FOR INDUCTIVE TEACHING, DRILLING AND TESTING CONSISTING OF BOOKS V, VI AND VII OF ARITHMETIC BY GRADES Common and Decimal Fractions, Denominate Numbers, Geometrical BY JOHN T. PRINCE, PH.D. AUTHOR OF "COURSES OF STUDIES AND METHODS OF TEACHING," BOSTON, U.S.A., AND LONDON 1895 NOTE TO TEACHERS. THE attention of teachers is called to the following features of this series of books features which should be kept in mind as the various subjects are presented. 1. The separation of teachers' and pupils' books, whereby pupils may be taught properly and may not be given too great assistance. Suggestions as to methods of teaching and drilling, as well as the illustrative processes, explanations, rules, and definitions which belong to the teacher to develop analytically are put into the Teachers' Manual, while in the pupils' books are presented only such exercises as are needed for practice. 2. The careful gradation of problems, by which pupils acquire inductively a knowledge of arithmetical relations and principles, and skill in arithmetical processes. This is in recognition of the well-known pedagogical principles of proceeding from the known to the unknown, and from the simple to the complex. It is advised that this plan be kept constantly in mind by the teacher, and that whenever a process is not understood or is not readily performed, the pupils should be taken back to processes which are well known and which can be performed readily, and then should be led forward by easy steps until the desired end is reached. 3. Frequent reviews, and such an arrangement of exercises as will enable pupils to have needed practice in the applications of each principle, first by itself, and afterwards in connection with other principles which have been learned. 4. The large amount of oral work, or work which may be done without the aid of figures. Three objects of Mental Arithmetic are sought in these exercises: (a) Illustration of principles and a preparation for written work, (b) Development of the logical powers, (c) Cultivation of ability to work with large numbers by short processes. 5. The great number and variety of problems. The aim has been to give the largest number of problems that will be needed for teaching and for drilling in all grades. For this reason, and because the forms of expression are varied, being taken from many sources, there will be no necessity of giving supplementary drill lessons on the blackboard. Blackboard lessons are objectionable not only on account of a waste of the teachers' time and strength, but also on account of the injury done to pupils' eyes in much reading and copying from the blackboard. 6. Practicalness of work in respect to the character of the problems, and the solution of them. Care has been taken to give problems which are most likely to be met in every-day life, and to give them in a practical form. Many of the miscellaneous review problems were made by mechanics, clerks, accountants, etc., with a view of presenting conditions most likely to occur. 7. The introduction of statistics and facts of physics, astronomy, history, geography, etc., thus enabling pupils to gain incidentally much useful information. 8. The use of drill tables and other devices to save the time of teachers. If the first section of this book is found too difficult, it is advised that such parts of the Elementary Arithmetic be reviewed as will be needed. It is suggested that the review be made with objects and by the development method. If the previous work in fractions has been well done, little objective teaching will be found necessary for the fractional exercises of Part I beyond representations that may be made by drawings. Whenever any difficulty is met in performing these exercises, reference should be made to similar exercises with halves, thirds, tenths, hundredths, etc., objects being used when necessary. The continued use of objects in teaching Mensuration and Denominate Numbers is strongly advised as well as the pupils' practice of drawing in the illustration of problems, especially when such drawing will tend to make clear an unfamiliar or difficult process. Since the Metric System of Measures and Weights is not in common use, it is not necessary to give very extended or long continued practice in it. Yet enough of practice should be given to show the pupils the great advantage of simplicity and economy of time that it has over our complex system. A clear statement of steps in brief formulas should be insisted upon until the principle or process is thoroughly known. Such statement should include what is asked for in the problem and the conditions that are given. The solution of problems by short processes and "on a line" by cancellation should be encouraged when the problems are not difficult. In the early stages of the study of Arithmetic, correctness in numerical computations is made of primary importance. In the higher grades, therefore, it ought to be assumed that the mere work of addition, subtraction, multiplication, and division can be done accurately and quickly, and that the logical processes are to be more and more emphasized. Frequently the pupils may be asked to indicate only the steps of analysis that would lead to the correct solution of a given problem. Short processes also, and the indication of processes "on a line," should be constantly encouraged. For methods of teaching the various subjects, see Teachers' Manual, which, although intended for use in connection with "Arithmetic by Grades," may be used with this book, it being remembered that all references to Books V, VI and VII refer to Parts I, II and III respectively. Thus VII, 91 at the head of page 177 of the Manual may refer to the problems on page 91, Part III, of this book. |