Every once in a while I get the question "what is eurythmy?" How to explain?!
It's an art form but one rather different than any others - it is a spiritual work.... it is a therapeutic expression and vehicle for healing..... it helps and heals when one watches it as well as when one perfoms it... it is a way of interpreting and giving expression to the Word, to soul gesture... it is something for groups, to help people find ways of working together - and it is something an individual can practice.
But it's not something that can be "picked up" - the study of eurythmy is long and very involved. However - one can bring grace and consciousness to gesture when one works with children (or goes about ones daily life) and thereby bring a quality to one's life and homeschoool that could be said to be akin to eurythmy. If one meditates on the essence of a verse, on the letters and sounds themselves - and most importantly, on the mood one is trying to convey - then perhaps one, out of oneself, can bring something which is just as special and healing as eurythmy might be - but different.
Both eurythmy and speech formation are extremely important (and esoteric) aspects of serious teacher training and preparation - and a parent could tackle this, too. But... the amount of study, inner preparation and devotion to anthroposophy required by such study.... well, it's hard to imagine someone working on this whilst homeschooling! So I don't really even mention this aspect of Waldorf in my books. But it is something very worthwhile if one has the inclination. Do look at www.eurythmy.org for more information.