By: Dr. Kristin Umland, IM CEO and Cofounder
A recent RAND survey found that the students who are the most likely to maintain interest in math are those who understand and enjoy it, feel supported, and see themselves as “math people.” It also found that nearly a third of high school students have never identified that way.
We know that both what students understand about mathematics and their beliefs about their math abilities shape how they do in school. But what comes first—mathematical understanding and skill, or building confidence in their own math abilities?
Why Early Math Experiences Matter So Much
When students make sense of math, they are more likely to be able to do math and see themselves as mathematically capable. When they believe they can do math, they are willing to tackle more challenging mathematical work. And when teachers and caregivers provide support, math achievement and confidence reinforce each other in a virtuous cycle.
The earliest mathematical experiences have the most profound impact on students’ beliefs about whether mathematics makes sense. If we want to change how students relate to math, we need early math experiences that connect to what they already know and care about.
When children build robust mathematical ideas and skills early, their later reasoning and fluency grows stronger. If they miss a key idea, the confusion can snowball, leaving gaps that grow as math becomes more complex. In fact, preschool children’s mathematical knowledge predicts their later academic success in both reading and math even more than reading skills do.
Young children are natural mathematical thinkers. Infants can tell the difference between two objects and three objects well before they know the words “two” and “three.” And by age two, they begin building on their intuitive numerical perceptions through exploring patterns, comparing objects, and counting blocks.
Early Math Is Not Simple—Even When It Looks That Way
Preschool through second grade—often referred to as early math—is sometimes dismissed as simple. But teaching it well takes significant expertise and skill.
Research underscores just how important it is for us to understand how young children really learn math. A recent meta-analysis of 39 studies found that guided play—playful exploration thoughtfully supported by an educator—was more effective than direct instruction at developing early math skills, and more effective than free play at building spatial vocabulary. If educators can channel children’s natural mathematical curiosity into playful, guided exploration that leads to mathematical competence in the early years, they set the stage for future success.
At Illustrative Mathematics, our mission is to help all learners know, use, and enjoy mathematics. Our K–12 curriculum supports problem-based instruction, giving students the chance to experience math as something they can do and make sense of. Teachers frequently tell us that this approach transforms how students see themselves.
That same vision is now thriving at scale in New York City and Los Angeles—the two largest school districts in the country. Building on that same approach, we have developed a play-based preschool curriculum that connects children’s intuitive ideas to mathematical language and symbols.
Play Is How Young Children Do Serious Math
Adults often underestimate the complexity of early math. What feels simple to us can be deep intellectual work for a four-year-old. Too often, what people picture as ‘math’—sitting at desks and completing worksheets—is not developmentally appropriate for preschoolers.
It’s a mistake to pit learning against play. Young children can play and do serious math at the same time. For young children, play often is the way they explore quantity, patterns, and relationships. By teaching math through play, educators tap into children’s natural ability to recognize numerical concepts and build formal language around them.
Most adults don’t remember what it was like before they knew that “two” is the same as “2,” which is the same as two fingers held up in the air. It can be tempting for grown-ups to move quickly from concrete examples to symbols on a page, but it takes time for young children to make the connections between concrete and abstract representations.
If students don’t have opportunities to connect mathematical notation to the ideas it represents, they start to see math as pushing symbols around on a piece of paper rather than something they’re already doing in the world.
Confidence Comes From Understanding—Not Affirmations Alone
The surest way to build mathematical confidence is through real experiences of success—and celebrating those breakthroughs.
Earlier in my career, a graduate student ran an experiment to try to influence her own students’ math success through building math identity. She asked half of her students to write “I am good at math” at the top of each test next to their name. Their test scores were no different than the half who wrote only their name. This simple experiment suggests that mathematical success doesn’t come from self-affirmation alone, but from real mathematical understanding and skill.
Conclusion
Getting early math right is essential to ensuring our children’s mathematical futures. Imagine if every child had an early math education that affirmed and built on their intuitive understanding of the world and gave them opportunities to make sense of and successfully do mathematics.
That vision is what drives me. Our goal at IM is simple: All students should know they are math people—capable of shaping their own futures and enjoying mathematics along the way.
Next Steps
The earliest math experiences shape what students can do and how they see themselves for years to come. As educators and leaders, we have an opportunity—and a responsibility—to get those experiences right.
We invite you to learn more about Illustrative Mathematics’ new Transitional Kindergarten (TK) curriculum, designed to build on children’s intuitive ideas through play, sense-making, and ultimately, success in doing mathematics.
The ideas in this piece are informed by research on early mathematics learning, math identity, and instructional practice, including the following sources:
Schwartz, H. L., Bozick, R., Diliberti, M. K., & Ohls, S. (2025). Students lose interest in math: Findings from the American Youth Panel (RR-A3988-1). RAND Corporation. https://www.rand.org/pubs/research_reports/RRA3988-1.htm l
Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. https://www.apa.org/pubs/journals/releases/dev-4361428.pdf
National Research Council. (2009). Mathematics learning in early childhood: Paths toward excellence and equity. The National Academies Press. https://www.nationalacademies.org/publications/12519
Clements, D. H., & Sarama, J. (2017). Play, mathematics, and false dichotomies. National Institute for Early Education Research. https://nieer.org/research-library/play-mathematics-false-dichotomies
Lee, G. R. (2020). The association between mathematics identity and student performance on mathematics tests: Is it a possible tool to mitigate inequality in educational outcomes? JScholarship: Johns Hopkins University. https://jscholarship.library.jhu.edu/items/df1ef098-a5c6-43f3-b36a-395243b8c3b9
Skene, K., O’Farrelly C.M., Byrne E.M, Kirby, N., Stevens, E.C., Ramchandani P.G. (2022). Can guidance during play enhance children’s learning and development in educational contexts? A systematic review and meta-analysis. National Library of Medicine. https://pubmed.ncbi.nlm.nih.gov/35018635/
Kristin Umland
IM CEO and Cofounder
Kristin Umland is a mathematician, educator, and visionary leader committed to transforming how students experience math. As CEO and cofounder of Illustrative Mathematics, she leads the organization’s vision to help all learners know, use, and enjoy mathematics.
Formerly mathematics faculty at the University of New Mexico, Kristin spent over two decades teaching math, leading K–12 initiatives, and researching how students learn. Since cofounding IM, she has served as vice president of content development, chief product officer, and president—roles through which she helped shape IM’s curricula and professional learning.
A recipient of the AMS Award for Impact on the Teaching and Learning of Mathematics and the Louise Hay Award from the Association for Women in Mathematics, Kristin remains a tireless advocate for helping all students see themselves as mathematicians.
