Free the Math Gnomes

I was part of a panel discussion on the future of Waldorf education last week. The moderator asked me to identify a “myth” about Waldorf education. My go-to myth is math gnomes (first appearing here: Playing "Steiner Says").

In the 1940s, Dorothy Harrer, then a teacher at the Steiner School in New York, needed an imaginative way to teach her students math. She couldn’t turn to Europe—most, if not all, of the continental European Waldorf schools were closed during the war. She couldn’t turn to colleagues at other schools in the U.S.—there weren’t really any. She couldn’t easily turn to Steiner’s works; many of them hadn’t yet been published, let alone imported or translated. She couldn’t turn to experts at a Waldorf teacher education program; such programs didn’t exist in the U.S.

There were probably resources from Rudolf Steiner and Hermann von Baravalle—Steiner’s colleague, then in the U.S., and a mathematician—but who knows if she could put her hands on these, was aware of them, and so on?

She was a humanities person and a former public school teacher, I believe, hired and trained on-the-job at the Steiner School. (She married a European anthroposophist—William Harrer—faculty chair at the Steiner School before Henry Barnes. I knew them both slightly; I worked in their garden in New Hampshire one summer, across the road from Camp Glen Brook.)

Anyway, Mrs. Harrer dreamed up the math gnomes, wrote them down, and, eventually, published them. Here’s a link to her book: Math Lessons for Elementary Grades. I don’t recommend it. I wish it would go out of print. But if you want to see what I’m talking about, this is the source.

Her math gnomes, which have no basis in Steiner’s work, and which actually contradict his recommendations for teaching math, have become the default position for many or most Waldorf elementary school teachers.

I asked Ernst Schubert, a German Waldorf teacher and teacher educator with a doctorate in mathematics, if he had heard about them. He smiled and said, “No, vat are zees mass gnomes?” They do not exist in Germany or, probably, in other countries. Here’s an elementary math book I recommend, and Schubert has written several others: Teaching Mathematics.

After the panel discussion, a friend and former Waldorf school teacher and I chatted. He related how he had not used gnomes, he had invented a prince, instead. (I’m honestly not sure if it was a prince—I was tired, we were talking about other things, and I didn’t necessarily register it properly.)

Then, a couple of days later, I received a sincere email from a former student, now teaching second grade, wrestling with how to bring some math concepts to her students. She knows my position on the gnomes, and was wondering about possibly using fairy-tale animals.

So here’s the point, guys.

It’s not about the gnomes, the princes, the animals, the characters of whatever size or shape or background!

Math brings the immaterial, the conceptual, the spiritual into the material world. Steiner recommends beginning with a pile of mulberries. Or beans. Or pieces of paper. These are real. Fairy-tale anything—gnomes, animals, princes, whatever—are not, at least not when it comes to teaching math. (If you don’t believe in gnomes, then why on earth would you introduce them in math class? If you do believe in gnomes, why on earth would you trivialize them by asking them to teach arithmetic to young children?)

There are lots of sources, beginning with Steiner and Baravalle, and continuing through Schubert, that are intelligent, thoughtful, anthroposophical, true to math and true to the world into which we bring math, that do not personify what should really not be personified.

This is not to make anyone who used or uses gnomes, princes, or animals feel bad. We are all doing the best we can. I mean that sincerely. A former trustee with whom I worked, to avoid saying that something was bad or wrong, would jokingly say that it was “suboptimal.” When we recognize that our performance is suboptimal, then we should change. We don’t need to feel bad, we just need to do better. There’s no shame in being wrong. We’re all wrong much of the time.

There is shame, however, in rationalizing bad practices as good practices because of history or ideology. There is shame in not doing the research once a practice has been seriously called into question to decide for yourself whether or not you will continue, knowing all that you can know. There is shame in continuing stubbornly because it’s easier than to change.

Free the math gnomes.

(I’m indebted to Christine Cox, a former student at Sunbridge College, for tracking the math gnomes to their source in her unpublished 2006 MSEd thesis, In Search of Math Gnomes.)