Abilene High School - Orange and Brown Yearbook (Abilene, KS)

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girl enter High School. At High School age the most important factor in education is the development of the newly awakened self-consciousness and individuality of the pupil. Algebra and Geometry function largely in this development in that they set before the student simple, definite examples of clear, accuiate, logical reasoning, and train him to rely on his own judgment rather than the authority of some one else. ln a more particular sense, they form an excellent introduction to scientilic study in general, for the reason that of all the sciences, 11l2LLil8ll1HLlcS is the most nearly exact in method and by far the simplest in material. r'tli-thermore, mathe- matics furnishes the language in which the results of all scientific investigation are finally stated, namely, the algebraic formula. The Freshman course in Algebra is an introduction to mathematics considered in this larger sense as a science and not as a body of rules by which problems may be Worked. 'lhe numbers and concrete terms of Arithmetic are replaced by letters, and the laws of the four combinations familiar in Arithnletic, addition, subtraction, multiplication and division, are applied to them. The use of letters instead of nunl- bers brings out the tact that expressions tend to group LHQIHSGIVGS under a lew dis- tinct types-for example, a may represent any whole number whatever, a over b any fractional number. 'lo classify problems under their type forms, and to discover and put to use the principle by which each type is handled, then becomes a very large part of the work. Fractions are treated very Illlllliil as in Arithmetirs, and about the same share ot time is given to tllein as in the average year s work in Arithmetic. The statement OL problems in Algebraic terms is emphasized in the chapters on the equation, and is very inlportaiit ln that it emphasizes the necessity or a definite, precise understanding OL what one has 1'6k:Lll. rowers and ioots are also discussed, as these are employed in the S0111L10I1 of the quadlatic equation, which is the last new topic studied in the year. 'l he solving of 13100161115 is really the least important pa1't of the course, as this is largely 11l6C1li:l.1l1C2l.1, and may DS purely iinita- tive. ALGEBRA II Algebra in the High School should be taught from two standpoints, first, as a tool, and second as a type of thought. From the first point of view, it is the most powerful instrument yet devised for handling the problems of science. Accordingly, the formation and use of the formula and equation should become so familiar to the student as to be automatic. To this end, constant repetition and drill are neces- sary, and consequently are a large and important part of the third year of Algebra. One point in which the state text is weak and which must be guarded against is the constant use of the same letters. Very frequently a pupil can think and work only in terms of 'xv and y, and has to translate the and V of Physics into those letters before he can proceed any further. For this reason, the literal equation such as D-RT, in which each letter is to be expressed in terms of the others, is a topic which requires particular emphasis. Another topic which is valuable on account of its usefulness and applicability is that of logarithms. ln logarithms, addition and subtraction take the place of multiplication and division, while the latter take the place of powers and roots. Thus the cube root of a number may be found by dividing its logarithm by 3. Very fre- quently, the work in Algebra is so crowded that there is not sufficient time left for logarithms. In this event the topic may be included in the course in Solid Geometry. Viewing algebra as a type of thought, its chief characteristic is the substitution of symbols for concrete things. The parts of Algebra in which this idea is brought out most clearly are those dealing with the theory of exponents and the quadratic equation. In the former, powers and roots, radicals, fractional and negative expo- nents and imaginaries are shown to be merely a development in various forms of such simple expressions as A.A equals A squared, and K-AJ squared equals A squared. To be sure, these topics are discussed in Algebra I, but the student is much better able in his Junior year to get a clear understanding and appreciation of the process of reasoning by which their relationship is established. The quadratic equation, however, is the most striking instance found in elementary science of the Way in which a single expression may serve as a type for a multitude of forms. The solu- tion of the quadratic is developed in three ways Q19 Factoring, Q21 Square root-or, TWENTY-TWO

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successful wars with these peoples. The composition of the Roman army, its man- ner of marching and its camp life are all items of equal interest. There is also a composition course studied in the second year. In this course a review of the main principles of grammar as presented in the first year is taken up with illustrative sentences based on the writings of Caesar. Besides this some new rules of grammar as illustrated by Caesar are studied, particularly the use of the subjuuctive mood in dependent sentences. The objects of the second year Latin are to fix firmly in mind the fundamental principles of Latin grammar, to translate readily and correctly into good English, and to relate the subject matter which is translated to Roman history and to practical life. THE J l'Nl0R YEAR Cicero's orations as edited by D'Ooge are studied in the third year. The four oraticns against the Catilinarian conspiracy are read, also one in defense of the poet Archias and one in behalf of the Manilian Law-six in all. ln this year we get an even better view of Roman life. The city of Rome, the Roman Senate, govern- ment officers, Roman religion and the home life of the Romans are all topics of vital interest during this year's study. The composition course in the third year takes up the more difficult rules of grammar as they are found illustrated in Cicero's orations and as the students find them illustrated in fourth year Latin. A thorough study of the use of the subjuuctive mood is made. This includes its use both in in- dependent and dependent clauses. Bennett's Latin Grammar is the reference text throughout the second, third and fourth year Latin. THE FOURTH YEAR In fourth year Latin the first six books of Vergil's Aeneid are studied. This is perhaps the most interesting Latin which is read in High School. The historical set- ting of the Aeneid, its mythological allusions, its inherent literary value, make it a subject of great interest and charm to the students. Some of the descriptive pass- ages are easily on a par with any descriptions found in English literature, and the making of these comparisons adds greatly to the interest and ability in translating. Due to the poetic style of the Aeneid there is much freedom of translation given, which demands tl1e use of the best English at the student's command. Naturally too, much attention is given to scansion and poetic structure. No course in composition is offered in this year. The grammatical principles are studied only as they are illustrated by the text. Thus the second, third and fourth years embrace three distinct styles of litera- ture-history, oratory and poetry. The three great authors-Caesar, Cicero and Vergil-are worthy of study by everyone. Department of Mathematics ALGEBRA I High School Mathematics owes its place in the curriculum not to the informa- tion obtained from it, but to the difference it makes in the thinking of students. So far as mere knowledge is concerned all the facts of Algebra and Geometry needed by the average individual are taught in Arithmetic under the topics of mensuration and the use of the equation. Nor is skill in computation the aim of the High School. The boy and girl who do not come out of the eighth grade able to handle figures accurately and with reasonable speed rarely get this ability later, for the simple reason that the operations of Arithmetic to be performed efficiently must become automatic, and consequently must be mastered during the years when memory is the chief activity of the mind. This period is past by the time the average boy and TWENTY-ONE

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completing the square, Q33 The use of a formula developed from solution by square root. In addition to this, a study is made of the features of the equation which determine the nature of the roots. The graph is used, not only as an introduction to the study of equations, but also as a means of relating Algebra to Geometry. Considered in this light, the first degree equation corresponds to the straight line, and the quadratic becomes the Algebraic interpretation of two-dimensional space. The solution of equations by the use of graphs, that is, the determination of points which satisfy the required conditions, gives a new meaning to the locus of Geometry. The object of the course is not to present Algebra as a complete and finished subject, but rather to impress the pupil with the idea that while he has gained enough knowledge to be of valuable assistance, he really has mastered only the a, b, c of mathematics, and that there lies ahead of him a world of thought which will challenge every faculty of mind and imagination to conquer it. PLANE GEOMETRY Geometry is both a mental and a physical science. It is concerned with every- thing which occupies space, for it is the study of forms. In this respect it is the business of Geometry to investigate and classify figures according to their common properties, and to formulate the laws which determine their relationship to each other. From this standpoint Geometry serves to point out the common laws which are in force in all forms of nature. For instance, take the regular hexagon, which may be made up of six triangles, the sides and angles of which are all equal. This figure is the basis for all the various forms of snow-flakes, the cell of the bee is in- variably hexagonalg the blood vessels of the human body under unusual pressure are forced into such a shape that a cross-section takes the shape of a hexagon, and an orchard may be planted to the best advantage by laying out the ground in a series of equilateral triangles with a tree at each vertex. A close observation will discover the fact that wherever in nature conomy of space is needed, the hexagon is the form chosen. Furthermore, Geometrical forms are the basis of architecture, of painting, and in fact, almost every other art, and a knowledge of them is necessary for an aD- preciation of the elements of proportion and symmetry wherever these occur. Ac- cordingly, drawing is an important part of the work in Geometry, as there is no bet- ter method of becoming familiar with the properties of a figure than by constructing it accurately. But Geometry is also a mental science in that the truth of its theorems- is es- tablished not by observation or measurement, but by a rigid process of reasoning, commonly called the demonstration Certain assumptions are made, and on these as a foundation, principles are carefully and logically worked out. Nothing is ad- mitted to be true merely because it looks reasonable, and on the other hand, nothing is accepted contrary to the guidance of common sense merely because a proof con- vincing in appearance has been worked out. From this point of view the object of Geometry is, as it has been for several hundreds of years, to train the brain to an appreciation of clear cut, logical thinking, unprejudiced by feeling. This is not ac- complished, of course, by the mere memorizing of proofs, but rather by original work, so arranged that the argument consists! of but one simple step at first, but gradually becomes more difficult. The demonstration of theorems- given in the text-book is required, in order to see how well the pupils have followed and under- stood the reasoning, but exact reproduction is neither demanded nor encouraged. In fact, some of the more complicated theorems are discussed in class, and the student required to master only certain points of the proof. Numerical exercises, While they do not call for any careful or sustained reasoning on the part of the pupil as a rule, are of value in that they help to make clear and fix in mind the more important theorems, and also show the applicability of the algebraic formula to the work of Geometry. The note book is a feature of the work enjoyed by neither teacher nor pupil, but is useful in that it emphasizes concise, accurate statements and neatly drawn figures. SOLID GEOMETRY The Geometry of two dimensions is studied today before that of three dimen- V TWENTY-THREE