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At the Waldorf School of Princeton, an innovative and research-backed approach to mathematics encourages skill-building, self-confidence, and an ability to connect math concepts to the real world. 

Good mathematicians are problem-solvers, creative thinkers, and resilient in the face of challenges. Yet many of us were taught that math is best learned through rote memorization: following a set sequence of steps to solve a problem—with a right and wrong answer at the end of the path!

“Many people think that pure math is up in the clouds, completely removed from daily life. But math is a way of thinking. It’s not about the specific problems that you’re working on. It’s about training your brain,” says Dr. Eugenia Cheng, mathematician, author, and scientist in residence at School of the Art Institute of Chicago, in an interview with the New York Times. Dr. Cheng believes that many students aren’t interested in math because they can’t see its use—or think it’s a difficult, unimaginative, and black-and-white discipline. So what can make learning math more engaging—and encourage students to see the beauty and relevance of mathematical thinking? 

At the Waldorf School of Princeton, our approach to mathematics helps children build sound foundational skills while simultaneously teaching them to bring math in their everyday lives, intuition, and thinking. Starting at the earliest ages, we teach mathematics as a creative and engaging discipline—and one in which every child is capable of excelling at and enjoying.

A Research-Backed Approach

Research consistently shows that children learn best through a multimodal, creative, and hands-on approach to mathematics. At WSP, our students don’t just learn math but experience it through play, stories, art, music, and movement—in addition to engaging in a range of hands-on projects.

Allowing students to approach math from a variety of angles is more engaging. It’s also more effective. “A growing number of studies reveal the neural underpinning of what researchers call ‘embodied learning’ or ‘multimodal learning’—using your body to encode material more deeply by drawing, singing, or dancing, for example—and provide a window into how and why the approach works so well,” write Youki Terada and Stephen Merrill in a 2025 article The Power of Multimodal Learning in Five Charts.

Through diverse activities and consistent, quality practice, students at WSP build foundational math skills while slowly developing an understanding of advanced-level math concepts that will fuel learning in high school, college, and beyond. Here’s how we do it.

Early Elementary School: Building Blocks 

Building on the rich foundation of our play-based early childhood, students at WSP begin formal mathematics instruction in 1st grade. Learning to understand and use the basic tools of math are the primary focus of early elementary school: Throughout 1st and 2nd grade, students learn to write out and identify numbers and equations, to work in depth with the four processes (addition, subtraction, multiplication, and division), and to understand foundational concepts like place value and patterns. 

Most of us remember the hours we spent memorizing the multiplication tables during early elementary school—and there is no shortcut for the task of learning the times tables! The process, however, is made more joyous and effective when teachers take an embodied approach to instruction, cementing foundational knowledge in the body and mind. For example, 1st graders at the Waldorf School of Princeton practice skip counting (“3, 6, 9, 12… 4, 8, 12, 16”) while jumping rope or while playing hand-clapping games. 

Visual, hands-on, and creative approaches to teaching further reinforce math concepts and mathematical reasoning. In 2nd grade, for example, students explore number patterns by drawing and numbering the points on decagons, decagrams, pentagons, and pentagrams. “Good mathematics teachers typically use visuals, manipulatives and motion to enhance students’ understanding of mathematical concepts,” writes Stanford University education researcher Jo Boaler in “Seeing As Understanding: The Importance of Visual Mathematics for our Brain and Learning,” a paper that underlines the importance of multisensory approaches to math.  

Importantly, even as teachers focus on essential skills in the early grades, they also connect math to bigger ideas. In fact, the very first math lesson that many Waldorf students receive explores the qualities of the number 1. Guided by their teacher, students ask: What does 1 represent, what does it describe, and how can it be a number that is both big (encompassing everything) and small (the first on the number line)? In this way, students begin their understanding of math not as a fixed science, but as a system used to describe the world.

Upper Elementary School: Math and the World

Walk into a 3rd grade classroom at WSP and you’ll often find students grouped around a desk, working together to build a sundial or measure the length of their hands. Math becomes relevant to students when abstract concepts are connected to practical experiences, and by 3rd grade, math learning takes a leap into the real world with the study of practical math, including time-telling, weight, measurements, and money. Practical mathematics continues to be woven into the 4th grade study of fractions and the 5th grade curriculum in decimals, both high visible and practical areas. 

Let’s return to the scene in 3rd grade, where students are divided into small groups to complete a math-related project. It isn’t just what our students are learning but how they are learning it that makes the difference. Active learning and problem-solving is key to achievement across disciplines, and especially in math, a subject that students must learn through doing—rather than as the passive recipients of information. Group work is particularly important in math, where children learn by observing the reasoning, mistakes, and processes used by their peers in solving problems. Why? Because making mistakes and learning from those mistakes is key to building a deeper understanding of math. “Every time a student makes a mistake in math, they grow a synapse,” writes Jo Boaler in her 2020 book Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching.

Art continues to play a large role in mathematics learning across the grades, and are fundamental to learning fractions and decimals in 4th and 5th grade. 5th graders also use tools like compass and straightedge to draw complex geometric shapes, building an understanding of shapes and spatial awareness that lays the groundwork for more complex study of geometry during middle school. 

Middle School: Problem Solving and Concepts

The typical middle schooler is curious, quick to question, and growing in their ability to think abstractly and independently. Building foundational skills and concepts remains central to our daily work in middle school math, but now students are ready to explore more complex topics in STEM (science, technology, engineering, mathematics), from lab sciences to pre-algebra and algebra. 

Real-world and experiential learning continues to play a large role in math instruction through middle school, and most especially in 6th grade, when the study of Business Math helps cement skills in fractions, decimals, percentages, estimates, and averages. 6th graders plan and execute a “math market” during their Business Math block, gaining experience about economics, currency, profit margins, and pricing. 

6th graders also dig deeper into the structure of shapes and spatial visualization through carefully planned and detailed geometric drawings, guided by their teacher. Working with tools like a compass and a straightedge, they build increasingly complex images, which lay the groundwork for the study of Euclidean geometry in 7th grade and the Platonic Solids in 8th grade.

With this rich multiyear foundation, students begin to exercise more advanced concepts in pre-algebra, algebra, Euclidean geometry, and technology. In all STEM topics, our teachers are focused on teaching the principles behind formulas and equations, emphasizing . Importantly, students continue to see math in its greater context, studying not just formulas and calculations but the history of math and mathematics thinkers. When learning about algebra, for example, students may be introduced to its origins in ancient Babylonia.

 

A Note on Mind-Set

Education researcher Carol Dweck work has shown that students with a “growth mindset”—defined as students who believe that their intelligence can be developed and they can learn anything through practice—outperform those who believe their intelligence is fixed. This is true across disciplines! At WSP, an interdisciplinary and broad-based liberal arts curriculum allows students to approach topics from multiple angles and perspectives, giving them confidence to achieve in math, science, music, writing, athletics, art—or anything they want to do.

There is no subject where attitudes matter more than in math education. At the Waldorf School of Princeton, we firmly believe that every student is capable of achieving in mathematics—an outlook that guides our teaching from the start, as well as our pedagogy. Approaching math from multiple angles, encouraging students to see mistakes as learning opportunities, and bringing math into a larger context, we help every student connect with mathematics learning.

Visit our dynamic classrooms during a tour of the Waldorf School of Princeton by scheduling a tour today.