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influence of Friedrich Froebel

Georges Cuisenaire

numbers in color

In 1952 George Cuisenaire published "Les Nombres en Couleurs" (Numbers in Colour). He was a Belgian primary school teacher who used the colored rods for teaching arithmetic.

Friedrich Froebel had originally developed a set of wooden building blocks which he used at Keilhau for children to learn about mathematics. The original Froebel set was based on a one inch cube and ranged in length from one to twelve inches, The Education of Man 1826. Georges Cuisenaire used a smaller unit cube (1 cm or about 0.375 inches) and a different color for each lengths.

Caleb Gattegno met Cuisenaire in 1953 and helped to make his work better known. Gattegno realized not only that the rods provide an algebraic model for the study of mathematics at all levels but also that they are means for learners to investigate mathematics for themselves. He also noticed how much precise language was generated through the students' discussion of the rods.

For many years Dr. Caleb Gattegno had been a leading figure in the movement to bring improvements to mathematics teaching at the primary and secondary school levels. He realised that the rods provided teachers with a means for making the lesson a personal investigation of mathematics for every child. This was why Froebel had originally developed these blocks at Keilhau.

Dr. Gattegno lectured in many countries to teachers wishing to know more about these rods. His work with children convinced him and others wherever he went that all have a latent ability which, in classroom situations where the rods are used and where teaching is learner centred, can yield truly remarkable results. And it was this experience and this technique of subordinating teaching to learning which Dr. Gattegno subsequently crystallised in his textbook series Mathematics with Numbers in Colour.

Mathematics as a reference

• With his background in mathematics, Gattegno observed for more than forty years how mathematical thinking is constructed.
• For Gattegno, mathematics is something any of us can do, since it involves reformulating mental structures that all human beings possess in mathematical terms. He called that process "mathematization."
• Thus, the role of the mathematics teacher is first and foremost to reveal to each person a certain aspect of oneself: the mathematician within.

A constructive and personal approach

• Mathematical situations are proposed to learners who, invited to participate actively, become aware, little by little, of the relationships that structure the situations, and at the same time understand better the dynamics of their own mental functionings.
• Centered on a given, clear and tangible problem, the situations presented for students' exploration lead each student to use their varied mental faculties, to formulate hypotheses and to test them, to develop personal strategies and to arrive at precise and profound understandings.
• Through those situations, from a perception of what they contain and from actions performed on them, mental representations are created and generalizations made, first verbalized and finally represented symbolically, in classic mathematical notation.

As the learners explore a mathematical situation, teachers observe them and lead the class, always ready to modify their pedagogical actions, based on what the learners are doing, what they are saying, their hesitations and errors, their understandings and misunderstandings, their attitudes and various reactions. Thanks to such constant, formative assessment and by paying attention to each learner, teachers can accompany their students and guide them step by step towards new insights.

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I like to learn by touching or doing things with my hands

The Cuisenaire Company in Reading, England, distributes the Cuisenaire Rods