Teaching Math in Waldorf
When and how we teach math in a Waldorf school
“We are all mathematics learners, and we can all develop active, inquiring relationships with mathematics,” writes Stanford math education researcher Jo Boaler in the research paper Prove It to Me! “When we do, and mathematics becomes a creative, open space of inquiry, mathematics learners will find that they can do anything, and their mathematical ideas and thinking can extend to the sky—and beyond!”
Boaler and her colleagues are on the forefront of math education research, which shows that with good teachers and self-confidence, all children are capable of achieving in math. Boaler's work shows that building a strong foundation in number sense—a feel for numbers and the ability to use them creatively—is key to becoming a successful math thinker, as is an ability to grasp big ideas and make connections between them.
At Marin Waldorf School, our approach to math is designed to do just that. Through a multidisciplinary, multilayered approach to math, starting at the earliest ages, students learn to see the joy and beauty in numbers, approach math work from many perspectives, and eventually build up to the conceptual ideas that fuel advanced-level math in middle school. Here’s how we do it.
Early Childhood: Encouraged to Explore
“In our preschool and kindergarten classrooms, math education is intentional, but not as directly articulated as you’d find in a traditional classroom,” explains Daniella Baker, early childhood director at Marin Waldorf School. “Math is taught through songs with numbers, counting, jump rope, marching, and other activities.”
“The approach is layered,” Ms. Daniella continues. “Activities in kindergarten lay the groundwork for math instruction in grades 1, 2, and 3, when students practice multiplication tables by skip counting on jump ropes or in songs, and begin to master math facts.”
Students are also given ample time for free play, the best way for young children to explore the world and their ability to discover and make connections on their own. In an interview with Ed Source, Gennie Gorback, president of the California Kindergarten Association, explains, “Children learn high-level, intangible concepts such as the laws of gravity, conservation of liquids/mass, mathematical concepts such as more vs. less, all through hands-on, interactive play."
"Watching the ease and joy of a preschool or kindergarten Waldorf classroom, it’s easy to assume that there is no set curriculum," says MWS middle school math teacher and math program coordinator Julia McIlroy. "Each activity, game, song, and task in which they engage has been carefully curated to develop every aspect of a child’s mind, body, and heart." (Click here to read from Ms. McIlroy on early childhood and math.)
Elementary School: Building Skills and Enthusiasm
Stories, visual exercises, mental math games, skip counting, and the use of wood manipulatives are some of the many ways our teachers help build an awareness of numbers and an enthusiasm for math in the lower grades. With a sense of wonder and play imbued in their math work, children are naturally drawn to the more complex problems they encounter as they move through the grades.
This year, our second grade teacher Ms. Terziev introduced the charming story of a mouse named Monsieur Fromage and his cheese bites to helps bring a more abstract concept like place value to life. With this imaginative story to guide their activities, 2nd graders practice working with and solving problems using increasingly large numbers. (Click here to read more about the lesson).
“My task as a second grade teacher is to ignite the fire of enthusiasm for learning. So right now my students are at play in the field of numbers, opening their eyes to the artistic beauty and wonder in math,” said then-2nd grade teacher Roland Baril in 2021, who uses a blend of artistic exercises and math drills to build a foundation for his students. Math exercises could range from skip counting while jumping rope to drawing decagons, decagrams, pentagons, and pentagrams to find the number patterns (and multiplication tables) in each. (See illustrations of student work below.)
“Good mathematics teachers typically use visuals, manipulative and motion to enhance students’ understanding of mathematical concepts, and the US national organizations for mathematics, such as the National Council for the Teaching of Mathematics (NCTM) and the Mathematical Association of America (MAA) have long advocated for the use of multiple representations in students’ learning of mathematics,” write the researchers in the Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning.
Middle School: Growth Mindset and Big Ideas
By 6th grade, students are ready for more complex and abstract mathematical thinking, and the curriculum meets their growing abilities with big ideas in math. Middle school math teacher Julia McIlroy aims to show students how mathematics is integral to all parts of life by looking at big ideas, patterns, and relationships between mathematical ideas and by grounding all subjects in experiential learning before moving to abstract principles.
"How do I develop a conceptual understanding? What I do is encourage more problem-solving and active learning. I want them to be engaged in learning, so they have confidence in themselves to go out and solve any problem that they encounter," says Ms. McIlroy.
In 7th grade, for example, students measure large circles on campus to discover the relationship between the diameter and circumference (which we know as pi), before looking at it through the lenses of geometry, ratios, and algebra.
"What I’m trying to do is bring more complex tasks, where there are no immediate right or wrong answers. This prepares them for higher education and the workplace and keeps everyone engaged,” explains Ms. McIlroy. “If you have rich tasks, the students who may be behind academically can do something, and the students who are really high-achieving can take it to the highest levels.”
Group work is also a key component to Ms. McIlroy’s teaching, requiring students to work together to solve unfamiliar problems in both concrete and abstract situations—to find patterns, make conjectures, and test those conjectures, and to understand that mathematical structures are useful as representations of phenomena in the physical world.
Interdisciplinary approaches are a hallmark of the Waldorf approach, and students are also introduced to math beyond the numbers. Creating a context can help students connect with material and understand how complex ideas evolved. In a recent algebra lesson, Ms. McIlroy introduced 7th graders to Mohammed ibn Musa al-Khwarizmi, considered the "father of algebra," was a mathematician who worked in the House of Wisdom in Baghdad during the 800s CE.
Want to learn more about our math program? Click here to read more about the lesson on the Father of Algebra, or click here to read a wonderful interview with our math program coordinator Julia McIlroy.