Elementary Algebra: Embracing the First Principles of the Science (1858)

This book is a newer addition of First Lessons in Algebra: Embracing the Elements of the Science. The layout is the same and begins with a very similar preface. Unlike the previous copy, this book includes an introductory lesson, which is a lesson in mental exercises to insure a student is prepared for the remainder of the course.

1. The introduction is designed as a mental exercise. If thoroughly taught, it will train and prepare the mind of the pupil for those higher processes of reasoning, which it is the peculiar province of the algebraic analysis to develop.
2. The statement of each question should be made, and every step in the solution gone through with/without the aid of a slate or blackboard; though, perhaps in the beginning some aid may be necessary to those unaccustomed to such exercises.
3. Great care must be taken to have every principle on which the statement depends, carefully analyzed; and equal care is necessary to have every step in the solution distinctly explained.
4. The reasoning process embraces the proper connection of distinct apprehensions, and the consequences which follow from such a connection. Hence, the basis of all reasoning must lie in distinct elementary ideas.
5. Therefore, to teach one thing at a time � to teach that thing well � to explain its connections with other things, and the consequences which follow from such connections, would seem to embrace the whole art of instruction.