FOR INDUCTIVE TEACHING, DRILLING AND TESTING BOOK NUMBER EIGHT Miscellaneous Questions involving the making of definitions, rules 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. In addition to the above features, some of which are distinctively new so far as American text-books are concerned, there is the separation of pupils' exercises for practice into small books somewhat on the lines of gradation in City graded schools. By this arrangement there are gained greater convenience of handling and economy of wear than in the use of a large book which is intended to be used for several years by the same pupil. Much of the arithmetical part of this book is supposed to be a review of what has been taught. There is little, therefore, of what may be called development work. If such work is found necessary, as it may be for the solution of the most difficult problems, it should be supplied by the teacher. Rules and definitions which have not been called for to a great extent in previous books should be required, not merely as a test of the pupil's knowledge, but as a good means of mental discipline. Let the rules and definitions be made by the pupils themselves, and be corrected by them as they see that other forms of expression are clearer or more accurate than those which they have made, In the exercises in Algebra an effort has been made to introduce such operations in simple equations as will lead to a familiarity with algebraic expressions, to a better understanding of principles, and to an ability to perform certain problems which are found too difficult to be solved by arithmetic. While the inventional and constructive side of mensuration and geometry is continued, somewhat of demonstrative work may be introduced, and definitions which have not before been used to a great extent should now be required frequently. Particular attention should be given to the practical applications of both Geometry and Algebra. The exercises in Book-keeping are believed to be practical and sufficient for any business which does not require an elaborate system of double entry. For methods of teaching the various subjects and for answers to problems, see Teacher's Manual, which is designed to accompany all books of the series. |
