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The nineteenth century was a time of great reform in education, with debate focusing on such questions as who should be educated, in what manner, and to what degree. Given the technical advances brought about by the Industrial Revolution, rigorous mathematical education was seen by many as essential. A mathematician, educator and examiner for the University of Cambridge, Isaac Todhunter (1820-84) was also known as a prolific and very successful author of mathematics textbooks. In his day, he was considered an influential, albeit somewhat conservative, figure in mathematical education. In these six essays, first published in 1873, he discusses topics raised by the reform movement (for which he had little sympathy), such as the examination system, teaching methods and materials. Born of Todhunter's vast experience in the field, this work reflects an insider's perspective and remains relevant to students and scholars interested in the history of mathematics teaching and the University of Cambridge.