“Two and two make four and cannot by any possibility that the universe affords be made to make five or three. From this point of view, of immutable law, children should approach Mathematics; they should see how impressive is Euclid’s ‘Which is absurd,’ just as absurd as would be the statements of a man who said that his apples always fell upwards, and for the same reason.”

 — Charlotte Mason, Towards a Philosophy of Education

“Most remarks made by children consist of correct ideas badly expressed. A good teacher will be wary of saying ‘No, that’s wrong.’ Rather, he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole of the art of teaching.”

 — W. W. Sawyer, Vision in Elementary Mathematics

“A bag of beans, counters, or buttons should be used in all the early arithmetic lessons, and the child should be able to work with these freely, and even to add, subtract, multiply, and divide mentally, without the aid of buttons or beans, before he is set to ‘do sums’ on his slate.”

 — Charlotte Mason, Home Education