"Children possess a far greater capacity for mathematics than has been granted them hitherto. As soon as a favourable pedagogical climate is produced what today seems extraordinary will be done simply as a matter of course."
Madeleine Goutard 'Mathematics and Children' 1964
George Cuisenaire was perplexed.
Why did children find it so difficult to learn math?
His solution to the problem was to invent the most complete math model ever devised. It consisted of a set of coloured cuboids of wood ranging in size from a 1cm cube to a 10cm cuboid.
In 1953 Caleb Gattegno met Belgian schoolteacher Cuisenaire and immediately recognized the potential of the rods to allow learners to investigate mathematics for themselves at every level of development.
He realised that the rods provided teachers with a means for making the lesson a personal investigation of mathematics for every child. His subsequent work with children convinced him and others wherever he went that all children have a latent ability which, in classroom situations where the rods are used and where teaching is learner centred, can yield truly remarkable results.
So why aren’t the rods used in schools today?
The answer is, in a percentage of schools they probably are. Unfortunately more often than not they are employed in piece-meal fashion to introduce concepts like fractions in isolation. The true potential of the rods is rarely recognised. It’s like owning a Porsche and never getting it out of second gear – not that I would know personally!
Unlike computers, Cuisenaire rods never crash, don't get overtaken by new technology and are truly interactive. What's more Cuisenaire rods are virtually indestructible. Their genius is in their simplicity. Like a piano, once the basics have been mastered it is possible to create an infinite variety of shapes, patterns and equations.
There are many excellent publications available on how to use the rods unfortunately most focus on a specific aspect of math and those that do not are not really very reader friendly and get ignored.
Unhappy with the standard of math teaching in my school I challenged my teachers to change the way they taught. They responded with a challenge of their own, “Show us how?” For years I immersed myself in research and development of a math programme that would ensure children acquired not only the concepts of math but a love for the subject.
One of my most treasured memories was seeing a mother, convinced she was a lost cause when it came to maths, almost in tears as she realised that she was actually ‘good at maths’ having undergone a six week workshop based on the program. Her confidence levels rose and shortly afterwards she enrolled in college and has since obtained a degree.
When I first asked her what she thought of when I said the word 'maths' she replied “Clouds”. I immediately knew what she meant. Most of my maths lessons were spent gazing wistfully out of the classroom window at the passing clouds blissfully ignorant of what the maths teacher was droning on about in the distance somewhere.
This approach to maths inevitably led to the most humiliating experience of my time in school. There were three of us, all boys, who were by now totally switched off to maths. We sat at the back of the class and were happily ignored by the teacher as beyond any kind of redemption.
Once a year the day we dreaded most would arrive, the maths exam results. We huddled together at the back for comfort and waited until the marks reached single figures before taking any real notice. Within our very limited little maths world we were fiercely competitive. With sinking heart I listened as my partners in crime were given their marks. I was the last in the class and so obviously the bottom of the pile.
Imagine my joy when the teacher moved on to another topic without reading out my mark. Relief flooded my being. She had somehow missed my paper. All was not lost. Seizing the day I sprang to my feet and shouted,
“Miss you haven't given me my mark.”
I still recall the look in her eyes as she turned towards me, a curious mixture of pity and amusement.
“That's because you haven't got one,” she replied.
Success is as powerful an influence on our lives as failure. The self esteem she experienced through mastering her ‘weakest’ subject overflowed into every area of her life. Isn’t that what we want for our children?
Get your children in the flow. The nature of Cuisenaire rods allows for open ended tasks and problem-setting that enables children to develop at their optimum learning level - what Csikszentmihalyi describes as the 'flow state'. Children frequently become so absorbed in whatever they are engaged in creating with the rods that they are oblivious to everything around them.
Cuisenaire rods reign supreme among math manipulatives. It is a tragedy for our children they are not more widely used and understood in schools generally. One of the 'hidden' benefits of using Cuisenaire rods is the enriched sensory stimulation children receive through plenty of handling and touching. Infants who receive enriched sensory stimulation become more mentally alert and physically stronger.
Neurobiologists Shatz at UC Berkeley and Jacobs at UCLA confirm this fact.
In effect using Cuisenaire Rods stimulates brain-friendly learning for your child. One of the brain's abilities is the capacity to recognise colour. Colour creates an emotional response. Imagine visiting London and trying to make sense of the underground system if the map were in black and white and not colour coded. Using Cuisenaire rods children can be introduced to basic maths concepts before having to cope with numbers. Number is itself an abstract concept and difficult to grasp. Caleb Gattegno called this approach 'algebra before arithmetic'.
In his book 'The Learning Brain' Eric Jenson states that 75% of teachers are sequential analytical presenters. Unfortunately 70% of their students do not learn in that way. He suggests that a better method would be to start with a global overview or ‘big picture’ and then move to a more sequential approach. Cuisenaire rods lend themselves perfectly to this method. Used effectively they can become your child's window on a rich landscape of pattern and relationships.
Not all of us learn in exactly the same way. Basically we are either predominantly: visual, auditory, kinaesthetic or tactile learners. Young children are strongly tactile learners as are many boys who benefit from a 'hands on' learning programme. Visual learners will respond to the colour of pattern and relationships revealed by Cuisenaire rods. An emphasis upon questions to instigate open-ended tasks will appeal to auditory learners. Play with the rods creates an environment kinaesthetic learners will thrive in and free play should always be factored in no matter what level of development the child is at.
The nature of the rods embraces all the learning styles. We all employ a mix of styles regardless of our particular preference. It would be totally impractical and extreme therefore to adopt a ‘learning style model’ that attempts to cater for a child’s individual learning preference as these are not fixed points but part of a dynamic process of development. It is more important to focus on the subject matter and ensure that the ‘teaching style’ is an effective fit for what is being taught.
Phil Rowlands is a semi-retired head teacher and author of educational programmes and fiction.