Montessori mathematics
Montessori materials for mathematics, for children aged 1–9.
Mathematics moves consistently from concrete to abstract. The child first holds the quantity — bead bars, number rods, golden beads — and meets the symbol only once the quantity is secure. A thousand is not a word but a cube with weight in the hand, and ten hundred-squares side by side make the decimal system visible rather than something to memorise. Only once the concrete is established is the material withdrawn and the arithmetic moves into the head.