NO PHYSICAL FILE The mathematical question is, is this a triangle? The cultural question is, is this a roof?" Posing the questions is Dr Julia Aghilleri, head of mathematical education at Homerton College, Cambridge, who is running a pilot project in Cambridge using Poleidoblocs G. Belying their quaint name, Poleidoblocs G are smooth, brightly coloured shapes with a timeless "clutch-appeal" for children and adults alike. They are also a key piece of primary mathematical apparatus, developed in the 1930s and 1940s. Practically every school has at one time had a box on the shelf, but they have fallen out of use. Dr Aghilleri has set out to discover whether there is still a place for them in the maths curriculum.
How do children develop cognitive skills? How does language fit in with perception, the sense of shape and space, relationships with others and sensory-motor skills? And how can our ideas about this development make for fruitful teaching? According to Margaret Lowenfeld, a pioneering child psychotherapist who developed her techniques working with severely deprived and refugee children and who founded the Institute of Child Psychology to train psychotherapists, children develop "proto-systems" of thinking before they develop language.
In her great work, Play and Childhood, she outlines a therapeutic structure that involves toys, a sand tray in which to build a "world", and dolls to help the child to regain control of life experiences which may have been too much. Out of this same thinking, informed by Piaget's work on how cognition develops from practical activity ("thought in action") came the Poleidoblocs. The G set is stained in vibrant primary colours to appeal to younger children; the A set is in smooth, natural wood and has many more mathematical possibilities. The Poleidoblocs exemplify, says Therese Woodcock, a Lowenfeld expert, the Lowenfeld tenet that "sensorial experience is the precursor of learning".
Earlier studies have shown children with special needs responding particularly well to Poleidoblocs: one six-year old girl with hyperactivity and speech problems was using the blocks after just one term, able to sit still for half an hour, take pride in her work and begin to speak. Almost miraculous, were it not for Lowenfeld's raison d'etre for the blocks: that they build up the infrastructure on which the brain and personality found the skills of language and spatial organisation. The recent pilot, in one village and two city schools in Cambridgeshire, concentrated on maths, says Dr Aghilleri, but brought benefits in other areas.
Over one term, each school received half a day's introduction to Poleidoblocs from Sarah Benton, Dr Aghilleri's research assistant and a trained teacher. At the end of the term Ms Benton visited again to check on progress in maths. The blocks were very popular, aesthetically as well as mathematically and, says Dr Aghilleri, are extremely good confidence builders in a "country where people's confidence in maths is being eroded". Although there are set constructions and suggested ways in which the shapes can be fitted together, mathematical prowess increased if the children used the blocks spontaneously, as long as the teachers interacted with them. This is "free construction", as Ville Andersen, one of the first practitioners, put it, but free construction that must always end with a session of "now tell me about it". Telling about it will always, if the teacher is mathematically aware, lead to consideration of symmetry and balance, of sets and sub-sets, of equality and equivalence , of volume, of the correct names of geometric solids, of measurement and area. The spontaneous creativity which the children display in building representational edifices - the "tallest tower in the world", the "widest bridge" - feeds back into the naming and understanding of geometric relations.
A box of Poleidoblocs G contains 54 wooden blocks. There are four large green cubes, four large red cubes, four small red cubes, and four small blue cubes. There are four large yellow cuboids and four smaller green ones, with four smaller blue ones. Additionally, four large cubes are divided into quarters by cuts at right angles, the red one diagonally, the blue from the mid point of each face. There are three sizes of cylinder, in blue (thin), green (middling) and red (squat) sets of four, three small yellow cones, and three small yellow pyramids. There are no obvious relationships between the colours of any shape and the ways in which they can be used together. But all the blocks can be interrelated in many ways, from the "you can't build a cylinder on top of a cone" kinds of lesson to the "but you can balance a cuboid on top of the three cones" sort.
At Fen Drayton primary school, headteacher Frances Dodd and receptionYear 1 teacher Mooreen Carmichael have been delighted with their set of Poleidoblocs. "I only hope they don't take them away," says Mrs Dodd with a conspiratorial smile (at Pounds 45.95 a set from NES Arnold they are not cheap). Says Mrs Carmichael, "They are just totally desirable, tactile things that the children never weary of." Set up on a little red table and available for "choosing", the blocks have been pressed into service as houses, marble runs, and as a rolling device for getting stone to build pyramids ("that was when they discovered that cylinders on their sides are not good building shapes"). Children have spent a long time rolling the cylinders and cones together, learning, says Mrs Carmichael, about forces and directions when they thought they were just finding out that cones roll in a circle.
Putting the box away, as Sarah Benton says, is a privilege. Adds Mrs Carmichael, "The children love the tidiness of the box and it really develops pre-reading skills."
Poleidoblocs can be used in many different mathematical ways. Some of the tasks which Dr Aghilleri's project have suggested include sorting according to shape, colour or size (quite a difficult concept). Then the teacher can go on to suggest building with no piece of the same shape, size and colour, or with pieces in prescribed patterns of colour, shape and size. Interestingly, they have found that if children are sorting out cubes, they look for the square faces first, but if they are sorting for cylinders the overall size predominates over the face shape. The "roof shape", the quarters of cubes cut diagonally, expose a tendency to prefer laying them on their largest face. It also takes a cognitive leap to recognise the flat and tall cylinders as the same shape. When one child made a marble run, he was fascinated to find out why the cylinder did not run as a sphere (a marble) would. In Year 1, the desire for symmetry grew stronger and stronger in the children's own constructions, as did the interest in what would balance on what. Perhaps, speculate the research team, this is because the Year 1 children were able to use both hands at once.
A bit of peer competition also set in, so that when Chris (aged six) got his complex square to stand next to Daniel's there was much punching of the air and cries of "Yeah!" From Year 1 and on into Year 2 (the classes were vertically grouped) children increasingly grouped the pieces by the shape of the faces and were attracted by right-angledness.
There is no doubt that Poleidoblocs are a good tool for delivering parts of the maths curriculum, particularly those aimed at developing mathematical vocabulary, understanding shape and applying knowledge. But that is not all they have to offer. As Ruby, aged two and a half, said, grasping the nice fat blue cylinder, "Ooh, that is a lovely one." The quality of the objects, the care with which they must be stored, the thought which has gone into them, reinforces Lowenfeld's primary aim: to help children by concentrating on what they do well, and develop their abilities through achievement. In this respect her work remains as visionary today as it ever was.
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