School Arithmetic: Primary Book (Classic Reprint)

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Excerpt from School Arithmetic: Primary Book

From the concrete TO the abstract. - The child's mind must be approached through those ever open doors, the senses. Primary number teaching must be begun by the pupil's Observ ing and handling Objects, yet the mere presence of concrete things does not guarantee the presence of definite numerical ideas in the mind of the pupil. They must be so presented as to stimulate and aid the mental movement of discriminating and relating which leads to definite ideas of number. The mind must (a) recognize the like Objects as distinct individuals, and (b) group (put together) the objects into a whole. The child's own activity must conceive a whole of parts, and relate the parts in a definite whole. It is not enough that he knows our country as 45 states; he must know the 45 states as one country. He should recognize five, for example, not only as five ones, but also as one fire, considering the component ones not chiefly for their own sake, but as giving definite value to the whole the' group. By repeated acts Of such measurement or valuation the mind advances naturally and inevitably from things to relations, from facts to principles, from the concrete to the abstract. Believing that the concept of ratio - an abstract idea - must be evolved in the young mind by its own activity, and that therefore it should not be thrown at the child in the earlier stages of his progress, the authors have not explicitly stated the ratio idea until it has had time to grow into a recognizable and useful product of the pupil's mind.

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