With only 28 percent of 8th graders demonstrating proficiency in mathematics, according to 2024 NAEP data, educators must reconcile how we make math accessible and meaningful for all students. Notably, Alabama is the only state that has shown improved math scores over pre-pandemic levels. The Next Generation Learning Standards call for students to explore math concepts as opposed to master them, which was what was previously prioritized within the Common Core Standards.
If we want students to explore math, it has to be accessible—and making math accessible requires a different approach. As Stanford University Professor Jo Boaler said in a recent podcast conversation, “Math can be a visually creative subject when kids get to look at an interesting mathematical situation, think about what it means, and talk about it with each other.” She explained that this visual, active approach helps students build deeper conceptual understanding. Through active engagement with math, students develop clarity about mathematical concepts rather than merely mastering computation.
This visual- and discussion-based approach brings up a key question: How can teachers present math concepts in ways that support student exploration? The answer lies in how we model. Most teachers use modeling—demonstrating how to approach problems, concepts, and procedures—to guide instruction. Effective modeling offers clarity, builds confidence, and strengthens procedural fluency. But many K–12 teachers aren’t modeling as effectively as they could—especially if the goal is for students to explore, productively struggle, and make meaning of math for themselves, becoming truly “math literate” in the process.
Building Mathematical Agency
Modeling is vital in building a mathematical foundation for students, particularly when introducing new concepts and strategies. Traditionally, most teachers first model the task (I Do), then guide students through practice (We Do), and finally allow students to try the task independently (You Do). In this process, when teachers provide direct instruction first, students passively receive information and mimic procedures. They rarely engage in deep thinking or exploration. Students also miss opportunities to apply, through productive struggle, what they might already know about mathematical concepts and procedures.
Effective modeling offers clarity, builds confidence, and strengthens procedural fluency.
Therefore, instead of a I Do-We Do-You Do approach to modeling, teachers should consider employing a You Do–We Do–I Do approach. In this framework, the release of learning to students is much more rapid than in the traditional modeling approach.
You Do
First, students, individually or in small groups, engage in productive struggle to complete a task (You Do). Productive struggle refers to the challenging yet engaging experience where students grapple with concepts and persevere through difficulties to reach understanding. The goal is to have students productively struggle to foster critical thinking and problem-solving skills, make SEL connections by encouraging cooperation, resilience, and perseverance, and develop deeper conceptual understanding and retention of math concepts.
Every task can be a thinking task, says Peter Liljedahl, professor at Simon Fraser University. Rather than immediately showing students how to solve a new math problem, Liljedahl suggests first presenting the unfamiliar problem and asking students to apply their existing knowledge to approach it. This method shifts learning from an accountability practice to a responsibility practice. What does a lesson look like in Liljedahl's approach? “It always starts with kids on their feet, standing around a vertical whiteboard or circular table. I usually ask them some simple questions to activate prior knowledge or show them something and off they go,” he says.
To make this initial phase successful, teachers can provide just enough structure without eliminating productive struggle opportunities. This might include clearly outlining expected deliverables and offering resource checklists while preserving space for student initiative. Visual aids such as number lines and math fact charts can help students engage with abstract concepts.
For example, when teaching 6th grade ratio concepts, a teacher might present a real-world problem: “A smoothie recipe calls for 2 cups of strawberries and 3 cups of bananas. How would you make larger batches while keeping the same ratio?” Students could use red and yellow counters to represent strawberries and bananas, exploring different batch sizes conceptually. Working in pairs or small groups, students might create ratio tables and discuss patterns they observe, all before receiving any direct instruction on proportional relationships.
We Do
Then, the teacher brings students together to review thinking (We Do). Paola Sztajn, professor at North Carolina State University and author of the book Activating Math Talk, notes that while teachers often engage in corrective discourse with students, the goal should be to foster responsive discourse, where students ask each other questions about their mathematical thinking, taking responsibility for their own learning. In high-level student-to-student dialogue, students might ask peers to explain how they arrived at their answer to a math problem, collectively investigate alternative ways to solve problems, and/or challenge each other, respectfully, when solutions to problems vary.
Referring back to our example of modeling 6th grade ratio relationships, during the We Do phase, teachers help students visualize and organize their thinking using structured representations. As a whole class, the teacher might lead students in creating a ratio table on the board showing the relationship between strawberries and bananas: 2 cups to 3 cups, 4 cups to 6 cups, 6 cups to 9 cups, and 8 cups to 12 cups. Throughout this process, the teacher asks guiding questions about the patterns students observe.
During this collaborative review phase, teachers might find themselves wanting to correct student misconceptions immediately. Instead, consider addressing these through strategic questioning that guides students to discover corrections themselves, maintaining their sense of agency in the learning process.
I Do
Finally, the teacher walks students through the steps they would take to solve the problem (I Do). Teachers still provide direct instruction within this reversed framework, but deliver this instruction after students have had time to think about and wrestle with the math task.
Teachers still provide direct instruction, but deliver it after students have had time to think about and wrestle with the math task.
During the I Do phase in our example, the goal would be for students to transition to solving proportions using abstract multiplicative relationships. The teacher can introduce the proportion equation by asking, “If ⅔ = x/12, how can we find x?” They can then model cross-multiplication to solve for unknown values: 2 × 12 = 3x, 24 = 3x, x = 8.
This is where digital tools like interactive whiteboards and simulations can be particularly effective, allowing teachers to connect students' earlier approaches with standard methods and visualize mathematical relationships. While many students will now be ready to independently practice solving proportions, teachers should still circulate around the room, checking progress and reminding students to reference the ratio table created during the We Do phase.
Growing Mathematically Literate Thinkers
Balancing direct instruction with opportunities for independent thinking encourages a reflective and flexible approach to mathematics teaching. By frontloading productive struggle and integrating mathematical discussions with the You Do-We Do-I Do framework, teachers can foster deeper understanding and confidence. The ultimate goal is to develop students who are engaged, mathematically literate, and resilient in their mathematical thinking.
Editor's note: The author acknowledges the use of artificial intelligence for idea generation and example development.
