Waldorf School at Moraine Farm | Blog

Exploring math education at the 1st International Waldorf Math Conference

Waldorf_Math_graphic_bannerLast October was the first International Waldorf Math Conference at the Goetheanum in Dornach, Switzerland, at which 38 countries were represented. Rebecca Rugo, seventh grade class teacher at Waldorf School at Moraine Farm, attended. Most of the participants were high school math specialists in Waldorf schools, but the issues and concerns discussed were relevant to math teachers all over the world. This first conference was a time to plant seeds for discussion and growth; time was spent listening to math teachers from around the world share their struggles and successes and beginning an ongoing dialogue regarding inspiring math teaching that meets the needs of our children today.  It is hoped that this meeting will be the inaugural conference for Waldorf math teachers.

This conference came at a time in which many educators are struggling with teaching high-quality math to students, and many of us (inside and outside of Waldorf schools) are feeling the societal pressure for students to conform to what is dictated by standardized testing and expectations of students as they prepare for high school and beyond. The stakes are higher than ever before for the students to “get ahead” and “do well” – yet many of us are becoming acutely and painfully aware of the sad cost of this unhealthy level of pressure on students. In the math realm, it often seems that this pressure trumps the time and space required for creative math explorations.

Most importantly, the conference participants noted that a main goal of Waldorf education is to work in concert with child development, bringing what is healthy and right for children at each developmental stage. This goal is of the utmost importance because it ensures maximum engagement, interest, and ability to work with the topic. For instance, in Waldorf schools we teach fractions in fourth grade when students are feeling a “fragmentation” in their lives: their “oneness” with the world is breaking apart as they become more of an individual. Because the child experiences this breaking apart in their inner soul life, fractions speak more clearly to them. They are emotionally and cognitively ready to engage in the subject, thereby enhancing their comfort with the topic.

Time was dedicated to discussions regarding the importance of curriculum guides not becoming “canonized” and dogmatic. Rather, it is important to understand that what Dr. Steiner wrote 100 years ago has much lasting value with enough “breathing room” and flexibility to meet the students before us today. In this regard, our Waldorf curriculum guides (or any other guides, for that matter) are just “snapshots” and need to be taken in the context in which they were written. The challenge is how to keep the curriculum alive and fluid enough to meet the needs of students, but also stay true to the most important tenets of Waldorf education. Cultural history has much to do with the curriculum of each country, and this needs to be periodically acknowledged and noted, while also looking ahead to what is needed in the contemporary world.

Waldorf Math FractionsAs the group explored the Waldorf math curriculum, they noted the emphasis in the 1900s on Euclidian methods of exploration. Back then, emphasis was on geometry and working from theorems to proofs. In fact, the earliest applications of algebra (thousands of years ago) were used to determine the amount of taxes that a farmer owed. These taxes were calculated on the size of their field and the crop yield. In those early days, algebra did not include the use of symbols to denote variables, but rather tax calculations were based on geometry. Only in the last few hundred years has algebra become a manipulation of numbers represented through a symbolic form with variables.

During the early emphasis on Euclidian math in Waldorf schools, what was written about algebra (as we know it today: more symbolic and abstract) was unclear and not readily available to the public. As the 20th century marched on, mathematicians all over the world became interested in symbolic algebraic explorations, and in the 1970s algebra emerged as a topic completely separate from geometry. By that time, there was a push throughout the world for all students to learn this new form of algebra. Since then, algebra has evolved as a manipulation of forms with little application.

Waldorf MathIn subsequent years, Waldorf math education has continued to evolve with the needs of the world while also staying true to the ideals of Waldorf education. This is no easy task.

And this brings us back to the importance of this world-wide conference in October which Rebecca attended. In addition to these important beginning discussions, Rebecca participated in many interesting and creative math explorations that she has been sharing with the middle school faculty. We look forward to our school’s participation in these future conferences and the strength they will bring us to persevere along the path to high quality, creative, inspiring math education that meets the needs of our children today and helps to build capacities that students will need to solve the riddles of the future. In fact, our faculty will continue these math discussions in the spring as we work toward a refreshed vision of math education at our school. Keeping the balance of conceptual understanding and skills is a monumental task, given what struggles lie at the heart of math education in the world today, but we feel we have the capacity to help lead the way and continue to deliver education that inspires and connects students with the world through beautiful, applicable, and inspiring mathematics.

By Dianne McGaunn (Eighth Grade Teacher and Math Mentor)




Why is Waldorf math education unique and powerful?

Waldorf Math Pyramid

Current seventh grade class revisiting the pyramid

Waldorf education lays the foundation for each individual to experience the internalization of mathematical thinking.  Like all Waldorf curricula math lessons are carefully planned to meet the needs of the developing child. Math lessons are brought through many subjects and modalities, while mindfully educating and experiencing math through the hands, heart and head.  Waldorf math education involves movement, music, rhythm, art, form drawing, language, creativity, curiosity and wonder, creating a truly multi-sensory approach to mathematics. As a result, Waldorf students acquire a deep mathematical understanding that they carry throughout their lives.

Below is a brief overview of how math progresses through the grades.

Math Through the Grades

The rhythm of the day, of nursery rhymes and poems, and the social considerations of how many friends need a place setting or a swing are all integral parts of the youngest child’s day in a Waldorf early childhood classroom.

Waldorf First Grade Math Story

Grade 1 – The story of King Plus, Queen Minus, Magician Multiply and Doctor Divide

In first grade, students learn that numbers exist everywhere in the world, especially in nature. Through this holistic approach to learning math, the special significance of the number one is discovered (as in one universe, one human being) and students explore the numbers that are found within each being (each person has two eyes and two ears, four limbs, and so on). In this way, the mystery of numbers is introduced and is further explored through the grades. In first grade, the four math processes are taught simultaneously because they reinforce each other (multiplication is fast addition, division is fast subtraction) and while learning math facts we begin to develop a general number sense which is so important for subsequent work in mathematics.

Grade 2 - Counting star for the four table

Grade 2 – Counting star for the four table

In third grade, practical math activities such as measuring, understanding the calendar, and furthering comfort with the four mathematical operations (addition, subtraction, multiplication and division) are the bulk of the math program.

In fourth grade, working with fractions is a perfect topic because the children are experiencing an “existential fragmentation” of their world as they begin to separate from their parents and the journey toward puberty begins.

Waldorf Math fraction tree

Grade 4 – The fraction tree

In fifth grade, comfort with decimals as additional expressions of fractions is a central math theme.

Sixth grade is a time to deepen the math learned thus far, and be introduced to the concepts of business math and more formal geometry lessons.

In seventh grade, learning about ratios (relationships of one number to another) complements the child’s experience of working through relationships between themselves and the world. During the seventh grade year, we continue with geometry studies and add formal algebra into the curriculum (although algebraic thinking has been part of the math work through all of the grades).

The culminating year, eighth grade, is dedicated to deepening the algebra work, geometry of solids, and might also include work with number bases and loci, among other math topics.

Along the way, math terminology and general concepts are also taught through the languages of German and Spanish, and all of the math work is beautifully complemented by many handwork activities and eurhythmy designed to bring mathematical understanding into the will.

By Dianne McGaunn, 8th Grade Math Teacher and Math Mentor

Pioneers in Soccer


This fall the Waldorf School at Moraine Farm team fielded its first ever soccer team. Calling themselves “The Pioneers,” they opened the season with a tie as they found their footing and began to gel as a team. It didn’t take long, as experienced and new players alike quickly became a cohesive unit. The team finished strong, winning its last 5 games for an undefeated (5-0-1) inaugural season.

Players, coaches and parents gathered after the final game last week to celebrate the team’s success and to thank the dedicated efforts of coaches Daniel Foster, Luciano Sappia and Christine Garcia-Akers. Coach Foster praised all of the players for their courage and for the support they showed one another throughout the season. Captain Quinton Dooley, speaking for himself and his teammates, closed the evening by noting how grateful he was finally to have a soccer team. Everyone is looking forward to building on these successes next fall!  -J. Cosco

An Inspiring Visit

Shabana and Susan

Shabana Basij-Rasikh, founder of SOLA, with Susan Viets, Administrator at Waldorf School at Moraine Farm.

The  7th and 8th grades were visited today by Shabana Basij-Rasikh.  Shabana shared that as a young girl in Kabul, Afghanistan, her parents, strong advocates for education for girls, dressed her as a boy in order for her to walk freely in the streets and secretly attend a school for girls. This was at great risk of death by the Taliban, which controlled the city. Shabana spoke to the students about her passion for education: “When you educate girls, you educate boys, too. For those girls become mothers who then have sons and share with them a passion for learning for all.”  She spoke passionately about students as leaders and told our students that they need to know that their work can change the world.

Eventually, Shabana came to the United States to attend Middlebury College. On returning to Afghanistan,  she founded the SOLA (School of Leadership Afghanistan), a boarding school for girls.  Students are taught in English and many find sponsorships to help continue their education in Europe and the United States.

We were happy to host Shabana today and her message served as an incredible reminder of the freedoms we enjoy in the United States — both in terms of educational opportunities and opportunities for girls and women.  She encouraged the students to travel and begin to get a perspective on their own lives by building their relationship to the whole world, and not just their town or country.

The following shares some of the stories from the young women at SOLA –


Letter from Our New Administrator


Dear Parents,

Welcome to the beauty of early September and all of the possibilities the beginning of a new school year holds. My daughter Maren, in fourth grade, and I are filled with joy at joining the Waldorf School at Moraine Farm community.

Having worked for non-profit educational organizations for more than 25 years I have come to realize that Waldorf Education worldwide is the healthiest model of education available today. At its highest striving, Waldorf Education serves as a vehicle for social change in our challenging world. On a regional level, it is a model for other school institutions in integrated curriculum and relationship building. And finally on a personal level, the teachers, staff, and parents who support Waldorf education are some of the most thoughtful, loving, and insightful people I have ever met, and we have consciously come together to raise our children as creative and engaged participants in life.

I know that even within such awareness there are struggles and challenges within communities; this is the wonderful tension of a growing and evolving group of people. As the new administrator, I look forward to facing these challenges with openness, honesty, and the willingness of heart to listen to other points of view. I know that amazing things can happen. In the few short weeks I have been at Moraine Farm I already feel an energy of positive potential all around. I feel blessed to have been invited to help support the next stage of development of this lovely school and school community.

I look forward to hearing from every one of you, your hopes and dreams, for your children and for the school.


Susan Viets



Waldorf School at Moraine Farm

701 Cabot Street
Beverly, MA 01915

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