depends on different educational partners. We, as a publisher that works directly with schools, are part of this system.
For this reason, we also reflect on our role and on how we can help ensure that all students, regardless of their starting point, have real opportunities to learn math.
Resources to support Differentiated Instruction
The Innovamat program includes a wide range of resources to create learning experiences that promote understanding and reasoning for all students, without exception. But what exactly are these resources that make it easier to support Differentiated Instruction in the classroom? Let’s take a look!
Building knowledge in the classroom
In knowledge-building sessions, we offer a variety of strategies, manipulatives, rich activities, and classroom management guidance so that all students can understand and participate in the tasks.
Low-floor, high-ceiling, wide-wall activities
The low-floor, high-ceiling, wide-wall activities are rich tasks that allow all students to access the task (low floor), go beyond for those who can (high ceiling), and propose multiple approaches and strategies (wide walls)
At Innovamat, we offer a large number of activities of this kind. Many of them start from an open prompt that invites everyone to begin exploring and, at the same time, allows new questions to be asked to go as deep as desired.
A good example of this can be found in the QUELI dynamics (short for “Which One Doesn’t Belong”), which make it possible to work on rich math even with very young students and, also, are easy to replicate in upper-grade classrooms.
Logbooks, resources, and practice adapted to each student
When recording what they’ve learned—a key moment at the end of the session—we have a standard version of the logbook full of practice activities.
But we also have two extra versions for those who need them. An adapted version with more scaffolds for students who need support. And an extension version, with more questions and activities, for those who can and want to go deeper.
Whenever possible, we should try for all students to share the same learning goal. But when that isn’t enough, the program makes explicit the connections between grades and allows access to resources from earlier grades to adjust goals to each student’s needs without separating them from their class group.
On systematic and individualized practice days, when the content taught is consolidated and practiced, we use Math Atlas, a digital tool that helps us identify each student’s needs, offer personalized supports, and create an individual pathway for them.
Additional math resources for Differentiated Instruction
Beyond all of this, we offer an intervention program designed specifically for students with a significant curriculum gap.
- The Early Intervention Program (COSMOS), aimed at 1st and 2nd grade students, is designed to identify and address difficulties early in the development of basic math skills. You can learn more on our website: https://www.innovamat.com/en/math-artist/
- Math Journeys are session sequences that allow you to teach and assess specific content in parallel with the class group. Each Journey is a structured pathway that addresses specific content, organized into key areas, and requires careful planning and adequate staffing to offer an adjusted and meaningful learning experience.
