An ancient Japanese craft can be used to make fractions easier to understand and use creatively. Marjorie Gorman explains.
ave you ever thought of teaching fractions by using the ancient Japanese craft of temari? Dr Tony Gardiner, in the recent TES article "For the love of maths" (September 8) lists fractions as "one of the cornerstones of maths". Whether you agree with him or not, one thing is certain: if you ask a group of adults what they remembered most about maths lessons it is quite likely to be fractions - because they could not make any sense of them. "Fractions," says Dr Gardiner, are downplayed for the wrong reasons - "because we no longer have imperial measures".
I have found that introducing temari to the classroom not only provides an opportunity to work on fractions, but also to use some of those numbers in the duodecimal system which are so useful when engaged in a practical activity.
Temari is described as "embroidery on the surface of a ball". It is a very old Japanese craft, recently revived by a group of enthusiasts. The words "te mari" means "hand ball". The mari was made with anything available - a bunch of herbs, or scraps of cloth or leather which were bound together tightly to make a ball. It was then decorated with embroidery and used as a plaything.
Originally, the craft of temari was confined to the leisured classes. Female servants of the Samurai class would compete with each other to embroider the most beautiful designs on the balls using expensive silk thread.
By the 19th century, cotton was more readily available and the craft became more widely practised. Thrifty women used old clothes and scraps to create attractive toys for their daughters. These poorer people even managed to use threads, too short for sewing, by knotting them together and wrapping them around the ball to create a pattern.
Fractions were not included in the original aims of the work I did with junior classes on temari. I could see there was some potential for mathematics but it was only after working with several Year 4, Year 5 and Year 6 classes that I realised how many of the pupils were coming to an understanding of fractions as they divided the ball into a grid to hold the decorative stitches. In fact, it was very encouraging to see the look of enlightenment on their faces as they said "Got it!" In the Number section of the new mathematics Order, key stage 2 pupils are required "to be taught to understand and use, in context, fractions and percentages to estimate, describe and compare proportions of a whole". This seems to me to be an opening for teachers to introduce work such temari while at the same time meeting the requirements of mathematics curriculum. For the past few years there has been an understandable tendency to concentrate on the separate subject areas.
Whenever I have introduced temari I have been impressed by the interest and enthusiasm of the pupils as well as the mathematical language that was used in a meaningful context. Boys and girls produced attractive, if not always accurate examples even at their first attempt. With judicious use of colour and metallic thread some very simple designs can be very effective. When all the mari are collected together they can provide quite a stunning display.
The pupils appreciated being able to re-cycle materials and produce something beautiful from material that would otherwise be thrown away. We used a variety of materials for the cores including PE balls, polystyrene balls, toy stuffing and scraps of quilting fabric as well as balls of wool and old nylon tights. If you want to have a go below is a brief description of the way of working.
Giving pupils the opportunity to make temari not only provides opportunities to study fractions in an interesting context, it can also enhance other mathematical experience. For example, from the Shape, Space and Measures at key stage 2: Pupils should be given opportunities to: o Extend their practical experience using a wide range of materials o consider a wide range of patterns, including some drawn from different cultural traditions o apply their measuring skills in a range of purposeful contexts.
Although the new geography Order omits Japan from the countries which can be used as a contrasting locality, any information about other cultures can be useful. Temari work would certainly meet the requirements of the Design and Technology Order for working with a range of materials and components and applying "knowledge and understanding from the programmes of study of other subjects, where appropriate, including art, mathematics and science".
The Art programme of study at key stage 2 says: o Pupils should be taught about visual and, where appropriate, tactile elements including the use of pattern and texture in designing and making.
o Pupils should be introduced to the work of artists, craftspeople and designers from a variety of cultures, Western and non-Western.
So I can recommend temari, not only for helping pupils in their understanding of fractions in mathematics but as an activity which meets several requirements of the programmes of study for several subject areas. It raises awareness of the need to conserve resources and it is easy to get good results early on.
Why not try it for yourself? You do not need to be an expert embroiderer to support you class, but I would recommend some practice of the basic techniques before introducing the idea. Do not panic if sometimes the cotton threads on the mari begin to shift while the gold thread is being used to create the guidelines.
Thread the loose ends through the eye of a needle and stick them back into the surface layer of wool. Pupils should be reminded to wind the wool and cotton or polyester thread very tightly and to handle the mari with care while marking out the guidelines. Many minor faults are completely hidden when the embroidery is complete.
Materials required Materials for the core: Polystyrene balls, PE plastic balls, old tights or toy stuffing in plastic bags. Each has its advantages and disadvantages. If tights are used, take care to roll the ball against a table top to make it as spherical as possible.
Wool: yarn up to four-ply.
Sewing thread: this can be cotton or polyester. You will need sufficient to wind on the ball to completely cover it. It is possible to join threads, but the colours must be identical. Local markets are often a good source for large, cheap reels.
Gold or silver thread: Gutermanns,Goldfingering, Twilleys or any other metallic threads which are suitable for hand sewing.
A selection of embroidery threads in bright colours: Coton Perle for the larger balls and Coton Broder for the smaller balls.
There are some shiny yarns which would seem an ideal choice as they are generally in bright colours, but since they slip easily, they are difficult to work with.
Stranded threads are not recommended since they tend to twist in use.
Glass headed pins: these will not disappear into the ball. Several colours are needed. Mapping pins are good.
Needles: long sharp needles.
Paper: a strip of paper, 10 mm wide and long enough to go round the ball.
o More detailed instructions can be found in: The Craft of Temari by Mary Wood. Published by Search Press Tunbridge Wells.
o More advanced mathemati-cians might like to link the work with: Spherical Models by Magnus J Wenninger. Published by Cambridge University Press o Tarquin Publications from Diss in Norfolk has produced a poster of several of the designs from the book by Mary Wood, which they also stock Marjorie Gorman is an advisory teacher in Wakefield
Temari--A brief summary of the method Stage 1 - Covering the core Cover the core with a tight, even layer of fine wool followed by a layer of matching polyester thread. Secure the ends by weaving them into the layers with a darning needle.
Stage 2 - Dividing the ball To mark out a ball divided into four: Using a headed pin, secure the paper tape, close to one end, at any point on the mari. This is called the north pole. (diagrame 1) Measure the circumference accurately by taking the tape round the mari to meet back at the north pole. Fold the trip where it meets the pin.
Make another fold halfway along the strip by taking the fold back to the north pole. Mark the south pole by a pin of another colour. (diagram 3) Bend the tape back again so that it is now divided into four bends. Using the "quarter" tape as a measure place pins at intervals round the middle of the mari between the poles - this is the equator. (diagram 4) Carefully detach the tape and cut notches at each fold line. If divisions other than four are required then the tape must be divided equally and notches cut accordingly. (diagram 5)
Hold the tape round the equator and move the (diagram 6) Stage 3 - Putting in the Guidelines Gold or silver thread is used to mark the guidelines which can be part of the final pattern.Thread a darning needle with a good long length of chosen thread. Insert a needle into the mari 25 to 50 mm away from the polar point and come up at the polar point pulling thread through until it just disappears into the ball. Take the thread round to the opposite pole via the equator, picking up a tiny amount of base thread at the equator pin to anchor the thread.(diagram 7)
Do just the same round the other side. From the polar point push the needle through to any equator pin and take the thread round the equator in the same way making eight equal divisions. Remove all the pins.(diagram 8) Stage four - the decorative pattern The simplest decoration is by "wrapping" embroidery threads along side the lines marked by the metallic threads. (diagram 9) More complex divisions can produce designs in which the mari is completely covered by embroidery. The mari can be divided as many times as required. Square and interlocking triangle designs use division into four, the hexagon six, the pentagon ten. The traditional chrysanthemum design can have as many as thirty two, but that would be rather advanced for 10 and 11-year-olds.(diagram 10)
Other designs use a herringbone stitch which is very versatile and can produce a variety of effects. A darning needle is used for the embroidery and all ends are lost inside the base for starting and finishing.(diagram 11) A Simple herringbone stitch (diagrame 12)