In this conversation, Dr. Cristina Santamaría Graff and Dr. Paulo Tan speak with The Center for Family Math about how families raising children with learning differences can reshape the way we think about math learning. Their conversation explores inclusive practices, Universal Design for Learning, the importance of time, and how families can be advocates, co-creators, and champions in their children’s math journeys.
Center for Family Math: You both believe that math is a domain that, in theory, holds the potential to welcome and include all learners, especially those with learning differences. How do you define inclusive math learning? And how can families, in particular, be part of that journey?
Cristina Santamaría Graff. Let me begin with this understanding: math learning, and the way we enter into spaces that are math-centered, begins with the idea that mathematics is not neutral. It’s cultural, creative, and relational. When math is approached as a domain that honors diverse ways of knowing and doing it can become a space where disabled youth are not just accommodated, but centered. You design with them in mind from the very beginning. They’re not an afterthought. It’s not “Here’s the general curriculum,” and then, “Oh yeah, we’ll figure out what to do with that student later.” No. We’re designing with every student in mind, with difference as a starting point, not as a deficit, but as an asset.
Center for Family Math: This is the idea of Universal Design for Learning, right?
Cristina Santamaría Graff: Yes! The new Universal Design for Learning guidelines ask us to intentionally design for the margins—not to treat people as marginalized, but to begin from a place that honors and includes them. Designing for the margins means that we don’t retrofit inclusion as an afterthought. Instead, we ask from the very beginning: How can we create learning environments that offer multiple means of engagement, representation, action, and expression?
So in math this means bending dominant frameworks of what “counts” as math knowledge, and expanding that notion. It’s a commitment to redesigning the learning environment to reflect students’ lived math experiences and their cultural wealth, their body-minds. Families are central to co-creating these inclusive environments. Their math stories, narratives, histories, strategies—their funds of knowledge—can all be embedded in learning. For example, I know a family with a little girl with Down syndrome. She learned to count by going up and down the stairs every day saying numbers in Spanish and English. Or by counting and organizing her toys, putting them into a bin. That’s how she started to learn addition and subtraction.
Paulo Tan: What you shared, Cristina, really resonates with me and overlaps with much of what I was thinking. Inclusive math happens when we recognize and honor the diverse ways of knowing and doing mathematics. When we think about the domain of mathematics, we often picture a very narrow slice. School mathematics is math, but it’s not all of math. By acknowledging other ways of knowing and doing, we enrich the experience for everyone. That, to me, is inclusive math learning.
In education, we often center those closest to the norm—able-bodied, white, neurotypical students—and everyone else becomes an afterthought. But if we begin by centering those furthest from that norm, we don’t have to modify later. We don’t have to retroactively fit them in. We start at the margins. And I really love that idea. It’s something I’ve been thinking about deeply in my own work. Families are such an important part of this journey, too. Families might see math as rote skills—memorization, worksheets—and say, “Okay, let’s do that.” But they can also push back against that narrative and recognize that math is happening in their homes all the time in games, in dance, in music, in cooking, in travel. So the work is twofold: embracing and honoring those diverse ways of knowing, and then bringing that into partnerships with educators. Reframing disability, too, not as a deficit, but as a different way of being in and with math. That’s a powerful shift.
The Center for Family Math: What does meaningful family engagement in math look like, especially for children with learning differences?
Cristina Santamaría Graff: When I think about family engagement and children and youth with learning differences, I think a lot about the literature on “cripistemology”. This approach to research asks us to rethink what counts as knowledge and to center disabled ways of knowing, thinking, and telling. From this standpoint families are critical in helping to remind us how body-mind differences influence how children and youth move through and experience time and space. There is a profound awareness that progress doesn’t always come at the expected milestones. And that doesn’t make a child less human or less capable.
In schools, time is often dictated by the clock—how many minutes of speech therapy or occupational therapy a child gets, how long a math lesson lasts. But that’s artificial. It’s not how real learning happens. A child might be deeply immersed in a project and just need 10 more minutes to make it meaningful, and instead, they’re cut off. We need flexible standards, extra time, wait time, event time. It acknowledges that learning happens at different paces. As educators, we need to internalize this and reflect it in how we design learning environments—not just for disabled students, but for all students.
Paulo Tan: When you talk about time, Cristina, it reminds me that mathematicians—the people who do math—take their time. They work on problems for years. Math is not about speed. But in schools, we send the opposite message: “Don’t think! Just react.” And that’s not real mathematics. I was also thinking about how curious young children are. They ask “why” all the time. And then somewhere in school, they stop. That’s a huge loss. When we talk about meaningful math, we have to hold onto that curiosity.
Meaningful math means connecting to what students care about. When youth ask, “Why am I doing this?” that’s not resistance, that’s curiosity. It means the math feels disconnected from their lives. So if we want math to be meaningful, we need to make space for that question. We also need to bring in the systems that shape students’ realities—oppression, ableism, racism, capitalism. These are not abstract ideas. Students live them. And math can be a tool for understanding and challenging those systems.
We often talk about math as problem-solving. We shouldn’t be just solving problems we already know the answers to. We should be engaging with real problems, the ones we don’t know the answers to yet. That’s what’s meaningful for students, and that’s what moves us forward together.
Cristina Santamaría Graff: That’s so important, Paulo. Because when we think about early childhood education, we give young children permission to explore. It’s okay for them to learn through play and mistakes. But that permission vanishes once we expect a “right answer.” That’s when students stop asking questions because they feel judged. They know the teacher holds the “right” answer, and they’re just trying to perform. For many students, especially those who struggle to meet that expectation, it’s not empowering. It’s deflating. Students end up feeling like they’re not good at math—not because they aren’t capable, but because they’re being asked to prove their worth in a system that doesn’t recognize the way they learn.
The Center for Family Math: What then can families do to counteract those deflating experiences and support a stronger, more joyful relationship with math and cultivate positive math identities?
Cristina Santamaría Graff: I think the first challenge is that we need to debunk the deeply rooted assumption that children with disabilities—or disabled youth—are inherently less capable of engaging in complex mathematical thinking. Too often, there’s this idea that they need to be remediated, fixed, or corrected—that their way of thinking is wrong. Let me give you an example. I watched a documentary about an autistic girl, around 8 years old, who was given a word problem. The expectation was that she’d extract the numbers and compute the answer. But the word problem mentioned a cat, and she became fixated on the cat. She wanted to know: Who owns the cat? Where did it come from? Is someone taking care of it?
The Center for Family Math: So many kids think this way!
Cristina Santamaría Graff: I know! But the teacher grew frustrated—insisting that “wasn’t the point”—but it was the point. This child had a relational orientation to the problem. She had a cat herself and needed to know the fictional cat was okay before she could move on. If the teacher had recognized that, they could have started there, building context around what was meaningful to her and then brought in the math. That’s how we begin to foster a positive math identity: by honoring how children make sense of the world.
Families can do this, too. Learning doesn’t just happen through flashcards or worksheets—it happens in everyday life. During cooking, a parent might say, “Mijita, go get me an ounce of flour.” Then, “What’s an ounce? Let me show you.” You’re making tamales for the family—that’s fractions, quantity, scale. Or during routines: “We have to leave in 20 minutes. Can you show me what that looks like on the clock?” It’s about embedding math into real moments, and affirming children’s curiosity along the way. And when a child asks a question, take a moment. Slow down. Recognize it as a spark of interest. That can become a learning opportunity, and it’s often where math identity begins to take root.
Paulo Tan: I love everything Cristina just said. When it comes to math identity, I think one of the biggest challenges is that many families themselves carry negative math identities. They’ve been told, or have come to believe, that they’re “not good at math,” or “not math people.” And even if they don’t say it directly, those messages get passed on, explicitly or implicitly, to their children. So part of cultivating a positive math identity in kids is also about doing that work as adults. It starts with the assumption that we are all powerful mathematical knowers and doers—just in diverse ways.
If I, as a parent, feel like I’m “not good at math,” I need to ask: Why do I think that? Where did that come from? Who told me that? And what did I internalize? We have to break free from those labels before we can help our children do the same.
And then, together, we can explore math in all its forms: cooking, dancing, storytelling, building. Math is everywhere. Our job is to recognize it and name it. “Hey, this has patterns. That’s math.” “This rhythm you’re tapping—that’s math, too.” And when it comes to encouraging curiosity, I think of the “Notice and Wonder” prompts that many teachers use now: “What do you notice? What do you wonder?” Families can ask those questions, too. It’s a great way to spark math conversations that feel open-ended and empowering, not evaluative.
The Center for Family Math: What I like about these open-ended questions is that they are just such a natural part of everyday life.
Paulo Tan: That’s right. There’s a very dominant belief in special education that the only effective way to teach math to students with disabilities is through direct instruction—explicit modeling, repetition, memorization. But what does that say? It assumes these students can’t think for themselves. That they have to be told exactly what to do. That their role is to replicate—not to explore, not to reason, not to own their learning. That mindset is deeply harmful. We need to challenge that. If we truly believe that all youth are capable math thinkers—and I do—then we must reject teaching methods that deny them that opportunity. Families and educators both have a role to play in resisting deficit thinking and embracing the full humanity and brilliance of our children.
The Center for Family Math: Paulo, I was really moved by your article and your personal story, where you begin your paper writing, “As a scholar, teacher educator, and ardent advocate for inclusive education, broadly, but with a particular focus on mathematics, I have often felt powerless during individualized education program (IEP) meetings…” How can schools better support partnerships with families when it comes to IEPs and math learning goals?
Paulo Tan: I love this question. It’s been a big part of my work over the last 17 years, and it’s something I’m still learning and growing with. I really appreciate you raising it, because I think there’s so much more we can, and need to do here. There’s a real hunger for better collaboration. Families and educators often say, “This IEP just feels off” or “These goals don’t quite fit.” People sense that something’s not working, but they don’t always have the tools, resources, or routines to make it better. That’s where we have such an opportunity. The IEP is a powerful document—it’s legally binding and has real weight. And it’s supposed to be built by a team. But in practice, it’s often dominated by the special educator or case manager, with others treated more like contributors than true collaborators.
So the first thing I’d say to schools is: truly treat families, and the students themselves, as central members of the IEP team. Not just symbolically, but in actual practice. Families bring so much knowledge, insight, and lived experience. Their ways of knowing are critical to building meaningful IEPs.
And that brings us to the second thing. To collaborate meaningfully, teams need the time to co-create. You can’t do this work well in a rushed, check-the-box way. When it comes to IEP goals—especially in math—I see a lot of goals that are overly narrow. For example, I’ve seen 9th grade IEP goals that say something like, “The student will solve one-step algebraic equations.” That’s the goal for the whole year! And what does that signal? It limits what we expect and plan for. It doesn’t reflect the rich, diverse ways students engage with math. And it certainly doesn’t invite us to think beyond isolated skills toward deeper practices or real-world applications.
So, the other important idea is to try to help teams write more expansive and powerful goals. Because goals drive the IEP. If the goals are meaningful, the rest of the plan has to follow. Ideally, we’d have goals that position students to engage with math in authentic, relevant ways. My dream goal? Something like: “The student will use mathematical reasoning to explore and address issues that matter in their community.” If we write that into an IEP, if it’s in black and white, then we’re accountable to it. We have to make it happen. Now, I know the law requires IEP goals to align with standards. And yes, standards do include specific math skills, but they also include math practices, like problem-solving and reasoning. So one step is to move from focusing just on isolated skills to incorporating those broader practices. And from there, we can push toward even more meaningful, justice-oriented goals.
Cristina Santamaría Graff: Paulo your ideas resonate with me so much. In my own work I often think about storytelling, dialogue, and communal reflection, as a way to move beyond traditional school-centric models to more inclusive practices that honor the lived realities of the families involved.
Paulo Tan: I agree wholeheartedly Cristina. One thing I always do is encourage families to come to the IEP meeting with stories. Come with examples. That helps counterbalance the formal assessments and gives the team a fuller picture. Too often, when teams ask, “What are your child’s strengths?” there’s silence. Not because there aren’t strengths—but because the process hasn’t made space for families to name them in meaningful ways. The focus tends to stay on test scores, grade-level benchmarks, and deficits. But families see their children doing math all the time; through play, cooking, budgeting, storytelling. Those moments are mathematical, and they are strengths. Bringing those examples to the IEP meeting helps reframe the conversation and push back against narrow definitions of ability. Because remember, goals are supposed to be built from a student’s present level of performance. And that level is usually based on school data—standardized assessments, progress reports. But families can bring a different kind of data. They can say, “Here’s what my child can do—and here’s how they do it.” And when that’s part of the conversation, we can build IEPs and math learning goals that reflect students’ true potential.
The Center for Family Math: As we wrap up this conversation, if there were just one recommendation you’d want to offer directly to parents of children with learning differences, especially around math learning, what would it be?
Cristina Santamaría Graff: I have several! But here’s a quick list: center joy and curiosity, use everyday moments, celebrate different ways of thinking, slow down the clock, advocate with confidence, and stay connected. We’ve talked about so many ideas here today but what I’d like to really emphasize is this: what families are already doing—puzzles, patterns, art, music—are math moments. Math exists all around us, all the time. It’s about noticing when math is happening and pointing it out. Families often think they need to carve out special time to “do math,” and that can feel burdensome. But if we shift that mindset it becomes more accessible and even joyful. Imagine there are 12 objects on the table—pencils, pens, a computer, a phone. You can ask: “How can we divide these into four groups?” And suddenly you’re doing math. You’re modeling it. And you’re showing that it can happen organically, not as a separate event.
Paulo Tan: A big “plus one” to everything Cristina just shared. For me, as a parent myself, I’ve been thinking a lot about the moment we’re in right now and how vulnerable many of our children are, especially those with disabilities. There’s a lot happening, including changes in protections from the Department of Education, that directly affect our kids. So here’s my tip: have conversations with your children about what’s going on in the world, even the hard stuff. Whether they’re young or older, they care. They’re experiencing it now, and they’ll inherit it in the future. And these conversations don’t just stay at home. They can become part of what they bring into school, into math class, into IEP meetings. Math can be part of those conversations, too. Whether it’s thinking about justice, community, or simply trying to make sense of the world. They’re already wondering, already asking questions. Don’t shy away from those. Engage them. Because math isn’t separate from life, it’s woven into it.
The Center for Family Math: We couldn’t be more grateful to you both for being here with us today and sharing so generously your ideas and time.
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Dr. Paulo Tan is an Assistant Professor of Education at the University of California, Santa Cruz, where he researches the intersections of mathematics education and disability studies. A former classroom teacher and a parent of a child with a disability, Paulo brings both personal and professional experience to his work.
Dr. Cristina Santamaría Graff is an Associate Professor of Special Education at Indiana University and a longtime advocate for inclusive family engagement. Her work centers on disrupting ableist systems in education and creating space for family voices and leadership, particularly in communities of color and families of students with disabilities.
