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Cuisenaire rods

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Cuisenaire rods used to illustrate the factors of ten

Cuisenaire rods are mathematics learning aids for students that provide a hands-on[1] elementary school 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 the Belgian primary school teacher Georges Cuisenaire (1891–1975), who called the rods réglettes.

According to Gattegno, "Georges Cuisenaire showed in the early fifties that students 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

The educationalists Maria Montessori and Friedrich Fröbel[5] had used rods to represent numbers, 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 to 10 cm. 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 students using the rods in Thuin. At this point he had already founded the International Commission for the Study and Improvement of Mathematics Education (CIEAEM) 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.[6]

Gattegno named the rods "Cuisenaire rods" and began trialing and popularizing them. Seeing that the rods allowed students "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 students to take a leading role:

A six-year-old student creates a pattern during a lesson of free play with Cuisenaire rods. Even though the student has not yet explored division or divisibility in formal math lessons, his creation shows a beginning awareness of them.

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.[6]

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

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.'[7]

Gattegno formed the Cuisenaire Company in Reading, England in 1954[8] and, by the end of the 1950s, Cuisenaire rods had been adopted by teachers in 10,000 schools in more than a hundred countries.[9] The rods received wide use in the 1960s and 1970s. In 2000, the United States-based company Educational Teaching Aids (ETA) acquired the US Cuisenaire Company and formed ETA/Cuisenaire to sell Cuisenaire rods-related material. In 2004, Cuisenaire rods were featured in an exhibition of paintings and sculptures by New Zealand artist Michael Parekowhai.

The rods

Cuisenaire rods in a staircase arrangement
Colour Common abbreviation Length
(in centimetres)
White w 1
Red r 2
Light green g 3
Purple (or pink) p 4
Yellow y 5
Dark green d 6
Black b 7
Brown (or "tan") t 8
Blue B 9
Orange O 10

The Silent Way

Though primarily used for mathematics, they have also become popular in language-teaching classrooms, particularly The Silent Way.[10] They can be used

  1. to demonstrate most grammatical structures such as prepositions of place, comparatives and superlatives, determiners, tenses, adverbs of time, manner, etc.,
  2. to show sentence and word stress, rising and falling intonation and word groupings,
  3. to create a visual model of constructs, for example the English verb tense system [11]
  4. to represent physical objects: clocks, floor-plans, maps, people, animals, fruit, tools, etc. which can lead to the creation of stories told by the students as in this video.[12]

Other coloured rods

In her first school, and in schools since then, Maria Montessori used coloured rods in the classroom to teach concepts of both mathematics and length. This is possibly the first instance of coloured rods being used in the classroom for this purpose.

Catherine Stern also devised a set of coloured rods produced by staining wood with aesthetically pleasing colours.[13][14]

In 1961 Seton Pollock produced the Colour Factor system,[15] consisting of rods from lengths 1 to 12 cm. Based on the work of Cuisenaire and Gattegno, he had invented a unified system for logically assigning a color to any number. After white (1), the primary colors red, blue and yellow are assigned to the first three primes (2, 3 and 5). Higher primes (7, 11 etc.) are associated with darkening shades of grey. The colors of non-prime numbers are obtained by mixing the colors associated with their factors – this is the key concept. The aesthetic and numerically comprehensive Color Factor system was marketed for some years by Seton's family, before being conveyed to Edward Arnold, the educational publishing house.

See also

References

  1. ^ "Cuisenaire® Rods Come To America". Etacuisenaire.com. Retrieved 2013-10-24.
  2. ^ Gregg, Simon. "How I teach using Cuisenaire rods". mathagogy.com. Retrieved 22 April 2014.
  3. ^ "Teaching fractions with Cuisenaire rods". Teachertech.rice.edu. Retrieved 2013-10-24.
  4. ^ Gattegno, Caleb. The Science of Education Part 2B: the Awareness of Mathematization. ISBN 978-0878252084.
  5. ^ Froebel Web. "Georges Cuisenaire created numbers in color". Froebelweb.org. Retrieved 2013-10-24.
  6. ^ a b Gattegno, Caeb (2011). For the Teaching of Mathematics Volume 3 (2nd ed.). Educational Solutions. pp. 173–178. ISBN 978-0-87825-337-1. Retrieved 28 October 2016.
  7. ^ Goutard, Madeleine (2015). Mathematics and Children (2nd ed.). Reading: Educational Explorers Limited. p. 184. ISBN 978-0-85225-602-2. Retrieved 28 October 2016.
  8. ^ "About Us". The Cuisenaire® Company. Retrieved 28 October 2016.
  9. ^ "Association of Teachers of Mathematics Honours Dr. Caleb Gattegno at Annual Conference", Associated Press, April 14, 2011, retrieved January 2, 2014
  10. ^ "Beginner Silent Way exercises using Cuisenaire rods". glenys-hanson.info. Retrieved 2015-04-25.
  11. ^ "English Verb Tenses: a dynamic presentation using the Cuisenaire Rods". glenys-hanson.info. Retrieved 2015-04-25.
  12. ^ "Silent Way: rods, describing a scene (part 6 of 8)". YouTube. 2010-04-11. Retrieved 2013-10-24.
  13. ^ "Stern Math: A Multisensory, Manipulative-Based, Conceptual Approach". Sternmath.com. Retrieved 2016-05-24.
  14. ^ "Stern Math: About the Authors". Sternmath.com. Retrieved 2016-05-24.
  15. ^ "ColorAcademy 2005 - Mathematics & Measurement". ColorAcademy. 2004. Retrieved 2016-05-24.(brief overview of the history of Colour Factor)

Further reading

Wikimedia Commons has media related to Cuisenaire rods.
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