A Key to the National Arithmetic, Exhibiting the Operation of the More Difficult Questions in That Work; For the Use of Teachers Only

The author's goal in this publication is to help the teacher communicate his instructions to the students and enable him to more readily detect any mistake they may have made in completing their questions. Every teacher who has a large number of students is aware of the fact that learning how to complete many of their students' questions is a big burden, especially when he is in school; at the same time, with the help of the key, he can detect any mistake in the operation in a few moments and thereby save most of his time, which can be devoted to more useful purposes. In addition, in a hurry with business, it is often very difficult for the most capable arithmetician to remember at the moment all the principles by which some difficult questions are resolved; but returning to the Key, its difficulty will be removed. The author would recommend to every teacher the following maxim: never give the student a direct answer to any question he has to offer in relation to the action of a task, and do not do the work for him, but offer principles that will allow him to answer the question himself. Answers to all examples in Arithmetic have been inserted in the Key for the convenience of those teachers who may choose to use the unanswered edition of Arithmetic.