Unlocking Mathematical Thinking: How to Build a Strong Math Foundation

By Michael Tauscher

At University School of Milwaukee, mathematics is more than numbers, formulas, or solving problems the “right way.” It is about cultivating flexibility in thinking, developing curiosity about patterns, and nurturing a belief that every child can be a mathematician. To explore how these ideas come alive in Preschool and Lower School—and how they set the stage for success all the way through high school—I sat down with Laura Blanchet, USM's Academic Resource Center math teacher and Preschool and Lower School Math department chair.

Laura has been a classroom teacher and department leader, and now plays a unique role supporting children, faculty, and families. She offered insights into how USM’s math program blends research-based practices, innovative curriculum design, and a whole-child philosophy to prepare students for a lifetime of problem solving.

Building Blocks in Preschool: Number Sense, Patterns, and Play

When it comes to math learning in the earliest years, Laura noted that it is not about worksheets or memorizing facts—it is about building number sense and flexibility with thinking. “Our focus in Preschool is really to help kids become flexible with their thinking around numbers, recognizing patterns, and building their number sense,” she explained. “One of the ways we do this is through subitizing—a child’s ability to recognize numbers instantly, without having to count.” For example, if you roll a die, you don’t count each dot one by one—you simply see the number six. That skill is a powerful predictor of later math success. And it doesn’t stop there.

“Once children can subitize numbers through five," Laura continued, "they begin to group larger numbers in ways that make sense—what researchers now call 'groupitizing.' A child might see six dots not just as ‘six,’ but as two groups of three. That ability to see structure in numbers is foundational for higher math.”

And the best part? Much of this practice happens naturally through play. Games with dice, dominoes, and cards—simple activities that might look like fun and games—are actually laying critical groundwork for mathematical reasoning.

Rethinking “New Math”: Preparing for Middle School and Upper School

As children move through the Lower School, parents often notice that math looks very different from when they were students. Instead of memorizing a single algorithm, children might solve a problem four different ways. While that may feel unfamiliar to adults, Laura explained why this approach matters. “Years ago, employers valued quick computation as a top skill," she said. "Today, that ability is near the bottom of the list. What employers want now are people who can reason, collaborate, and problem-solve in flexible ways. That’s exactly what our math program prepares children to do.”

At USM, the Reveal Math curriculum—now in its fourth year—intentionally incorporates collaboration and critical thinking into each lesson. Children analyze errors in sample work, debate which solution strategies are most efficient, and are frequently asked to prove their reasoning. Teachers prompt them with questions such as:

• Can you explain your approach?
• Is there another way to solve it?
• How do you know this is always true?

“It’s beyond just solving it,” Laura emphasized. “We want them to understand why it works.” That kind of deep sense-making carries through to Middle School, when students begin tackling algebra and beyond. “In 3rd and 4th grade, when students use area models for multi-digit multiplication, they’re not just solving bigger problems. They’re also developing a structure they’ll later use to multiply algebraic expressions. That early exposure makes abstract concepts much more accessible.”

Algebra Begins Earlier Than You Think

Parents are often surprised that algebra isn’t reserved for middle school or high school—it begins as early as kindergarten. “When a 1st grader sees the equation ‘4 + ⬜ = 5,’ that’s algebra,” Laura shared. “They’re learning about the unknown and how to balance equations. Reveal Math actually introduces variables in 2nd grade, so by the time our students reach Middle School, they’re already comfortable with that kind of thinking.”

This early exposure builds confidence, which pays off later when students encounter the more abstract symbols and processes of algebra, calculus, and beyond.

A New Role: Supporting Children, Teachers, and Parents

Laura’s transition from classroom teacher to Academic Resource Center teacher has expanded her impact in meaningful ways. “I really see the role as supporting not only children, but also faculty and parents,” she said. “Sometimes I work with small groups of students who need either extra support or extra challenges. Sometimes I join a classroom to help with the language or provide an extra pair of hands. And often, I meet with teachers to make sure we have strong resources that connect directly to what we’re already doing.”

Parents Get Help, Too

“I’ve already invited families in if they’re struggling to support their child at home," Laura shared. "I’ll sit down and show them how we’re teaching a concept. Sometimes the hardest part for parents is that math doesn’t look the way they learned it. My job is to bridge that gap and reassure them that these strategies aren’t arbitrary—they’re research-based and incredibly effective.”

Most importantly, Laura wants to shift the narrative many adults carry from their own childhoods: I’m just not a math person. “That’s not even a real thing,” she insisted. “Everybody has the ability to be good at math. My role is to help children and parents believe that—and to provide the tools that make that belief a reality.”

From Answers to Thinking: Shaping Mathematical Identities

One of the biggest shifts in USM’s math program is moving away from the idea that math is about getting “the answer.” “For a long time, math was about speed and accuracy,” Laura said. “Now, it’s about reasoning, perspective, and flexibility. When a child shows their thinking in multiple ways, or when they can explain why a method works, that’s when true mathematical understanding happens.”

USM faculty celebrate this diversity of thinking. Teachers encourage children to share different strategies, recognize patterns, and value reasoning as much as results. This culture of openness builds confidence, which in turn shapes how children see themselves. “Helping kids feel like they are capable mathematicians—that excites me most,” Laura reflected. “Every child can see themselves as a problem solver if they’re given the chance to explore, explain, and connect ideas.”

Looking Ahead: Excitement for USM’s Math Journey

As department chair and resource teacher, Laura sees USM’s math program moving in an exciting direction. “What excites me most is helping kids believe in themselves, that they can do math, that they are mathematicians,” she said. “Even if their way isn’t the traditional way, they can find a way that makes sense to them. It all ties back to flexibility with numbers—building that from Preschool through 4th grade so they’re ready for everything that comes next.”

That “everything that comes next” extends well beyond USM’s walls. Whether it is analyzing data in a college course, coding in a new career, or simply making decisions in everyday life, the skills of reasoning, flexibility, and problem solving endure.

A Connected PK–12 Experience

The beauty of USM’s program is its coherence from the earliest years through graduation. Preschoolers playing with dice and dominoes are developing subitizing skills that will support algebra years later; 4th graders modeling multiplication are preparing for polynomial expressions in Middle School. By the time students reach calculus in Upper School, they aren’t just crunching numbers—they’re applying the habits of mind built from day one: curiosity, flexibility, collaboration, and confidence.

“From Preschool through 12th grade, it all connects,” Laura concluded. “The foundation we build here in Lower School isn’t just about math facts. It’s about equipping children to reason through challenges, to approach problems from different angles, and to believe in their ability to succeed.”

At USM, math is not reserved for the so-called “math kids.” Every child, beginning in Preschool, is encouraged to see themselves as a mathematician. Through play, pattern recognition, flexible problem-solving, and supportive instruction, children develop the confidence and skills they need for a lifetime of learning. As Laura put it: “Everybody does math. And everybody can do math.” That philosophy—rooted in research, embraced by faculty, and lived by children every day—makes USM’s math program not only unique, but transformative.

About Michael Tauscher:

Michael Tauscher has served as the head of Preschool and Lower School at University School of Milwaukee since 2015. Born and raised on a family-owned farm in Pulaski, Wisconsin, he holds a bachelor’s degree in elementary education and a master’s degree in educational leadership. With 24 years of experience as an educator, including 17 years as an administrator, Tauscher has worked in early childhood, elementary, and middle school settings, including teaching 3rd, 4th, and 5th grades and gaining international teaching experience in Kyoto, Japan.