Making Sense, Persevering, and Connecting: A UDL Approach to SMP #1

Podcast Description:

In this episode of Math Universally Speaking, we explore Standards for Mathematical Practice #1—Making Sense of Problems and Persevering in Solving Them—through the lens of Universal Design for Learning (UDL). Too often, students struggle with problem-solving because they lack strategies for making sense of math, persisting through challenges, and connecting new learning to what they already know. We’ll discuss how educators can create flexible learning environments that support student autonomy, optimize challenges, and encourage productive struggle—ensuring that all students become confident, resilient problem solvers.

Join me as we examine practical strategies for helping students navigate math with independence, collaboration, and deep understanding. Let’s rethink how we approach math instruction—moving beyond quick tricks and shortcuts to build meaningful mathematical thinking.

References:

CAST. (2018). Universal Design for Learning Guidelines version 2.2. Retrieved from https://udlguidelines.cast.org

Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. Retrieved from http://www.corestandards.org/Math/

Agarwal, P. K., & Bain, P. M. (2019). Powerful teaching: Unleash the science of learning. Jossey-Bass.

Transcript

Introduction

Hello and welcome to Math Universally Speaking! I’m Ron Martiello, and today, I invite you to explore an essential yet sometimes overlooked aspect of mathematics—the Standards for Mathematical Practice, or what the cool kids call “SMPs”. While we often focus more on content standards, these practices shape how students reason, interact with the math, and communicate their thinking to others.

In this episode, we’ll dive into SMP #1: Making Sense of Problems and Persevering in Solving Them. We’ll start by identifying some common barriers students face when tackling problems, from struggling to make sense of what’s being asked to knowing which strategies to use. Then, we’ll explore ways to support students in developing mathematical thinking that lead to success.

Let’s take a deeper look at how we can help students engage meaningfully in problem-solving—equipping them with the tools they need to make sense of math and confidently work toward solutions. Now, let’s jump in!Breaking Down SMP #1: Making Sense, Perseverance, and Connections

SMP #1 is often summarized as making sense of problems and persevering through them. However, there’s a third, often overlooked component: making connections. Let’s take a look at all three.

Making Sense of Problems

When students are introduced to a math task, they often rush toward a solution. However, it’s crucial to pause and allow time for sense-making. This is where we address one potential barrier for students who are having difficulties and others who may be finishing too quickly: Can students understand the problem?

Before jumping into strategies, we need to make sense of the problem itself. Students need time to explore the situation and the relationships between the quantities before attempting a strategy. By allowing some autonomy, we create space for students to approach problems through their own understanding, reinforcing their confidence and ownership of the learning process. And this ties right into Universal Design for Learning (UDL)—it’s all about giving students the freedom to make sense of math in their own way.

Students come to the problem with a mathematical toolbox, filled with prior knowledge and problem-solving strategies. Our role as educators is to honor their strengths and give them time to explore those tools so they can find entry points into a solution attempt. A simple yet effective strategy is allowing students a few minutes of quiet reflection before discussing solution attempts. Silence can feel uncomfortable, but it provides students with the cognitive space to evaluate their choices to see if their approach fits the problem.

Persevering Through Problems

Once students attempt a solution, perseverance becomes essential. Problem-solving is rarely a linear process—it involves trial, error, and revision. That’s why perseverance isn’t innate; it’s nurtured and cultivated. Students must learn how to persist through challenges without relying on teachers to provide immediate answers.

As educators, we must resist the urge to save students from their own struggle. Instead, we stay beside them, guiding with questions rather than solutions.

What’s not making sense?
Is your strategy working?
Can you recall a similar problem you’ve solved before?

These questions help students self-assess, recognize alternative approaches, and build confidence in their reasoning. This aligns directly with UDL, particularly in optimizing challenges and supports. By fine-tuning the level of challenge and support, we ensure students push through difficulties without feeling overwhelmed while still maintaining agency over their learning.

Students need different pathways to navigate the struggle. Some may benefit from working independently, reflecting on their solution pathway. Others may thrive by bouncing ideas off classmates, engaging in productive discussions to refine their thinking. Collaboration fosters perseverance by allowing students to discuss strategies, gain new perspectives, and refine their reasoning. Comparing different approaches highlights math’s flexibility, reinforcing that multiple valid pathways lead to a solution while strengthening both conceptual understanding and communication skills. Some students may want to conference with a teacher, checking if their reasoning is sound or if they need a new tool to solve the problem. By offering these options, we ensure that every student has the support they need while still building perseverance and independence.

Making Connections

The final piece of SMP #1 is making connections. Students must relate new problems to their prior knowledge, recognize familiar patterns, and learn from their peers. Encouraging strategies like brain dumps—where students list everything they know about a given concept—helps activate background knowledge and prepare them for problem-solving.

That said, teachers must be mindful of striking the right balance between guidance and independence. A major pitfall to avoid is the “Just do this” approach, where teachers provide a shortcut or trick to quickly arrive at an answer. While well-intentioned, this prevents students from truly understanding concepts and making meaningful connections. Instead of rescuing students from their struggle, we should equip them with strategies to navigate challenges, ensuring they build confidence and problem-solving resilience.

Brain dumps can be incorporated at different stages of the learning process. At the beginning of a lesson, they help students recall relevant prior knowledge, setting the stage for application. If a student gets stuck, calling a quick time-out for a brain dump can provide a productive way to reflect on what they already know and find a way forward. And at the end of the problem-solving process, brain dumps allow students to reflect on their work, organize their thoughts, and document key takeaways that will support future problem-solving attempts.

By actively connecting new learning to prior knowledge, students develop a deeper understanding of mathematics. This aligns with UDL’s emphasis on connecting prior knowledge to new learning, reinforcing that math is not a series of isolated skills but a web of interconnected ideas.

Closing and Key Takeaways

Today, we put a spotlight on SMP #1: Making Sense of Problems and Persevering in Solving Them. But more than that, we emphasized the process—not a set of steps, but an ongoing cycle where students move fluidly between making sense, persevering, and making connections.

We also explored the connections between SMP #1 and Universal Design for Learning, particularly in:

Making Sense → Optimizing Choice and Autonomy—Giving students space to develop their own problem-solving strategies fosters a sense of ownership and confidence.
Persevering → Optimizing Challenges and Supports—Providing guidance without rescuing students from struggle helps them persist and build resilience.
Connecting → Connecting Prior Knowledge to New Learning—Helping students activate what they already know to make meaningful mathematical connections strengthens their understanding.

By proactively addressing barriers and fostering mathematical thinking, we can create learning environments where every student becomes a confident problem solver. I believe in empowering educators with the strategies and insights needed to cultivate equitable, high-quality math instruction that ensures all students thrive.

So let’s continue this journey together. Just like our students, we grow through making sense, persevering, and making connections. Share your experiences, insights, and challenges in fostering mathematical thinking—because the more we collaborate, the stronger our community becomes!

Until next time, keep exploring, keep pushing through challenges, and keep making those meaningful connections. Thanks for listening to Math Universally Speaking! Take care!

Professional Development

Here are three professional development questions to deepen reflection and discussion related to this podcast episode:

What shifts can you make in your classroom to help students take ownership of sense-making in problem-solving? Think about the role of choice, autonomy, and collaboration in math learning and how these elements impact student engagement and confidence.

How can we design math instruction that fosters perseverance without creating unnecessary frustration? Consider the balance between productive struggle and appropriate scaffolding. How might Universal Design for Learning (UDL) principles guide your approach?

In what ways do you currently encourage students to make connections between mathematical concepts? Reflect on strategies you use to activate prior knowledge and support students in seeing math as an interconnected system rather than isolated skills.