“In the course of this free play, the child learns many things about the rods upon which, later on, he will be building his mathematical knowledge. He will discover:
 1. that rods of the same colour are equal in length;
 2. that those of the same length have the same colour;
 3. that those with different colours have different lengths;
 4. that if he wishes to make equal lengths he can only do so by putting particular rods end to end;
 5. that the rods have been made so that whatever he constructs corresponds to the number of white rods.”

Caleb Gattegno, Now Johnny Can do Arithmetic [1963]