Cuisenaire rods are mathematics learning aids for pupils that provide an interactive, hands-on way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions and finding divisors. 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."
History
The educationalists Maria Montessori and Friedrich Fröbel 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 (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) 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.
Gattegno named the rods "Cuisenaire rods" and began trialing 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:
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.
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:
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."
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 seem to be using them this way. But this is a great mistake. What we ought to do is use these materials to enable children to make for themselves, out of their own experience and discoveries, a solid and growing understanding of the ways in which numbers and the operations of arithmetic work. Our aim must be to build soundly, and if this means that we must build more slowly, so be it. Some things we will be able to do much earlier than we used to, fractions for example.
Gattegno formed the Cuisenaire Company in Reading, England, in 1954, and by the end of the 1950s, Cuisenaire rods had been adopted by teachers in 10,000 schools in more than a hundred countries. 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.
Rods
| 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 |
Another arrangement, common in Eastern Europe, extended by two large (> 10 cm or 4 in) sizes of rods, is the following:
| Colour | Length (in centimetres) |
|---|---|
| Wood (or Wood) | 1 |
| Pink | 2 |
| Light blue | 3 |
| Red | 4 |
| Green | 5 |
| Lilac (or Purple) | 6 |
| Yellow | 7 |
| Granet | 8 |
| Dark blue | 9 |
| Brown | 10 |
Use in mathematics teaching
The rods are used in teaching a variety of mathematical concepts, and with a wide age range of learners. Topics they are used for include:
- counting, sequences, patterns and algebraic reasoning;
- addition and subtraction (additive reasoning);
- multiplication and division (multiplicative reasoning);
- fractions, ratio and proportion;
- modular arithmetic leading to group theory.
The Silent Way
Though primarily used for mathematics, they have also become popular in language-teaching classrooms, particularly The Silent Way. 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;
- to represent physical objects: clocks, floor-plans, maps, people, animals, fruit, tools, etc., which can and has led to the creation of stories.
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, and published books on their use at around the same time as Cuisenaire and Gattegno. Her rods were different colours to Cuisenaire's, and also larger, with a 2 cm (0.8 in) unit cube rather than 1 cm (0.4 in). She produced various resources to complement the rods, such as trays to arrange the rods in, and tracks to arrange them on. Tony Wing, in producing resources for Numicon, built on many of Stern's ideas, also making trays and tracks available for use with Cuisenaire rods.
In 1961, produced the Colour Factor system, consisting of rods from lengths 1 to 12 cm (0.39 to 4.7 in). 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. A patent is registered in Pollock's name for an "Apparatus for teaching or studying mathematics". The aesthetic and numerically comprehensive Color Factor system was marketed for some years by Seton Pollock's family, before being conveyed to the educational publishing house Edward Arnold. The colors of Pollock's system were named distinctively using, for example, "scarlet" instead of "red", and "amber" instead of "orange". They are listed below.
| Colour | Length (in centimetres) |
|---|---|
| White | 1 |
| Pink | 2 |
| Light Blue | 3 |
| Scarlet | 4 |
| Yellow | 5 |
| Violet | 6 |
| Grey | 7 |
| Crimson | 8 |
| Royal Blue | 9 |
| Amber | 10 |
| Dark Grey | 11 |
| Mauve | 12 |
See also
References
- "Cuisenaire Rods Come To America". Etacuisenaire.com. Archived from the original on 2013-01-23. Retrieved 2013-10-24.
- Gregg, Simon. "How I teach using Cuisenaire rods". mathagogy.com. Archived from the original on 13 September 2014. Retrieved 22 April 2014.
- "Teaching fractions with Cuisenaire rods". Teachertech.rice.edu. Archived from the original on 2013-10-29. Retrieved 2013-10-24.
- Gattegno, Caleb. The Science of Education Part 2B: the Awareness of Mathematization. ISBN 978-0878252084.
- "Georges Cuisenaire created numbers in color". Froebel Web. Retrieved 2013-10-24.
- International Commission for the Study and Improvement of Mathematics Education (CIEAEM)
- Gattegno, Caleb (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.
- Goutard, Madeleine (2015). Mathematics and Children (2nd ed.). Reading: Educational Explorers Limited. p. 184. ISBN 978-0-85225-602-2. Retrieved 28 October 2016.
- "About Us". The Cuisenaire Company. Retrieved 28 October 2016.
- "Association of Teachers of Mathematics Honours Dr. Caleb Gattegno at Annual Conference". Associated Press. April 14, 2011. Archived from the original on June 10, 2014. Retrieved January 2, 2014 – via HighBeam Research.
- Gregg, Simon; Ollerton, Mike; Williams, Helen (2017). Cuisenaire – from Early Years to Adult. Derby: Association of Teachers of Mathematics. ISBN 978-1-898611-97-4. Retrieved 3 October 2017.
- "Beginner Silent Way exercises using Cuisenaire rods". glenys-hanson.info. Archived from the original on 2016-03-04. Retrieved 2015-04-25.
- "English Verb Tenses: a dynamic presentation using the Cuisenaire Rods". glenys-hanson.info. Archived from the original on 2016-03-16. Retrieved 2015-04-25.
- "Silent Way: rods, describing a scene (part 6 of 8)". YouTube. 2010-04-11. Archived from the original on 2021-12-12. Retrieved 2013-10-24.
- "Stern Math: A Multisensory, Manipulative-Based, Conceptual Approach". Sternmath.com. Retrieved 2016-05-24.
- "Stern Math: About the Authors". Sternmath.com. Archived from the original on 2018-04-06. Retrieved 2016-05-24.
- Wing, Tony (1 December 1996). "Working towards mental arithmetic... and (still) counting". Mathematics Teaching (157): 10–14.
- "ColorAcademy 2005 - Mathematics & Measurement". ColorAcademy. 2004. Archived from the original on 2016-04-12. Retrieved 2016-05-24.(brief overview of the history of Colour Factor)
- "Apparatus for teaching or studying mathematics". United States Patent Office. 1965. Retrieved 2020-02-05.
- Ewbank, William A. (1978). "The Use of Color for Teaching Mathematics". The Arithmetic Teacher. 26 (1). National Council of Teachers of Mathematics: 53–57. doi:10.5951/AT.26.1.0053. JSTOR 41190497.
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
- Learn Fractions with Cuisenaire Rods. Introduction Archived 2021-04-22 at the Wayback Machine
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)
- Online interactive Cuisenaire rods
- The Cuisenaire Company – registered UK trademark holder, with background to Cuisenaire and Gattegno.
- La méthode Cuisenaire – Les nombres en Couleurs – site officiel (in French)
- History of the number rods from 1806 to 2020 (in French).
Cuisenaire rods are mathematics learning aids for pupils that provide an interactive hands on way to explore mathematics and learn mathematical concepts such as the four basic arithmetical operations working with fractions and finding divisors 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 reglettes Cuisenaire rods illustrating the factors of tenA demonstration the first pair of amicable numbers 220 284 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 HistoryThe educationalists Maria Montessori and Friedrich Frobel 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 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 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 Gattegno named the rods Cuisenaire rods and began trialing 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 rodsCuisenaire 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 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 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 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 seem to be using them this way But this is a great mistake What we ought to do is use these materials to enable children to make for themselves out of their own experience and discoveries a solid and growing understanding of the ways in which numbers and the operations of arithmetic work Our aim must be to build soundly and if this means that we must build more slowly so be it Some things we will be able to do much earlier than we used to fractions for example Michael Parekowhai s Cuisenaire rods inspired installation at the Queensland Art Gallery 2015 Gattegno formed the Cuisenaire Company in Reading England in 1954 and by the end of the 1950s Cuisenaire rods had been adopted by teachers in 10 000 schools in more than a hundred countries 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 RodsCuisenaire rods in a staircase arrangementA young child using a staircase of red and green rods to investigate ways of composing the counting numbersColour Common abbreviation Length in centimetres White W 1Red R 2Light Green G 3Purple or Pink P 4Yellow Y 5Dark green D 6Black B 7Brown or Tan T 8Blue B 9Orange O 10 Another arrangement common in Eastern Europe extended by two large gt 10 cm or 4 in sizes of rods is the following Colour Length in centimetres Wood or Wood 1Pink 2Light blue 3Red 4Green 5Lilac or Purple 6Yellow 7Granet 8Dark blue 9Brown 10Use in mathematics teachingThe rods are used in teaching a variety of mathematical concepts and with a wide age range of learners Topics they are used for include counting sequences patterns and algebraic reasoning addition and subtraction additive reasoning multiplication and division multiplicative reasoning fractions ratio and proportion modular arithmetic leading to group theory The Silent WayThough primarily used for mathematics they have also become popular in language teaching classrooms particularly The Silent Way 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 to represent physical objects clocks floor plans maps people animals fruit tools etc which can and has led to the creation of stories Other coloured rodsSix year olds in class using a Cuisenaire track to explore multiplication Note the foreground paper has an error on its first line and should read 1x5 5 not 1x1 5 Trays for use with Cuisenaire 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 and published books on their use at around the same time as Cuisenaire and Gattegno Her rods were different colours to Cuisenaire s and also larger with a 2 cm 0 8 in unit cube rather than 1 cm 0 4 in She produced various resources to complement the rods such as trays to arrange the rods in and tracks to arrange them on Tony Wing in producing resources for Numicon built on many of Stern s ideas also making trays and tracks available for use with Cuisenaire rods In 1961 produced the Colour Factor system consisting of rods from lengths 1 to 12 cm 0 39 to 4 7 in 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 A patent is registered in Pollock s name for an Apparatus for teaching or studying mathematics The aesthetic and numerically comprehensive Color Factor system was marketed for some years by Seton Pollock s family before being conveyed to the educational publishing house Edward Arnold The colors of Pollock s system were named distinctively using for example scarlet instead of red and amber instead of orange They are listed below Colour Length in centimetres White 1Pink 2Light Blue 3Scarlet 4Yellow 5Violet 6Grey 7Crimson 8Royal Blue 9Amber 10Dark Grey 11Mauve 12See alsoNumber lineReferences Cuisenaire Rods Come To America Etacuisenaire com Archived from the original on 2013 01 23 Retrieved 2013 10 24 Gregg Simon How I teach using Cuisenaire rods mathagogy com Archived from the original on 13 September 2014 Retrieved 22 April 2014 Teaching fractions with Cuisenaire rods Teachertech rice edu Archived from the original on 2013 10 29 Retrieved 2013 10 24 Gattegno Caleb The Science of Education Part 2B the Awareness of Mathematization ISBN 978 0878252084 Georges Cuisenaire created numbers in color Froebel Web Retrieved 2013 10 24 International Commission for the Study and Improvement of Mathematics Education CIEAEM Gattegno Caleb 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 Goutard Madeleine 2015 Mathematics and Children 2nd ed Reading Educational Explorers Limited p 184 ISBN 978 0 85225 602 2 Retrieved 28 October 2016 About Us The Cuisenaire Company Retrieved 28 October 2016 Association of Teachers of Mathematics Honours Dr Caleb Gattegno at Annual Conference Associated Press April 14 2011 Archived from the original on June 10 2014 Retrieved January 2 2014 via HighBeam Research Gregg Simon Ollerton Mike Williams Helen 2017 Cuisenaire from Early Years to Adult Derby Association of Teachers of Mathematics ISBN 978 1 898611 97 4 Retrieved 3 October 2017 Beginner Silent Way exercises using Cuisenaire rods glenys hanson info Archived from the original on 2016 03 04 Retrieved 2015 04 25 English Verb Tenses a dynamic presentation using the Cuisenaire Rods glenys hanson info Archived from the original on 2016 03 16 Retrieved 2015 04 25 Silent Way rods describing a scene part 6 of 8 YouTube 2010 04 11 Archived from the original on 2021 12 12 Retrieved 2013 10 24 Stern Math A Multisensory Manipulative Based Conceptual Approach Sternmath com Retrieved 2016 05 24 Stern Math About the Authors Sternmath com Archived from the original on 2018 04 06 Retrieved 2016 05 24 Wing Tony 1 December 1996 Working towards mental arithmetic and still counting Mathematics Teaching 157 10 14 ColorAcademy 2005 Mathematics amp Measurement ColorAcademy 2004 Archived from the original on 2016 04 12 Retrieved 2016 05 24 brief overview of the history of Colour Factor Apparatus for teaching or studying mathematics United States Patent Office 1965 Retrieved 2020 02 05 Ewbank William A 1978 The Use of Color for Teaching Mathematics The Arithmetic Teacher 26 1 National Council of Teachers of Mathematics 53 57 doi 10 5951 AT 26 1 0053 JSTOR 41190497 Further readingCuisenaire 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 Learn Fractions with Cuisenaire Rods Introduction Archived 2021 04 22 at the Wayback MachineExternal linksWikimedia Commons has media related to Cuisenaire rods 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 Online interactive Cuisenaire rods The Cuisenaire Company registered UK trademark holder with background to Cuisenaire and Gattegno La methode Cuisenaire Les nombres en Couleurs site officiel in French History of the number rods from 1806 to 2020 in French
