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COPYRIGHT, 1902, BY
THE WHITAKER AND RAY COMPANY

1

PREFACE.

ON GENERAL METHOD. - The author is permitted to quote from a bulletin on "The Teaching of Primary Numbers," by Professor Frank F. Bunker, of the San Francisco State Normal School:

“The study of every topic generally included in a course in arithmetic can be begun either from the objective side or from the side of the purely formal. For instance, in beginning the study of fractions the teacher can give a more or less extended course wholly within the field of the concrete, or she may choose to begin with the formal and mechanical side, — the side which is concerned alone with the various manipulations of fraction symbols. Just so with square root, with division, with multiplication, or in fact with almost any phase of arithmetic. On the one hand, there is the field of the objective, -the concrete; on the other, the field of the formal. Careful observation of practicework will show, as we have just said, that facility in one field will by no means give facility in the other. A child, by careful teaching in the field of the concrete, will soon acquire great skill in adding simple fractions, and yet he may never have seen those same fractions expressed by figure symbols. He does this by reason of the fact that to him a fraction is as much a concrete thing as is his dog or his horse. To him, adding fractions is nothing more than calling up and counting mental images of familiar things. On the other hand, the mind is never more devoid of mental images than when engaged in formal calculation. To have images of things floating around at such a time means that attention is diverted, with ineffectiveness as a consequence. Obviously, the child needs training in both these fields. He needs to be accurate and tolerably rapid in the mechanical work of fractions, and at the same time he needs the power to see visually the relation between and } of a foot."

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