multiplied crazy

this seems to be a very confusing way of teaching the multiplication table. Please do watch the entire film even if it’s boring and repetitive, because the more it goes on, the more confusing it feels. Why the geometric shapes? As a waldorf student, I recognize all the star-shaped thingies created within circles (often creatively coloured), and I think maybe there were some maths lessons to it, but can’t remember this multiplication stuff at all. What’s the point? Can someone explain this? (Thanks to reader who posted the link.)

19 thoughts on “multiplied crazy

  1. *puts his hand up* Please Miss, I know! Steiner teachers fetishize geometry. It’s often a main lesson on its own, separate from maths. It’s used everywhere else it possibly can be, throughout the curriculum. The human body, the solar system and plants are illustrated using geometrical ratios. Unusually, Chladni patterns are one of the first things studied in physics. The latter, though beautiful, are unfortunately historically linked with the distinctly kooky alt. medicine of cymatic therapy.

    Surely it’s no coincidence that Steiner told us the study of geometry allows us to improve our perception of the spiritual realm? Ref: “The Fourth Dimension: Sacred Geometry, Alchemy, and Mathematics”.

  2. This a neat way of presenting base 10 – think of it as the patterns being created by the multiplication rather than the other way around. Either way, it shows the relationships between the base of a number system and pattern produced by adding incrementally to a circle marked with the base digits. (this works regardless of Steiner and pastel-coloured chalk, by the way). I had a (non-Steiner as far as I know) maths teacher called Mr. Holt who used the same method in the 1960s. He had a German accent so perhaps it is a German or N. European method of teaching base 10 tables (not that we learned any other tables)?

  3. Mark — a gold star for you!! It’s definitely so. Which explains the quaint attachment many anthroposophists have to geometry. Bear in mind that in eurythmy, geometrical patterns reappear for the children; you eurythmize these shapes and forms.

    There was a lot of drawing them; circles with stars, intersecting circles making big patterns, et c. We even sew these kinds of patterns — with threads, on cardboard. I never had a huge problem with this, to a certain degree it can be entertaining (which is more than you can say for many activities in waldorf). And some people are very skilled at making beautiful… I’d almost call it objects of art. I’m quite uncertain as to what it taught us though. Or if it taught us something that justified the amount of time spent on this activity.

    Interestingly, Steiner reports in his autobiography (which should be taken with a grain of salt, as it was written to ‘explain’ his later career, but I do think there’s truth to this particular statement) that ‘through geometry, I understood for the first time what joy meant.’ (My haphazard translation from the swedish edition.) It gave him, he writes, satisfaction and consolation.

    Nick — what you write makes a lot of sense: maybe this was a method used more generally than I though, and perhaps it was even more prevalent in germany. It’s understandable why this particular method would appeal to waldorf teachers (anthroposophists), though, not only because it might be german! If I remember I’ll ask my father if he was taught multiplication this way. Actually, I’ll ask — anyone else who’s reading this who was taught that way?

  4. The kids have to remember 5 different patterns and which way to go round. Even the “teacher” struggles and says “two times six is thirty-twelve” you can hear it for yourselves around 2.30 (ish)

  5. and my guess is naturally he’ll have been mentally working out the 6x table whilst another part of his brain was trying to work patterns and by pointing to the 6 and the 6x is in the centre, his brain will have automatically remembered 36!

  6. I have to say I thought it was pretty interesting. As a way to actually teach the mult. tables, I can’t see how it would work, but it was pretty entertaining to me, as a person who, well, already knows them. Of course the Waldorf teacher will take any opportunity to draw a star on the chalkboard (you know, cosmic).

  7. So what they do is making a circle out of the number line which creates these geometric shapes.

    Here are 103 videos about “waldorf math” some with variants of this exercise:

    And finally a pdf describing the waldorf approach to math in grades 1-2

    I found this useful in trying to understand why teachers can become interested in waldorf pedagogy. They are absolutely on to something important! Which has to do with how you “divide” and order knowledge. Which can make learning more or less meaningless. Or in other words with reductionism/holism. But of course the author can’t refrain from making a weird mess of it in the end by adding some extra anthro stuff. Like connecting addition, division etc. to the four temperaments

    An interesting question is if and how e.g. the idea that mathematics might be connected to rhythm and body experiences could be translated to specific teacher-led activities. I think it is difficult or impossible without recreating the very division you set out to overcome. The result; boring, meaningless exercises. But I’m sure there are other ways …

  8. Oh dear, 103 videos!

    I found this one on youtube:

    ‘Like connecting addition, division etc. to the four temperaments’

    Haha! We had angels. Not sure what they were doing. Or perhaps they were fairies.

    There’s lots of woo in that document (I’ll shorten your link, Ulf, usually it line-breaks automatically, but that one’s running all over the page…). Already on the early pages I find this:

    ‘Academic learning demands memory and a formal way of thinking, using up life forces that are needed to grow, develop and refine the physical body. The results of expecting academic learning before about 7 years of age are a weakening of the physical body, and later in life more easily getting serious diseases, such as nervous disorders. It can also cause ‘burn-out’, even in young children.

    The child’s body gives us signs of when the life forces have completed their work.’

    I feel like singing the little songs/verses on p 31.

    ‘5 little ducks, swimming in a pond
    Round and round and far away
    Mother duck said Quack, Quack, Quack
    And 4 little ducks came swimming back’

  9. Thanks for taking care of my monster link ;-). Yes I saw the usual “cognophobic” stuff too, but I tried to read it from the perspective of a young teacher with romantic and artistic sensibilities, dissatisfied with mainstream education. The Fear of Thinking is at least sort of comprehensible (assuming you are not told about the occult reasons behind it). Now that I think of it, the idea that children with different temperaments would prefer different ways of counting might also sound attractive. Like having access to a “Higher Knowledge”. with a sort of “symmetrical beauty”.

    The mystic waldorf math link was fun and scary!

    Does anyone here remember a children’s book (might be by Michael Ende) where one of the characters (probably on a sea journey) is becoming more and more crazy while getting lost in numerology?

  10. Yes, and it provides a great story that makes sense — internally and without critical thinking engaged…!

    ha! Anthroposophists like Michael Ende! (Who was a waldorf school proponent. — No, now looking it up on wiki — not to be believed, but ok, this time… — he was a former waldorf student.) I have only read Momo, but should probably read the Neverending Story. Don’t know which book you’re thinking of though!

  11. Haha! I missed that.

    At least this teacher knows most of the multiplication tables (with or without the complicated circle), but it is my impression that some of them don’t…

  12. Alicia,because there is no one to one correspondence/concrete tools, this seems like a very abstract and confusing way to teach children. Plus, is that a magic wand he is pointing with?

  13. In a Steiner school by the time they get to anything like this the children will have already learnt the multiplication tables by rote using rhythmic clapping and stamping as an aid to memory.

    This lesson is about the PATTERN in number not about learning multiplication.

  14. I showed the maths lesson to my husband a maths graduate, and have rarely seen him looking so confused…
    Guess he is not so good at patterns.

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