This report, prepared by the mathematician H. S. Carslaw, provides a comprehensive overview of the state of mathematical education in Australia in the early 20th century. Drawing on a wide range of data and analysis, Carslaw makes a compelling case for the importance of mathematics to modern life and the need for high-quality mathematics instruction at all levels of education. A pioneering work in the field of mathematics education, The Teaching of Mathematics in Australia remains a valuable resource for educators and policymakers alike. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.