with the most important arithmetical operations performed with whole The third part is mostly practical, and composed of such rules and NOTE. In his progress through the second part the pupil should be ARITHMETIC. PART I. INTELLECTUAL ARITHMETIC. PRELIMINARY OBSERVATIONS. That frequent exercises in mental computations, have a salutary influ ence upon the mind, by inducing habits of attention, by strengthening the memory, and by producing a promptness of recollection, is, at present, very generally admitted. And, that exercises of this kind should be more extensively introduced into our primary schools, is acknowl. edged, and even urged, by our most experienced and successful teach ers. The success, which has, in most cases, attended the introduction of Intellectual Arithmetic into schools, has been such, as would doubtless appear incredible to those unaccustomed to witness it; but experience has shown that children may be made acquainted with the first principles of Arithmetic at as early an age as they can be taught the Alphabet and its most simple combinations. We have seen, says Dr. Griscom, a class of girls, whose ages everage not more than nine years, by the force of memory, and a few plain rules, multiply seven or eight figures by an equal number, enumerate and announce accurately the product and then extract the square root of this large product, and state the root and the remainder, without varying a figure from the truth. In the ordinary course of instruction, Arithmetic has been studied only by the boys; and by them it has usually been defered to the very last portion of their attendance at school. The consequence has been, that few have become familiar with its first principles, before they have been obliged to quit school and enter upon the business of life. Commencing the study of Arithmetic at this advanced period, the scholar is sensible that he has but little time to devote to it, but, being determined to cipher through his book, he applies himself with diligence, yet he hurries on from rule to rule with such rapidity, that he learns nothing as he ought. He may indeed reach the end and thus accomplish his principal purpose; but, of what he has gone over, scarcely a trace remains upon his mind. He has not even made him self thoroughly acquainted with the elements of the science, nor has he made himself so familiar with the rules as to derive from them any considerable advantage in the transaction of business. It is asserted with confidence, that children, after having learned to talk, cannot too soon be made acquainted with numbers, and exercis ed in mental computations. But great care should be taken that these exercises be adapted to the age and capacity of the child-that the questions proposed, be such as the child can fully comprehend. And as young children are incapable of the exercise of abstraction, the instructer will find it necessary to begin by employing sensible objects. These should be placed before the child, and the first questions proposed should relate to the objects themselves, and be solved by them. Questions may then be asked respecting things which are not present; and the child may soon be led to conceive the objects before him to represent men, cents, or any other things you please. In performing these exercises the child will at length discover that numbers are not inherent qualities of the objects themselves, but that they merely denote a succession of similar quantities, and may be applied as well to one kind of quantity as another. After this discovery the child will find but little difficulty in forming a conception of abstract numbers, that is, of numbers, or successions, without applying them to any specific objects. By repeating and varying these simple operations, children will soon become familiar with the fundamental principles of Arithmetic and their application to practical purposes. They will at the same time be acquiring habits of attention, and a promptness of computation, which will be of inestimable value to them in after life. And this may be done in our primary schools, as an amusement and relaxation to the scholars, without interrupting, in the least, their other pursuits. The proper place to commence these instructions is in our summer schools. These, it is true, are usually taught by females, many of whom have not had the advantages of much arithmetical instruction. But this defect in their qualifications, is not owing to a want of capa. city to learn, but to a fault of the times when the study of Arithmetic was regarded as proper only for boys. But those times are passing by and with them this defect will vanish. A moderate share of attention to the subject would enable every young lady, who en gages in teaching, to give instruction in the Intellectual Arithmetic contained in this work, and it is believed that they would find themselves amply repaid for this attention by the improvement of their own minds. By beginning with children at the commencement of their going to school, every boy and girl of ordinary capacity may be made more thoroughly acquainted with the principles of Arithme tic before they arrive at the age of ten years. than most of our scholars are on leaving school, after having plodded through all the rules of Arithmetic in the ordinary way. Some knowledge of Arithmetic is no less necessary to the female sex than to our own; and experience has proved, that, if the course, here recommended, be pursued, they will not be found less capable of proficiency in this science. It is hoped that our instrncters, both male and female, will take this subject into consideration and unite their efforts in bringing about a reformation so desirable in the course of arithmetical instruction. SECTION I.* 1. In commencing a course of instruction in Intellectual Arithmetic with very young children, it should be the teacher's first object to learn them to count. For this purpose beans, small blocks of wood, marks on a slate or paper, or some other sensible objects must be employed. It would perhaps be advisable to use no more than five counters at first, and in selecting these, care should be taken that they resemble each other as nearly as possible, that the child may not be led to suppose that the names used in counting denote a difference among the objects employed. Having called the little class around him, the instructer should begin by laying down one of the counters, which he has provided, and which we shall here suppose to be beans, and saying, there is one, require the children to repeat after him, one. Then, putting down another, he should say, one and one are two. Another bean may then be laid down, and the children taught in like manner to count three; and so on to five. After the children have learned to count five with facility, five more beans may be taken and the children taught in the same way to count ten; after which they may be taught, by the help of the beans, to answer the following questions: 2. 1. How many beans are one beans and two beans? bean and one bean more? 2. How many beans are two beans and two beans? beans and one bean? 15. How many beans are sever 16. How many beans are eigh 3. How many beans are three beans and two beans? beans and one bean? 17. How many beans are two 4. How many beans are four beans and three beans? beans and one bean? 5. How many beans are beans and one bean? 6. How many beans are beans and one bean? 7. How many beans are beans and one bean? 8. How many beans are beans and one bean? 9. How many beans are beans and one bean? 10. How many beans are beans and two beans? 18. How many beans are three five beans and three beans? 19. How many beans are four six beans and three beans? 20. How many beans are five seven beans and three beans? 21. How many beans are six eight beans and three beans? 22. How many beans are seven nine beans and three beans? 23. How many beans are two two beans and four beans? 24. How many beans are three 11. How many beans are three beans and four beans? beans and two beans? 12. How many beans are beans and two beans?, 13. How many beans are beans and two beans? 14. How many beans are 25. How many beans are four four beans and four beans? 26. How many beans are five five beans and four beans? 27. How many beans are six six bears and four beans? *This Section is designed for very young children; older ones may com mence at Section II. 28. How many beans are two beans and five beans? 29. How many beans are three beans and five beans? 30. How many beans are four beans and five beans? 31. How many beans are five beans and five beans? 32. How many beans are two beans and six beans? 33. How many beans are three beans and six beans? 34. How many beans are four beaus and six beans? 35. How many beans are two beans and seven beans? 36. How many beans are three beans and seven bears? 37. How many beans are two beans and seven beans? 38. How many cents are two cents and two cents? 39. How many cents are three cents and two cents? 40. How many plumbs are three plumbs and three plumbs? 41. How many nuts are four nuts and three nuts? 42. How many feet has one horse? 43. How many feet have two horses? 44. How many hands have two boys? 45. How many hands have four bays? 46. How many hands have five boys? 47. How many legs are there to la chair? 3. 1. How many beans are two times two beans? times one bean? 2. How many beans are times one bean? 3. How many beans are times one bean? 4. How many beans are times one bean? 17. How many beans are three three times three beans? 18. How many beans are four four times two beans? 19 How many beans are five five times two beans? 20. If I give two boys two plumbs a piece, how many plumbs will both have? 21. At one cent a piece bow much do four apples cost? 22. At two cents a piece how much do three pears cost? 23. What animal bes as many again feet as you have? and how ten many feet has it? 24. How many eyes have two one boys? 25. How many ears have three 11. How many beans are one boys? time two beans? 26. How many eyes and ears 12. How many beans are two have two boys? times two beans? 27. How many gloves do two 13. How many beans are two pair of hands require? times three beans? 14. How many beans are times four beans? 28. How many ear rings must I twoget for three pair of ears? 29. I gave a boy three cents and 15. How many beans are twee gave me twice as many apples, times five beans? 16. How many beans are threel how many did he give me? |