to be individually approached and trained, "not for school, but for life"? To summarize: 1. Do not go too fast; hasten slowly. 2. Assign lessons with care, keeping in mind that "too much is not good." 3. Repeat constantly; "repetition is the mother of all learning." 4. Require hard work; "the harder a pupil has worked for what he knows and can do, the better for him.” 5. Be methodical, enthusiastic, persistent, and patient. 6. Remember the ancient maxim, that "to the boy is due the highest reverence." PRACTICAL ARITHMETIC PART I. DEFINITIONS. 1. A Unit is a single thing or one. 2. A Number is a unit or a collection of units. 3. Arithmetic is both a Science and an Art: as a science, it investigates the principles of numbers; as an art, it applies those principles to practical purposes. 4. A Principle is a fundamental truth or ground of action. 5. A number is Concrete or Denominate when its unit is named, as in one man, two books, three ships. 6. A number is Abstract when its unit is not named, as one, two, three. When named, the unit of a number is one of the things expressed by the number, as one tree, one man. When not named, the unit of a number is simply one. 7. A Simple Denominate number has a single unit, as in five feet. A Compound Denominate number has two or more related units, as in three yards two feet six inches. What is the unit of the concrete number three ships? Of the abstract number three? Tell which of the following numbers are concrete and which abstract, and what is the unit of each: 8. Analysis (Greek, taking apart) examines the separate parts of a subject, or proposition, and their connection with each other; it solves problems by a comparison of their elements; it reasons from the given number to one, and then from one to the required number; it reasons, also, from particular instances to general principles. 9. Synthesis (Greek, putting together) unites separated parts, in accordance with their obvious relations. 10. A Rule is founded on some principle, and is a precise direction for solving a problem. 11. A Problem is a practical question requiring a solution. 12. A Solution consists of a process and an explanation made by the application of a rule or by analysis and synthesis. NOTATION AND NUMERATION. 1. Notation is the art of writing numbers. 2. Numeration is the art of reading numbers. 3. There are three methods of notation in common use: 1. The word method. 2. The Arabic or figure method. 3. The Roman or letter method. 4. The Arabic method employs the Arabic figures: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. 5. The word method names these figures and expresses their values as follows: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. One, two, three, four, five, six, seven, eight, nine, naught (cipher, zero). The script forms are as follows: 1 2 3 4 5 6 7 8 9 0 These figures are frequently called digits (Latin, digitus, finger); those preceding O are called significant figures. ARABIC NOTATION. 1. Each of the first nine numbers, you perceive, is expressed by a single digit; higher numbers are expressed by combinations of the digits. One prefixed to naught (10) is ten. 2. Our system of notation is "due to the fact that we have ten fingers," and the basis of it is the first ten numbers formed into a model group. 10 is one ten, or simply ten (Latin, "decem"). 11 is eleven (Gothic, "ain, one; lif, ten"), one and ten. 12 is twelve (Gothic, "tva, two; lif, ten"), two and ten. 13 is thirteen, three and ten. |