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. 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.
As 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.
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)