Cuisenaire rods
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.
Contents
History
Cuisenaire rods were devised in the 1920s by the wife of Georges Cuisenaire, a Belgian educator.[4] Similar to how written musical notes make music visible, Cuisenaire rods were designed to make mathematics visible by using wooden rods of varying lengths and colours.[5] By 1931, the Cuisenaire rods, which were then known as réglettes,[6] had been improved and the use of Cuisenaire rods in the 1930s by Cuisenaire at one primary school in Thuin, Belgium led to others seeing that school as one where students "learned mathematics faster than most other students in the world."[5] In 1953,[5] Egyptian-born, British mathematician and education specialist Caleb Gattegno named the math devices "Cuisenaire rods" and began popularizing these visual aids since he believed the rods allowed students "to expand on their latent mathematical abilities in a creative and enjoyable fashion."[5] Gattegno's formed the Cuisenaire Company in 1954 and, by the end of the 1950s, Cuisenaire rods had been adopted by teachers in 10,000 schools in more than 100 countries.[4][7] The rods received wide use in the 1960s and 1970s.[4] However, by the 1980s, most schools which previously used Cuisenaire rods stopped[4] using them.[why?] In 2000, the United States-based company Educational Teaching Aids (ETA) acquired the 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.[5] In 2013, Lugano, Switzerland based company Primo developed Cubetto, a robot designed to teach four-year-olds computer programming similar to how five-year-olds in the 1960s were taught math using Cuisenaire rods.[8]
Overview
The educationalists Maria Montessori and Friedrich Fröbel[9] had used rods to represent numbers, but it was Cuisenaire who introduced their use to teachers across the world from the 1950s onwards. He published a book on their use in 1952 called Les nombres en couleurs. 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 Gattegno came to visit him and observe lessons in 1953. With Gattegno's help, the use of the rods for both mathematics and language teaching was developed and popularised in many countries around the world.
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 (Cuisenaire) material. They became 'very good' at traditional arithmetic when they were allowed to manipulate the rods."[10] Some countries, such as Australia, use the term "crimson" to describe the four-unit rod. [11]
| colour | Length (in centimetres) |
|---|---|
| White | 1 |
| Red | 2 |
| Light green | 3 |
| Purple[12] | 4 |
| Yellow | 5 |
| Dark green | 6 |
| Black | 7 |
| Brown | 8 |
| Blue | 9 |
| Orange | 10 |
The Silent Way
Though primarily used for mathematics, they have also become popular in language-teaching classrooms, particularly The Silent Way.[13] They can be used
- to demonstrate most grammatical structures such as prepositions of place, comparatives and superlatives, determiners, tenses, adverbs of time, manner, etc.,
- to show sentence and word stress, rising and falling intonation and word groupings,
- to create a visual model of constructs, for example the English verb tense system [14]
- 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.[15]
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.[16][17]
In 1961 Seton Pollock produced the Colour Factor system,[18] 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.
Issues
Use of color as a teaching aid disadvantages students with color deficiencies or color blindness. Males are overwhelmingly more disadvantaged by color dependencies in teaching aids. Up to 10% of males have color blindness of some kind, compared to less than 1% of females.[19]
References
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- ↑ Lua error in package.lua at line 80: module 'strict' not found.(brief overview of the history of Colour Factor)
- ↑ Lua error in package.lua at line 80: module 'strict' not found.(Colour Blindness)
Further reading
- Cuisenaire Rods in the language classroom – article by John Mullen
- Maths with Rods - 40 exercise tabs to play with parents – downloadable book with Creative Commons License
External links
- A 1961 film from the National Film Board of Canada. Caleb Gattegno conducting a demonstration lesson with Cuisenaire rods: In 3 parts on YouTube
- Online Cuisenaire rods (NumBlox Freeplay)
- The Cuisenaire Company - registered UK trademark holder, with background to Cuisenaire and Gattegno.
