Prof. Hanna Neumann gave the Presidential Address at Australian Association of Mathematics Teachers inaugural conference in 1966. The conference was held at Monash University and had the theme of "mathematical unity". In this address, Prof. Neumann described some features of the teaching of mathematics in schools. While she did not know of a country in the world where the features she described were all present, she did not describe anything that was not in operation in some country, on some continent, and that she observed herself from close quarters. [This transcript was originally published in: "The Report of the Inaugural Conference," Australian Association of Mathematics Teachers, 1966.]