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Cuisenaire rods

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Learning aid for mathematics

"Fraction bars" redirects here. For the bar separating the numerator and denominator of a fraction, see Fraction bar.

Cuisenaire rods illustrating the factors of ten<br>A demonstration of the first pair of amicable numbers, (220,284)<br>Cuisenaire rods are mathematics learning aids for pupils that provide an interactive, hands-on[1] way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions, and finding divisors.[2][3] In the early 1950s, Caleb Gattegno popularised this set of coloured number rods created by Georges Cuisenaire (1891–1975), a Belgian primary school teacher, who called the rods réglettes.

According to Gattegno, "Georges Cuisenaire showed in the early 1950s that pupils who had been taught traditionally, and were rated 'weak', took huge strides when they shifted to using the material. They became 'very good' at traditional arithmetic when they were allowed to manipulate the rods."[4]

History<br>[edit]

The educationalists Maria Montessori and Friedrich Fröbel had used rods to represent numbers,[5] but it was Georges Cuisenaire who introduced the rods that were to be used across the world from the 1950s onwards. In 1952, he published Les nombres en couleurs, Numbers in Color, which outlined their use. Cuisenaire, a violin player, taught music as well as arithmetic in the primary school in Thuin. He wondered why children found it easy and enjoyable to pick up a tune and yet found mathematics neither easy nor enjoyable. These comparisons with music and its representation led Cuisenaire to experiment in 1931 with a set of ten rods sawn out of wood, with lengths from 1 cm (0.4 in) to 10 cm (4 in). He painted each length of rod a different colour and began to use these in his teaching of arithmetic. The invention remained almost unknown outside the village of Thuin for about 23 years until, in April 1953, British mathematician and mathematics education specialist Caleb Gattegno was invited to see pupils using the rods in Thuin. At this point he had already founded the International Commission for the Study and Improvement of Mathematics Education (CIEAEM)[6] and the Association of Teachers of Mathematics, but this marked a turning point in his understanding:

Then, Cuisenaire took us to a table in one corner of the room where pupils were standing round a pile of colored sticks and doing sums which seemed to me to be unusually hard for children of that age. At this sight, all other impressions of the surrounding vanished, to be replaced by a growing excitement. After listening to Cuisenaire asking his first and second grade pupils questions and hearing their answers immediately and with complete self-assurance and accuracy, the excitement then turned into irrepressible enthusiasm and a sense of illumination.[7]

Gattegno named the rods "Cuisenaire rods" and began assessing and popularizing them. Seeing that the rods allowed pupils "to expand on their latent mathematical abilities in a creative and enjoyable fashion", Gattegno's pedagogy shifted radically as he began to stand back and allow pupils to take a leading role:

Example of Cuisenaire rods

"}},"i":0}}]}'/>Cuisenaire's gift of the rods led me to teach by non-interference making it necessary to watch and listen for the signs of truth that are made, but rarely recognized.[7]

While the material has found an important place in myriad teacher-centered lessons, Gattegno's student-centered practice also inspired a number of educators. The French-Canadian educator Madeleine Goutard in her 1963 Mathematics and Children, wrote:

{{cite book|last1=Goutard|first1=Madeleine|title=Mathematics and Children|date=2015|publisher=Educational Explorers Limited|location=Reading|isbn=978-0-85225-602-2|page=184|edition=2nd|url=http://shop.cuisenaire.co.uk/mathematics-and-children/|access-date=28 October 2016}}"}},"i":0}}]}'/>The teacher is not the person who teaches him what he does not know. He is the one who reveals the child to himself by making him more conscious of, and more creative with his own mind. The parents of a little girl of six who was using the Cuisenaire rods at school marveled at her knowledge and asked her: "Tell us how the teacher teaches you all this", to which the little girl replied: "The teacher teaches us nothing. We find everything out for ourselves."[8]

John Holt, in his 1964 How Children Fail, wrote:

This work has changed most of my ideas about the way to use Cuisenaire rods and other materials. It seemed to me at first that we could use them as devices for packing in recipes much faster than before, and many teachers...