Teaching for Understanding: Helping Students Make Sense of Math

In math intervention, students often arrive with gaps in knowledge and a history of frustration. They may know how to follow steps, but not why those steps work. This lack of conceptual clarity can make math feel arbitrary and difficult to retain.

That’s why teaching for understanding is a critical principle in effective math intervention. It’s not just about getting the right answer. It’s about helping students make sense of the mathematics they’re learning.

Why Teaching for Understanding Matters in Math Intervention

Students who struggle with math often rely on fragile procedural knowledge. They may be able to compute, but they can’t explain their reasoning or apply it to new problems. Without a strong conceptual foundation, learning remains surface-level and easily forgotten.

Teaching for understanding helps students build that foundation. It involves modeling mathematical thinking, guiding students to explore relationships, and encouraging them to verbalize their ideas. When students understand the “why” behind math, they’re more likely to transfer knowledge, solve unfamiliar problems, and grow in confidence.

What Research Says About Teaching for Understanding in Math

Research consistently supports the value of explicit, concept-focused instruction in math intervention. Studies show that:

• Instruction that moves from concrete to representational to abstract helps students build lasting understanding.
• Timely feedback improves student learning outcomes.
• Explicit modeling of mathematical thinking benefits students with math difficulties, especially in problem-solving and computation.

Students also benefit from opportunities to talk about their thinking. When they explain their reasoning—whether to a partner or the whole group—they clarify their ideas and deepen their understanding.

Supporting Students Through Guided Mathematical Inquiry

Teaching for understanding doesn’t mean abandoning structure. In fact, it requires intentional planning. Teachers present carefully sequenced experiences that help students develop concepts, learn skills, and make connections. This might include using manipulatives to model a problem, transitioning to visual representations, and finally connecting those models to abstract equations.

For example, when exploring division, students might use tiles to model 12 ÷ 4. They arrange the tiles, count the groups, and write the equation. Then they connect the division problem to a related multiplication equation. Through this process, they’re not just solving—they’re understanding.

Creating a Math Classroom Where Meaning Matters

In intervention settings, it’s easy to feel pressure to move quickly. But teaching for understanding is about long-term growth. It helps students build the kind of knowledge that sticks—and that they can use flexibly in future learning.

This approach is central to the Do The Math program, developed by Marilyn Burns and a team of master classroom teachers. Each lesson is designed to support conceptual development through explicit instruction, modeling, and guided inquiry. To learn more about the research foundations behind this approach, download Do The Math Research Foundations: Evidence and Efficacy Report.

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This post is part of an eight-part series exploring effective strategies for math intervention. Each post highlights one of eight key instructional principles designed to help students thrive in intervention settings.