PREFACE ONE noticeable weakness in elementary education of to-day is the pupil's inability to use a textbook correctly. The CITY ARITHMETIC is an effort to remove this weakness. The appeal is first and foremost to the pupil. The language used is within his comprehension; the explanations are such as he can easily grasp. The work advances step by step. The drill is ample and sufficiently varied, and the problems are within the experience of the average child. These are books which the pupils can use at home as well as in school. Business men complain that boys and girls whom they employ cannot perform correctly the four fundamental operations. Teachers in the upper grades state that the pupils come to them so weak in addition, subtraction, multiplication, and division of integers that the work in the last three years is seriously handicapped. The authors feel that this is in part due to lack of persistent drill. To offset this, a large number of examples and problems in these operations has been furnished for daily practice. Overemphasis on the explanation of processes and excessive variety of appeal to the interest of pupils are other causes of weakness in arithmetic. The authors have striven to avoid refinements of explanation, to eliminate processes with little practical application, and to provide an intelligent but not excessive variety of drill work. Every teacher knows how heavy a burden is the organization of material. These books lift the burden. A moderate spiral is used. In the third and fourth years, the work has been arranged by weeks and with the greatest care. In the fifth and sixth years, the work has been arranged by months; in the seventh and eighth years, the arrangement is topical. Easy examples have been selected for the beginning of each term and the matter is presented in a way that avoids the usual stumblings and discouragements. Type problems for each grade have been given to illustrate how particular methods are to be carried out and to show with how much detail each subject is to be presented. Ample material for oral drill has been furnished, and a great number of examples and problems has been introduced so that teachers may lay stress on any phase of the work that requires emphasis. How many of these examples and problems are to be worked by the class, the teacher herself may decide, according to the needs of the pupils. PLAN OF WORK THE work of the second half of the fifth year is divided into quarters, and presents an orderly arrangement of the arithmetic topics of this term for the guidance of the teacher. Numerous examples, both oral and written, in all the fundamental processes, are given in response to the repeated demands for accuracy and rapidity in this work. Addition is tested by a slight modification of the civil service method, and frequent tests in approximating answers give other means of checking results. Short methods in multiplication, in division, and in fractions and decimals, are presented in steps of graded difficulty. The teacher is advised to urge the pupils to apply the principles of testing, of approximating, and of short methods in all possible cases, and not to limit their use to the designated examples under these headings. Daily drills in fundamentals are strongly recommended. The teacher will use judgment in adapting to the needs of the class the amount and character of the review, for it is not expected that each class will complete all the review work of the book during the term. Decimal fractions, emphasized in the fifth grade and treated fully in this book, are introduced by a simple comparison with the units of United States currency. Common fractions are completely reviewed in each quarter, and their basic principles are applied to the processes with decimals in such a way as to establish clearly and firmly the relations between common and decimal fractions. The problems are grouped under type forms, and are adapted to the experience and interests of the children. |