Our Teachers Dive Deep into Our Math Curriculum

A Summary of Math-Based Professional Development This Year By Dianne McGaunn, Math Teacher and Math Mentor “We possess mathematical truths through the fact that we ourselves behave mathematically in the world. We walk, we stand, and so forth; we describe certain lines on the earth. Through this will relationship to the external world we actually receive the inner perception of mathematics. – Rudolf Steiner This year, teachers have dedicated several pedagogical meetings to exploring our math curriculum more deeply. Some of our time has been working with Rudolf Steiner’s indications (see above) and their applications to our math teaching. As a result of our work together, we are developing a clearer understanding of the richness and power of our math curriculum and we can better communicate this to our community and beyond. In our math discussions in the fall and early spring, it became clear that mathematical thinking in Waldorf education is cultivated from the earliest stages and through many different experiences. In the early childhood programs, opportunities to experience the world and its mathematical truths in an age-appropriate way abound. For example, if four students want to use the swings but there are not enough swings for all of the students to use at once, a teacher might ask: how many students will need to wait if there are four students but two swings? In addition, balancing on objects and experiencing the physics of the world through running, jumping, balancing and playing are all mathematical experiences that are integral to the youngest students’ day. In the grades, we experience math in our classroom work, including measurement, movement and...

Frederick Tudor the Ice King: A Hike With the Fourth Grade

As part of the fourth grade’s local geography block we ventured out to learn about Frederick Tudor, who in the mid 1800s was nicknamed the “Ice King.” He became known for revolutionizing the ice selling industry. Prior to his endeavors, the average American would not even think of enjoying a glass of ice water.  Because of him and his persistence, ice from Wenham Lake was favored by people around the world, as far as Cuba and India and even by Queen Victoria herself. It was not an easy path for Frederick; there were many preliminary trips where his shipments arrived melted and resulted in financial loss. Frederick Tudor learned from such experiences and over time advanced the tools and methods used to both harvest and ship ice. Our hike began with the students working together to create a grid of 2-foot by 2-foot squares. We later referred to this grid when looking out on Wenham Lake and imagining how the ice was cut into a grid of the same size ice blocks. As we hiked towards the lake, navigating through many intersections and trails towards the JC Phillips Preserve, the Ice King’s story was shared in parts. The story was interspersed with many riddles told by the students. For example, if there are two fathers and two sons who went fishing, and each of them caught a fish, how is it possible that only three fish were caught? Don’t know? Ask a fourth grader—they will be happy to tell you! Near the lake we came upon a recently fallen tree that had been freshly sawed. Upon further investigation, it...

Inside and Outside Our Classrooms

A Curriculum Update Twice a year our teachers share a brief summary of what’s been happening inside their classrooms. As you read through these curriculum updates, you can sense how a Waldorf education actively engages the body, mind, and will, allowing the students to grow and unfold their inner capabilities. Nursery By Caroline Mercier We are now in the thick of our rain and mud season.  However, the children come well prepared, covered from head to toe in their waterproof gear. There are puddles to splash in; mud-cakes, muffins, and stews to make; holes to be dug; hills to climb; horses to care for; wagons to pull; and buckets of water and mud to be carted here, there, and everywhere! This week, we left buckets and wheelbarrows under the dripping roof to catch the rain drops in the morning, and it is was such fun to come back after lunch to see how full they got. Every morning, we share a sunflower seed and apple snack at our picnic table, and every day the chickadees gather up above, waiting for us to finish. When we are done and sometimes before we are done, these sweet little birds come and pick up the seeds that have dropped, while we quietly watch. But one day, something very special happened… After many patient days of trying, one little bird was brave enough to eat out of our hands. What a joyful surprise that was. Our nature walks are getting longer as the children grow and their stamina increases. One of our latest walks took us through the “magic forest” to the babbling...

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. These 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,...

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 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. 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.   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...

Exploring math education at the 1st International Waldorf Math Conference

Last 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....