Waldorf School at Moraine Farm | Blog

An Example of How Handwork Supports Math Learning in Waldorf Schools

By Heather Collis-Puro, Handwork Teacher

At Waldorf School at Moraine Farm, beautiful geometric drawings are often what come to mind when we think about math in sixth grade.   Many of us have purchased the notecards that Mr. Yoors’ (sixth grade) class sold at the Holiday Fair last year.  I have a hard time using them!  Working with accuracy and patience to create these incredible forms is just developing in the 12-year-old, and understanding symmetry gives a basis for grasping further mathematical concepts like algebraic equations that are taught later in middle school.  In handwork, the students work with symmetry and geometry starting with knitting in first grade, creating simple animals from knitted squares and rectangles.  In sixth grade the students make dolls, using the mathematical concepts of the Golden Ratio in order to create a symmetrical pattern for the body of the doll.  Creating a doll by hand takes accuracy and skill, and the students spend the year honing their ability to be precise.  Often the students will take a break from regular project work to take up some other craft around a holiday or vacation, and this year, the sixth graders created these star lanterns at the new year.

Winter 2016 749These lanterns are made in the form of a dodecahedron. The dodecahedron form is one of five platonic solids, each solid assigned by Plato to represent the one of elements and the universe.  Plato’s theory was a bit premature, only a first step to understanding the chaotic world of earth, air, fire and water.   Although we are not learning about these shapes in order to further our understanding about science, we are stretching the students’ imagination: we are taking a shape from an idea, to a two dimensional form and then into a three dimensional solid. This imaginative capacity is an important skill to develop.  Therefore, the lantern-making process supports further learning in math, bringing concepts into real experiences for the students.

Winter 2016 751In order to create these lanterns, each student used a compass to create a pentagon inside a circle.  This rendering was used as a template for cutting, folding and gluing 12 pentagons to create a dodecahedron.  When a light is placed inside, a precise star is revealed to us.  Is it no wonder that Plato considered the dodecahedron to be a representation of the universe?

Waldorf Alum Joins Staff of Cape Ann Orthopedic and Sports Physical Therapy Center

We are pleased to announce that Philip Kobus, a 2005 graduate of our former Cape Ann Waldorf School, has joined the team at Cape Ann Orthopedic and Sports Physical Therapy Center in Manchester, MA as their newest physical therapist. Congratulations, Philip!

After graduating in 2009 from Manchester-Essex Regional High School, Philip earned his Bachelor’s degree in Health Science Studies and his Doctorate in Physical Therapy, both from Quinnipiac University in Hamden, CT. Working under Jodi Llacera-Klein, founder and owner of the orthopedic rehab practice since 1988, Philip plans to continue developing his abilities to use advanced manual techniques as part of his treatment plans. He is highly regarded for his passion for providing the highest quality care for his patients, partnering with them to encourage their determination and steadfast commitment to their course of treatment.

Philip volunteered as an assistant boys’ basketball coach at our school during his high school years. He continued his interest in youth sports during college and graduate school as well, earning his certification as a referee from the International Association of Approved Basketball Officials (IAABO). He also worked as a Graduate Assistant and supervisor in the Quinnipiac Intramural program, and volunteered as a skiing instructor for children with physical disabilities. He was honored with a “Behind the Scenes” award from the university for his work in the Athletic Department.

Philip continues to appreciate his connection to our school, having recently participated in an Alumni Panel discussion along with other former students, including his sister, Marisa (class of 2003). He is excited about the opportunity to use his skills to serve the North Shore communities as a dedicated physical therapist.


Waldorf School at Moraine Farm’s Science in Nature Program: Our Students as Scientists

“Science is not flat knowledge, formulae, names. It is curiosity, discovering things, and asking why. . . We must always begin by asking questions, not by giving answers . . . You can teach only by creating interest in what is around you, by creating an urge to know.” —Physicist Victor Weisskopf


Second grade discovering the first Snowdrop blooming in the early spring.

In Waldorf schools, science education begins with experiencing and observing phenomena. Children are natural scientists—constantly exploring, observing, asking questions, and experimenting to understand the world around them. Young children in a Waldorf school acquire the basis for later scientific thinking through rich, sensory experiences, a variety of physical activities, and opportunities to observe and explore the natural world. Teachers share stories—fairy tales, animal fables, and nature stories—that help develop children’s imaginative relationship to the kingdoms of nature.

6,7 grade thermal heat lesson

Sixth and seventh graders exploring solar heat.

As they reach the older grades, children are beginning to develop a more objective relationship to the natural world. Students in main lesson blocks, such as botany, chemistry, and physics learn to carefully observe phenomena, and then engage in active thinking to discover order, patterns, and relationships; draw comparisons; refine observations; and experiment.

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A tree-house building project by a third grader.


The science curriculum, like all aspects of Waldorf education, works with children’s developmental stages. For example, a third grader begins to feel him/herself growing up, gaining independence, and becoming part of the outer world. The third grade science curriculum—which includes farming, building, and measuring—gives students the opportunity to learn about three essential requirements for all of humankind: how we work with nature to provide ourselves with food, clothing, and shelter. These practical activities resonate with the children as they develop and solidify students’ scientific knowledge.


In science, as in other subjects, Waldorf teachers avoid giving students abstract, lifeless concepts and definitions. Instead, they strive to help students develop concepts that can grow and change. This “phenomenological” approach to science not only develops rigorous thinking, but also helps preserve the sense of wonder and reverence for the natural world that will serve the child for a lifetime.

The Science in Nature Program at the Waldorf School at Moraine Farm

Science in Nature second grade

Second grader observing a floating vessel in a stream at Moraine Farm.

Our Science in Nature program supports our teachers and the Waldorf curriculum through engagement with the rich and diverse natural world at Moraine Farm and nearby J.C. Phillips Preserve.

As part of the program, Coleen Ryan, an experienced environmental educator, thoughtfully identifies outdoor activities that can be integrated into the curriculum and helps class teachers engage the students in these activities.  The third grade yurt visit organized by Coleen Ryan is an example of a recent Science in Nature excursion.


The Third Grade Visits a Yurt

In January, the third grade class visited a yurt at Project Adventure, a partner organization on our shared Moraine Farm property. This visit coincided with the students’ shelter block, in which they learned about and constructed different types of shelters and dwellings. Exploring the inside of the yurt enabled the students to study the internal structure and imagine where they would sleep, eat, and work—an experience that fueled their thoughts about how they would build their own shelters.

Third grade Science in Nature

Third graders reflecting on their surroundings as they gaze upon the mist above Wenham Lake.

After the yurt visit, the class headed down a trail and found a quiet spot overlooking Wenham Lake. It was an unseasonably warm day for January and there was a blanket of mist on the water. Each student sat next to a tree, taking some time to reflect in silence. During this time, they noticed what they could observe using their senses: touch, smell, hearing, and sight. Ducks swam by, crows cawed, and lichen was discovered in the minutes that passed. The group even saw a bald eagle fly across and land on a tree on the opposite side of the lake. When it was time to leave, all the students wished they had more time, and agreed they would need to return again soon.

For more information about the phenomenological approach to science in Waldorf schools, see The Teaching of Science by David Mitchell and Learning to See Life: The Goethean Approach to Science by Craig Holdrege.

By Jenny Helmick, Coleen Ryan and Miriam Silva Preas

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

Waldorf School at Moraine Farm

701 Cabot Street
Beverly, MA 01915

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