Excerpt from New Complete Arithmetic: On the Inductive Method, With Parallel Mental and Written Exercises

The best way to awaken interest, stimulate a spirit of self reliance, and open the mind to a thorough knowledge of the subject is to lead a pupil by easy and graded steps to discover principles and methods for himself. Therefore a practical union of induction and deduction is one of the strongest possible features of a good arithmetic. A special effort has been made to construct the present work on this plan. Not only are new topics introduced by carefully pre pared inductive exercises, but, under the heading of parallel problems, each exercise intended for written work is pre ceded by an inductive question. The teacher should en courage the pupils to look to these oral questions for such hints as they may need in solving the more difficult problems, and thus train them in induction and deduction, as well as in mental and written work.

The notation of numbers, operations, and relations forms the language of mathematics. It is not only the vehicle of thought, but very largely the means by which thought is directed and energized. In this, as in other things, it is a mistake to pass hastily from the concrete to the abstract.

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