A Summary of Math-Based Professional Development This Year
“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 balance activities, and other outdoor activities. The students’ math learning is further enhanced through music, an artistic expression of math; eurhythmy, in which students can experience math through beautiful movement; handwork, in which students create attractive and useful objects that incorporate mathematical concepts, precise work, and objective experiences; and German and Spanish classes, in which students reinforce important math vocabulary. In other words, math is an essential part of every Waldorf student’s life; students receive their math education through many different modalities, thereby building a strong mathematical foundation for advanced learning and thinking.
During our professional day on March 8, we discussed topics such as the importance of physical movement in math learning, issues surrounding math anxiety, and how to support different math learners. First, we brainstormed all of the ways that movement is used in a Waldorf curriculum to support all learning, and math in particular. From eurythmy to handwork, main lesson movement work and gym, outside play and exploration, it is clear that our curriculum considers healthy movement and sense experiences as paramount to strong math learning.
Next, we explored the general topic of math anxiety. As many of us know, negative feelings associated with math can have lifelong, deleterious effects on learning and how we feel about ourselves. (Although math anxiety is not very common with our unique, multi-sensory and multi-faceted math education, it does exist for some students.) We discussed the value in learning from mistakes and the importance of a positive mindset for embracing struggle and hard work in math (based on the work of psychologist Carol Dweck and Jo Boaler, professor of mathematics education at Stanford University). We reflected on how important it is to allow time and space for deep mathematical thinking that might not be speedy or completely correct, but has immense value in the learning process. In addition, we emphasized the importance of art and beauty in mathematics education, and the social impact of how math is learned in the classroom. These topics led to a discussion on how to best support different math learning styles and needs in the classroom. We plan to take this up in more depth in the future, as it is critical to supporting all students.
Finally, we shared some of our best practices in math lessons, which was an excellent opportunity to learn from and with each other. Some teachers discussed how to modify lessons for different kinds of math learners; others gave sample lessons on math topics such as teaching proportions, how to find the algebraic equation for the total number of degrees in any polygon, inspiring ways to teach place value and carrying, and tricks for mathematics calculations.
In summary, this year we have generated enthusiasm and a renewed appreciation for our math curriculum and we have begun to better articulate the gifts of a Waldorf math education. Along the way, we have identified some areas for renewal in our math education and have reiterated our commitment to continually grow as math teachers and to meet the changing needs of students while keeping true to the foundations of Waldorf education. We look forward to next year as an opportunity to deepen this work and to further strengthen our outstanding math curriculum.