EducT 119.01.260 HARVARD COLLEGE LIBRAR? GIFT OF GEORGE ARTHUR PLIMPTON Copyright, 1901, by GLOBE SCHOOL BOOK COMPANY. M. P. 1 "If a child learns how to use the text-book, he W. T. HARRIS, LL.D. United States Commissioner of Education. MANHATTAN PRESS NEW YORK PREFACE For boys and girls who know the numbers from one to ten thoroughly, there is here about a year and a half's work. When should boys and girls begin to study numbers in books? As soon as books can help them forward to the mastery of numbers. This time comes as soon as children can read. How should boys and girls study numbers? The interrelations of number-facts and of number-principles are such as to make progress very slow and very difficult through their intricate maze. Is there any Ariadne's thread to follow through the labyrinth of numbers? Is number ratio or counting? Is it comparison, or magnitude, or multitude? Is it a logic of thought, which can be analyzed after the topical style, addition, subtraction, multiplication, division, rule of three, and so forth, - of which we may complete one part before beginning the next? Shall we learn every discoverable fact about twenty before taking up twenty-one, or every conceivable fact about of of of 12 before taking up liquid measure? This book is neither "topical" nor "spiral" in plan. Its substance is neither ratio nor counting. Its purpose is to conform numbers in their facts and principles to the usual processes and powers and interests of children's minds. The graded reader has opened the way for the graded arithmetic. Grading all books is part and parcel of the new education, which means to discover and to obey the facts of the child-mind, its methods, nascent periods, and order of growth. The core of the concentric theory is recognition of the value of finding something that is known even in the mass of the unknown. Let us not hesitate in schoolbooks as we do not hesitate in life to branch out into the new and to return again to the old. Because comparing is the root and numbering is the top, let us not forget reasoning which is the main trunk of arithmetic. The child's knowledge of arithmetic should grow as evenly in all directions as the most careful and the most open-minded education can secure. |