Learning arithmetic and mathematics for young children can be an exploratory experience where the child discovers for him or herself how numbers work. One excellent tool for this is Cuisenaire Rods.
A great learning tool for children aged four and up is Cuisenaire Rods.Wikipedia says: “Cuisenaire rods are mathematics learning aids for students that provide a hands-on elementary school 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 the Belgian primary school teacher Georges Cuisenaire (1891–1975), who called the rods réglettes.”
On YouTube there is a film by the National Film Board of Canada that demonstrates the art of teaching with Cuisenaire rods. It’s called Mathematics at Your Fingertips – 1961 NFB Full Video.
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.'”