Excerpt from Advanced Arithmetic
The purpose of this book is to aid the teacher in making conditions favorable for the contact of the learner with mathematical realities. Since the simplest as well as the most complex relations become known only through mental activity in comparing, attention is given to an environment which shall continually induce this activity. The compari son of magnitudes includes all the other Operations of arith metic. This is apparent when we reflect that all advance in knowing is by progressive acts of analysis and synthesis. Whether we compare by means of the object or by means of its symbol, the mind should still be free to move from the vague to the definite through its own acts.
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