By Sarah Addae

As I am teaching a block, I often notice all of the different things a particular subject connects to. It is actually amazing sometimes how many different connections exist – not only between subjects, but between different years and grades. I’ve been able to pull in a memory from several grades earlier with the children and point to where we are going in a particular subject.

Math lends a grounding to the social sciences like history. If you’re studying geography, for instance, and you discuss distances, temperatures, topography, and population, in the upper grades, you’re looking at how to use navigational instruments and how to use the stars to navigate. That experience of not knowing where you are but trying to orient yourself from the sky is one that can arise time and again through camping trips and wilderness experiences, too.

The curriculum relates to life and life relates to the curriculum. Children see the connections everywhere, once we start showing them they exist.

And math is enlivened by the humanities because it ties into all of these other subjects. Sometimes math is also very, very artistic; geometry, for instance, is a beautiful subject.

In 8th grade, our students not only study platonic solids; they also create them. Holding a platonic solid in hand, they see the distance from the very center of this shape to the outside, the length of an edge. They are looking at shapes that exist in natural form, naturally occurring shapes, and then exploring them.

This means lessons are not just happening somewhere mysterious “out there,” but students are working with the actual physical presence of the earth and questions that go along with them.

I’ve been asked, “Do students remember better because they have had the tangible experience?” My answer: I hope so.

So many subjects interweave. I feel we are super lucky because when we study botany, we can look at the curve of a fern and two years later, we can teach them the geometry of it, and refer back to that same curve.

Consider when we teach astronomy and history in the upper grades. Much of the history from the Middle Ages onward actually has to do with discoveries in math. For instance, the argument about whether the earth is the center of the universe or the sun is actually a math conversation.

As the children progress, the lessons become more sophisticated, and we can see the math, they learn the geometry of circles and also the geometry of ovals and ellipses, which have to do with planetary travel.

Lessons they learn in math are then applied to the understanding of the world. And it actually goes all the way back to when we study right triangles, back to the Egyptians and how they measured land. Our students learn this in 5th grade, and it comes back again in 6th grade and 7th grade and even more in 8th grade, learning how to work with right angles and the Pythagorean Theorem.

The Greeks did a lot of studio of ratio and ratio as it applies to sound. We do a really beautiful study of the ratio of string lengths, like in stringed instruments, ratios that produce an octave, a fifth, a third, a sixth. If you divide a string in half, you’re producing two octaves, for example. And our students begin their musical study in third grade with violin, and starting in fifth grade can choose another instrument as well. Everything informs everything else, creating a common thread of understanding that builds and builds on itself through the years and the grades.

We see math in the world, changing it from a purely theoretical conversation to being alive and true in the world around us.

There are so many ways we see this play out! The five petals of a flower, for instance, shows division into equal parts. We explore how we find geometry in nature, the geometry of plant structures, and examine the root structure of a six-petaled flower compared with a five-petaled one. Students draw conclusions from these lessons and start to make sense of the world.

Sometimes we think things look a certain way but then when we go to create the image, we notice the geometry is a little bit different, and see the way we might cut corners in our mind. Science has a lot of math to it. Physics has ratio and when you get to simple machines, you’re working with ratio of force applied to load lifted, so students do a lot of math in combination with the sciences.

The same thing occurs with water pressure and air pressure. We are always working through the math of how many pounds per inch, and those are pretty amazing numbers. For our students, to explore it themselves is beautiful.

I know that there is so much more, such as form drawing relating to math and architecture. In my last class, we produced the play Archimedes in 6th grade. That same year, they studied the geometry of Archimedes. Having a person connected with mathematical ideas, and experiencing how exciting it was in those times to have a new mathematical idea, was eye-opening and groundbreaking for the students.

If you can create that experience once, then as you’re going through mathematical and scientific discoveries, you have the sense of how the world can shift through a new way of understanding its truth. That’s how mathematicians and scientists make sense of the world – and it’s how Detroit Waldorf students do, as well.

Enabling our students to have an emotional connection to the subjects they study allows them to immerse fully in the subjects. A topic like math can seem so far removed from our everyday lives. In the way we interweave subjects throughout the grades, we ensure that each subject is not merely something to be good at, but truly something to really understand at a soul level and live fully. When a subject becomes part of us, we more fully enter the world. And that is the beauty of the Waldorf approach to education.

Waldorf’s Interweaving of Subjects in the Grades