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Welcoming Interests and Identities on Math
How do we truly invite students into mathematics?
In this episode of Math Universally Speaking, Ron Martiello explores the connection between Universal Design for Learning (UDL) and high-quality mathematics instruction, focusing on the engagement guideline of welcoming interests and identities. When students feel invited into the learning process, they are more likely to stay engaged, persevere through challenges, and develop a strong math identity.
Drawing connections to the Standards for Mathematical Practice and NCTM’s Principles to Actions, this episode explores how teachers can design math classrooms that honor learner variability while maintaining high expectations for all students.
You’ll hear practical ideas for:
- Using multiple mathematical tools and strategies to support conceptual understanding
- Designing instruction that promotes choice, relevance, and authenticity in math learning
- Encouraging strategic thinking and problem solving rather than relying on a single algorithm
- Creating opportunities for joy, collaboration, and productive mathematical play
- Using asset-based language to nurture positive math identities for every student
Ron also discusses how welcoming student identities can transform math classrooms from places of compliance into spaces where students feel valued, capable, and invited to think deeply about mathematics.
This conversation connects directly to ideas explored in the book Conquering Math Myths with Universal Design: An Inclusive Approach to Instruction K–8, co-authored by Ron Martiello and Dr. Jenna Rufo.
If you’re passionate about inclusive math instruction, equitable teaching practices, Universal Design for Learning, and developing confident math learners, this episode will give you practical insights and inspiration for your classroom.
Follow Math Universally Speaking and join the conversation using #MathUniversallySpeaking.
Transcript
This transcript has been professionally edited for clarity and readability. It reflects the content and intent of the conversation but is not a verbatim, word-for-word record.
Welcoming Interests and Identities in Math
Intro
Welcome back to Math, Universally Speaking.
Today’s episode sits at the intersection of math instruction, Universal Design for Learning, and student identity—specifically the Principle of Engagement and what the framework calls welcoming interests and identities.
One of my ongoing passions is making clear connections between authentic math instruction and the UDL framework. This is what inspired my collaboration with Dr. Jenna Rufo on our book Conquering math myths with Universal Design. And I want to be honest right up front—those connections are not always straight lines. Sometimes they’re curved. Sometimes they’re blurry. And that’s okay.
They’re blurry because learners are variable.
They’re blurry because classrooms are variable.
They’re blurry because our resources, our contexts, and our systems are variable.
So today, I’m taking more of a 300-foot view of the framework, focusing on how welcoming interests and identities connects to strong mathematics instruction, drawing from the Standards for Mathematical Practice and **NCTM’s **Principles to Actions.
Why Welcoming Interests and Identities Matters in Math
In the UDL framework, welcoming interests and identities lives in the upper-left quadrant—and that placement matters. This is about access through engagement.
This is how we:
- Invite students into the work
- Motivate them to stay in the work
- Build a culture of learning where all students feel they belong
When we talk about math identity, we have to acknowledge the full spectrum in every classroom and proactively design learning experiences.
There are students who are highly confident in math.
There are students who are unsure, hesitant, or anxious.
And there are many students in between.
Some students are quick calculators but may have gaps in conceptual understanding.
Other students may struggle with calculation but have strong reasoning and mathematical thinking—they just need support connecting that reasoning to symbols, numbers, and representations.
Welcoming interests and identities means recognizing all of that variability—and designing instruction that honors it.
Optimizing Choice: Tools Are Not Band-Aids
One powerful way we do this is by optimizing choice.
Math has traditionally been taught as if there is:
- One right way
- One right strategy
- One right tool
That often means heavy reliance on a so-called “standard algorithm”.
We sometimes send the message:
“If you just learn this way, everything else will fall into place.”
But math is bigger than that.
Welcoming interests and identities means offering multiple tools and strategies for students to show their thinking—and explicitly coaching them to use those tools strategically, not randomly.
Concrete manipulatives—base-ten blocks, fraction bars, algebra tiles—are not band-aids.
They are tools for understanding.
Too often, we reserve them for “those kids who don’t get it,” when in reality:
- They help students create meaning out of the math
- They support strategic tool use
- They slow down fast calculators and deepen conceptual thinking
- They elevate students who reason well but need support with language, numbers and symbols.
The same is true for open number lines, partial products, partial sums, and alternative algorithms.
Students should be supported in:
- Discovering their preferences
- Comparing tools and strategies
- Evaluating which tool best fits the problem
Just like in real life— a hammer is a great tool…unless you’re fixing a piano.
That kind of strategic decision-making is authentic mathematics.
Optimizing Relevance, Value, and Authenticity
Choice alone isn’t enough.
It has to be purposeful.
When we force students into one way to solve a problem, we unintentionally tell them that math is rigid and disconnected from real life. But in real life, there are many ways to solve problems.
Authentic choice empowers students to:
- Reflect on their thinking
- Evaluate efficiency and appropriateness
- Connect their strategies to others’ strategies
- See the underlying mathematical structure
Relevance also means helping students understand where they are on a learning continuum.
We need to:
- Accurately connect to prior learning
- Clarify what they are learning now
- Show how it connects to future learning
“Because it’s on the test” enforces compliance. It does not motivate and engage learners.
Students need to know why the learning matters and where it’s going. That requires us to understand the standards below and above our grade level.
At the same time, we must coach students toward more efficient and appropriate strategies as the math becomes more complex.
Early strategies may be foundational and relevant at the time—but part of welcoming identities is helping students let go of strategies that no longer serve them and giving them ones to move forward.
Nurturing Joy and Play in Mathematics
Another powerful way we welcome interests and identities is by nurturing joy.
Strategic math games invite students to:
- Collaborate
- Anticipate moves
- Analyze possibilities
- Adjust strategies
Joy and play allow students to explore tools and strategies in low-risk, high-engagement ways and help answer the question: What are the possibilities here?
Addressing Bias, Threats, and Distractions
Welcoming interests and identities also means confronting bias—including our own. Our words and our actions matter. All student have a right to grade level instruction and educators who believe in them.
We cannot label students as:
- “Not a math person”
- “A struggler”
- “A high flyer”
Every student is a learner.
Asset-based language fuels identity, courage, and persistence:
- They haven’t learned it yet.
- I know you can do this.
- Mistakes are part of learning.
Feedback, Forth, and Student Voice
Welcoming identities requires feedback and forth.
Students need space to:
- Reflect on how they’re learning
- Share what’s working
- Communicate how math feels to them
Providing opportunities such as math biographies, drawings, songs, or identity choice boards helps students express how they relate to math, the content, and themselves as learners.
Closing
When we talk about welcoming interests and identities, we’re talking about engagement as access.
We’re preparing students’ minds and hearts to do the work of mathematics.
When students feel invited, valued, and capable, they are far more likely to engage deeply, persist through challenge, and become the math learners we already know they can be.
That’s the work.
And that’s math—universally speaking.
Before we close, I want to remind listeners that many of the ideas we discussed today are explored more deeply in the book Conquering Math Myths with Universal Design: An Inclusive Approach to Instruction K–8. If you’re looking for practical ways to connect Universal Design for Learning with strong mathematics instruction, that book is a great place to continue the conversation. Feel free to direct message me on LinkedIn or email me at ronmartiello@mathuniversallyspeaking.com if you would like to continue the conversation or make a plan for a book discussion. I am currently scheduling summer learning dates. Thanks for listening to Math, Universally Speaking.
Show Notes
Professional Development Questions
1. Welcoming Identity and Engagement: How do our current instructional practices in mathematics invite students into the learning—or unintentionally push some students out?
2. Choice of Tools and Strategies: In what ways do we provide students with meaningful choices in the tools and strategies they use to solve mathematical problems?
3. Relevance and Learning Progressions: How clearly do students understand where their current learning fits within the larger mathematical progression?
References
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. http://www.corestandards.org/Math/Practice/
Rufo, J. M., & Martiello, R. (2024). Conquering math myths with universal design: An inclusive instructional approach for grades K–8. ASCD.
Math, Universally Speaking 
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