MATHEMATICAL THINKING IN WSA HANDWORK PROGRAM

A flourishing handwork program is one of the unique hallmarks of Waldorf education. Dr. Rudolf Steiner, the creator of this educational system, identified handwork as an important component, famously remarking that “knitting is cosmic thinking.” But how are we to interpret this concept, and what relevance does handwork have today? Remarkably, recent research, such as Frank R. Wilson’s The Hand: How Its Use Shapes the Brain, Language, and Human Culture, elucidates Dr. Steiner’s observation, and begins to show why working with the hands supports the development of logical and mathematical thinking.

At WSA, our handwork program covers a variety of crafting knowledge including knitting, crochet, cross stitch, hand sewing, wet felting and machine sewing. Each of these areas facilitates the development of coordination and fine motor skills through the wide variety of techniques presented and mastered as the children move through the grades. In addition, these activities support the acquisition of new math skills as they are presented by the class teachers and stimulate thinking through awakening the hands.

grade 1 knitted chickGrade 2 knitted gnome

At WSA, we begin our handwork journey in first and second grades with knitting. In The Recovery of Man in Childhood, Steiner remarks “…both boys and girls should learn to knit. This is good training for the fingers in skillfulness, but it is far more than that. The rhythmical thinking with the fingers which knitting demands grows with the child, and when he grows up the man will think more cogently and more harmoniously because the child practiced this skill just at a time when his first independent thinking was born.”

During these first two years in handwork class, we are overtly working with basic math facts and number sense. We are continually counting our stitches, and discovering what happens when we lose one or gain two. Later we learn that “ridges” are made by knitting two rows, and the children delightfully calculate that two ridges are equal to four rows. Ambitious second grade mathematicians might discover that their rainbow ball, which is made of four ridges each of six colors, has a total of 48 rows or 24 ridges. They will continue to progress through several patterns which provide questions in applied mathematics. For instance, our washcloth begins with three stitches and adds one lace stitch per row. It continues to grow until 30 stitches are reached. But how to maintain the lace pattern and make the washcloth shrink back to 3 stitches again, thus creating a serviceable square? The answer is to take away one stitch, (-1) add the lace stitch (+1) and finally take away one stitch more (-1).

As the second graders knit their way through this question, their nimble fingers are, as Steiner indicates, absorbing much more than how to make a washcloth. They are developing number sense in a practical, meaningful way, and they are learning how to think.

Conversely, sensory integration researchers have shown that children with certain arithmetic challenges show a high incidence of finger agnosia – they are unable to identify the position of their fingers in space. Knitting in Waldorf schools provides regular “rhythmical thinking with the fingers” that awakens motor control and brings the children’s awareness to their hands.

 grade 3 mug mat, pencil case and hat

After two years of knitting, the children are generally quite dexterous with their needles, and are ready to move on to another challenge. In third grade we bring crochet. Third graders are increasingly aware of themselves as individuals, and as they are stepping into the world we present a form of handwork that relies on the dominant hand. However you knit, both hands will have to work the needles to some degree. But crochet works with one hook. With that hook our third graders work to create a variety of useful everyday objects which all have a practical purpose in the real world.

In this pragmatic tone, we do not forget our math skills. Third graders have to learn to “read” their crochet. First they identify their own stitches, and then they move on to working with patterns of stitches. For instance, circular items begin with a 10 stitch round. If they are to stay circular, we must add stitches as the project grows, or it will begin to curve up and make a bowl shape quite quickly. The practical exploration of this concept resulted first in a flute case, which started with 10 stitches, grew to 20 and stayed there. As a result, the base curved up into a pouch shape, which was elongated to a tube.

Next we are ready to try a more complex sequence. Our rainbow circle mats deepen the concept of the circumference – we are trying to make a large flat piece, and so we must go from 10 stitches to 20. Soon this will not be enough, and we again work to increase the circumference by doubling our stitches. This is accomplished by identifying each stitch in the circle and placing two stitches into it on the next round. And so we have 40. From here third graders begin to work with the individual nature of their own creation, using their observation to determine when and how to add stitches in order to expand the circumference of their work evenly. This provides an opportunity for working in patterns: 2 stitches in each stitch doubles, but a pattern of increasing every other stitch will work differently, as will increasing in every third stitch. And so our third grade handwork classes continue to strengthen fine motor skills and reinforce basic math skills such as counting, addition and subtraction, but they also add number patterns and a smattering of practical geometry and fractions.

 grade 4 pincushion

Fourth grade brings greater intensity to our work with dexterity and fine motor skills. Now we take up small needles and cross stitch. Waldorf cross stitch is unique in that there are no patterns to follow except those which the children create themselves. In main lesson, the class teacher is bringing the leap of faith that is fractions. In handwork we support this work by making bookmarks and pin cushions. The bookmark consists of a canvas that is divided into two equal halves. The children are set the task of filling every hole in their canvas with a color of their choosing – but they must mirror the design exactly on both halves of the canvas. This is a real world image of the concept of “one half ”. The children rise to the challenge of creating one thing which is exactly like another. Next, they move on to pincushions, which have a midline and four quarters. Here there is nothing for it but to plot a point in space – I have put one yellow stitch four steps over from the center and two steps in – and to plot its coordinating point in three other areas. The result is a design which is mirrored horizontally, vertically and diagonally, all four sections exactly alike; the representation of one quarter.

 Grade 5 socks

Fifth grade sock knitting is perhaps the culmination of our mathematical handwork experience. The children work on three needles at once, wielding a fourth to knit in a circle. By now most Waldorf children are so dexterous that they have very little difficulty adapting to this challenge. However, it is still a magical moment when, having worked a few rows back and forth in order to begin, they divide their work onto three different needles, bend it into a triangular shape and join it together so that they are suddenly working in the round. Even more interesting is the fact that once they are knitting in the round, they no longer have to alternate knitted and purled rows in order to create a smooth surface – now knitting alone will suffice because they are only working on one side of the surface. There are so many instances of flexible thinking and fascinating cases of applied mathematics in sock making that it would be impractical to address them all here, but suffice it to say that we work with percentages of our stitches and decrease using ratios (sets of 10, 20, 10 stitches become sets of 9, 18, 9).

All of the work mentioned above is encased in a form that is enticing to the children. Items the children have created with their own hands become so precious that they inspire a sense of reverence, and rightly so. In the creation of each of these projects we find experiences in applied mathematics and flexible thinking, in addition to a world of information about color and texture to stimulate other types of thinking and knowing. In this context, knitting is truly an experience in cosmic thinking.

In the larger world, researchers are continuing to discover connections between how we use our hands and how we learn to think. Meanwhile, young knitters in Waldorf schools develop number sense and work their way through problems in applied mathematics while they labor to create toys and practical items to enjoy.

~Lisa Roggow

Handwork Teacher

This article was originally printed in the March 2012 issue of the Garden Breeze of the Waldorf School of Atlanta.

No Comments.

Leave a Reply

You must be logged in to post a comment.