Jefferson county prides itself in its many good school buildings and in the educational interest of its citizens. Recently there was dedicated in the village of Sullivan a modern three room state graded school building which has attracted considerable attention in the outside world owing to the civic center movement in the district that resulted in the erection of this school house at a cost of $4,000. The building completed it is now used as a social center, and under the leadership of Superintendent A. J. Thorne most interesting neighborhood meetings are held here. The new school building at Sullivan This building is constructed of brick and cement and heated with a modern furnace in connection with which is an efficient ventilating system. Here is the center of a traveling library that has done much to interest the people in the cause of education. Teachers' meetings, lectures, socials, debates, and other entertainments for the pleasure and profit of the neighborhood are giving the Sullivan school a state wide reputation. Why should this movement not spread to every community in Wisconsin? The school house ought to be the common meeting place for the people of every district in the state. The interior of one of the rooms THE ECONOMY OF GOOD ASSIGNMENTS IN THE RECITATION W. J. SUTHERLAND, President State Normal School, Platteville, Wisconsin. N increase in the efficiency of any school depends upon the multiplication of its positive and the division of its negative factors. Among all of the other conservations there should be conservation of teachers' energies. An efficient school must direct its efforts toward well-considered ends. Educational waste is due. Educational waste is due. in general, either to a poor direction of effort and power, or to the direction of effort and power toward unworthy ends. A concurrence in the truth of this statement, places great importance upon the assignment as one phase of the teaching process. The absolute efficiency of a school is measured by its contribution toward the development of personal power in specific directions. Individual efficiency always takes into account the environment in which the individual lives. As already stated, waste may result in one of two ways: The teaching may be conducted so clumsily that even the most worthy fail to be reached, or the aims themselves are so foreign to individual interests, as determined by environment, that the acquired experiences and knowledge find but little opportunity for expression. Therefore the acquisition of knowledge or power may or may not increase absolute individual efficiency. Knowledge is power only when it is a dynamic factor in the conquest of the abundant life. If intellectual acquisitions do not enable their possessor to compete more advantageously in the struggle for better existence, such attainments will not increase individual efficiency. Such knowledge may even decrease efficiency inasmuch as it may wrap and prejudice the mind that would otherwise be rational. That knowledge should "function in life" is indeed a hackneyed expression, but it suggests the law governing the absolute efficiency of knowledge. It is admitted that knowledge should function in life, then the utmost care must be exercised by the teacher in the selection of subject-matter units that bear the proper relationships to the environment in which the future citizen is to live and move and have his being. If educa tional waste is avoided, the evaluation of materials is imperative. Conversely, a more efficient educative process and a more thorough evaluation of subject-matter are most effective in eliminating waste. All too long has endured the presupposition that all topics treated in test books, are worthy of study by all pupils. Test books are not often designed for local use. Commercialism has decreed otherwise. It must follow, therefore, that the needs of pupils in one locality will differ from those of other localities. For one to have studied certain subjects, to have gone through certain school books, to have at the tongue's end certain verbal accomplishments,to have possession of diplomas, has, for many years, satisfied the popular mind that such individual is educated and cultured. The wisdom of the Twentieth Century now demands that education and culture be recognized not for existence in form but for efficiency in practice. New standards, therefore, subject both materials and methods of instruction, to severe criticism. The evaluation of subject-matter, then, is a prerequisite to an ideal assignment. To pass judgment on the functional value of subjectmatter is a difficult task. But as long as lessons which have no particular bearing on practical life, are assigned to pupils, just so long and inso-far will educational waste be involved. The value of subject-matter is estimated upon various bases. It may be of value as an introduction to, or foundation for, other knowledge of recognized value; it may serve as a mental stimulus the resultant activity of which contributes to mental development; or, it may function directly in the practical experiences of life. Briefly stated, subject-matter is preparatory, disciplinary, or functional. The teacher of much wisdom will recognize in his assignment some particular value of the subject-matter. The general recognition of the social phase of education leads also to the recognition of an "extra instructional value idea that commends so strongly and makes so popular, vocational education. Extra-instructional value is here used to des ignate subject-matter that not only serves as a mental stimulus, but at the same time contributes some knowledge or experience immediately useful. Many lessons assigned to pupils are so conventionalized that they appear ridiculous outside the schoolroom. The elementary and high schools cannot begin to exhaust the materials of study that possess this socializing value. A study of common weeds may be made good botany and be also of the highest practical value in rural communities, where economic success depends upon their extermination. In physics, capillarity may be studied through experiments with mercury and water, but its ultra-instructional value appears when ideas of soil-capillarity and waste of moisture, get into the problem. The English Corn Laws may be studied as independant facts, or they may be considered as preparatory materials illustrative of the principle that in American life, as suggested by the tariff, some knowledge of which is essential to intelligent suffrage. In carefully considered assignments the practical or functional value of subject-matter is of first importance. A good assignment necessitates first of all, the selection of those subject-matter units which, for the particular class, are pertinent and functional. Often these units must be broken into smaller units suitable for a daily lesson. Such selection and sub-division of subject-matter must be followed by the method of attack. Much depends upon the manner in which the teacher refers the materials to his class. A generalized question, or problematical statement, seems to be an excellent form of assignment, inasmuch as it is of necessity definite and arouses interest by seeming to challenge the mind. The problem stated, some direction of procedure is necessary depending, of course, on the maturity of the pupils. Some of the new geometries have selected a method that would seem almost ideal. The theorem states the problem most clearly, and just enough of suggestion follows to put the pupil "on the track," and still to allow leeway for originality of thought. Such method absolutely prohibits passive memoriter work characteristic of older methods. Laboratory exercises in physics and chemistry possess a definiteness comparable to the geometrical proposition, with perhaps a less appeal to originality. Why cannot the same general problematical method of work be adopted in studies that are descriptive and historical? Suppose, instead of a memoriter recitation on Burgoyne's invasion, problems like the following be given: (1) Explain the object of the invasion. (2) Why did it not succeed? (3) What effect did Burgoyne's failure have on the outcome of the War? Such assignments direct the attention to the most significant factors in the topic, and encourage pupils to place emphasis where it properly belongs. Lessons in geography lend themselves to presentation in the form of problems. What relationship exists between rainfall and distribution of forests? What effect do cyclonic storms have on the precipitation of moisture in the Upper Mississippi valley? etc. It is very clear that if assignments of this nature be made, that some direction should be given to the study. Otherwise grade pupils might be quite at sea. might be quite at sea. Hence, carefully selected questions and directions should follow. In preparing such questions, the teacher really decides on the general character of solving the selected problem, whether it be an inductive or deductive procedure. Here again the rather far-reaching importance of the assignment is manifest. It has been pointed out that great waste is due to the poorly directed efforts of pupils. Vagueness of motive always dulls interest and eventually kills enthusiasm. Clear and definite assignments, on the other hand, stimulate interest and inspire confidence in pupils. Is it too strong an assertion that the teacher who assigns well cannot fail in either instruction or discipline? Pregmatically, it is true, at any rate. Too often school work fails for lack of generalization and organization of subject-matter. How much of detail and matter of minor importance, find their proper places when work is well planned! And in time, will not pupils come to recognize a difference in value in statements that look equally important on the printed page? "How to study" is a popular slogan, and still a careless and sloven use of text-books quite defeats any reasonable method of study. Often there is no better time to do some real teaching than when making an assignment. Pupils' time may often be saved by clearing up some point that would otherwise prove a stumb ling block. Waste in time and decrease in in- cultness, it augurs well for a successful recitaterest are thus avoided. The success of a class recitation, except in the case of a development lesson, which in the truest sense is not a recitation, is determined in large measure by the assignment. If definite, of proper length; and of the right degree of diffi Я tion. An ideal assignment includes purpose SOME FUNDAMENTAL PRINCIPLES IN THE TEACHING OF FIRST YEAR ALGEBRA VIII. QUADRATIC EQUATIONS WALTER W. HART, Asst. Professor of Mathematics, University of Wisconsin few yearsago there would have been generadisbelief in the possibility or the desiral bility of including quadratic equations in a first year course in algebra. With the general agreement that the essentials only of each topic should be included in a first course and that the equation should be made the dominant topic of the course, has come a realization that quadratics not only can but should be included in the first year, in schools which have a full year or even an eight months course. Can this topic be reached in time to treat it adequately may be asked? Only a qualified answer may be given as the special conditions in a particular school may modify normal conditions. As a rule, it ought to be possible to cover the topics A to H, enumerated in the September (1911) article, in from 25 to 28 weeks, when these are covered in the spirit of the articles that have appeared in this magazine in the intervening months. This will leave from 4 to 8 weeks for the topics I and J (Quadratics,) according as the school has an 8 months or a 9 months course. If the high school course in algebra is preceded by an eighth grade course, obviously even more time will remain, so that additional topics may be undertaken. It is unquestionably possible to treat the preceding topics adequately in this time. Is it desirable to bring in the quadratic equations? Decidedly, yes. It extends the otherwise limited view pupils will have of equations; it is, relatively, much simpler than many of the topics formerly taught, such as cube root, radicals and exponents; it opens up the way to a wider range of problems, many of them of real interest; it is distinctly in accord with the fund amental principles enunciated in the first article. The first treatment customarily comes with the chapter on factoring, when solution of quadratics by the factoring method becomes possible. This practice gives additional purpose to the topic factoring; on the other hand, many of the essential ideas of quadratic equations may be taken up by this method, together with some of their applications. Later on, in most texts, comes the time for additional treatment of quadratics. Then, after topic I, (see March Wis. J. of Ed.,) the pure and complete quadratics should be discussed thoroughly. The essentially new ideas in quadratics are first that a quadratic has two roots, and second that, in contrast with the roots of linear equations, these roots may be irrational. That an equation has two roots is clear to most pupils as long as the roots are rational. Often when the roots are irrational, this fact is not clear. Two devices are suggested as valuable in this case; one is to illustrate the meaning of irrational roots graphically; the second is to have the pupils regularly write each root separately and, frequently, have them get the approximately decimal values of the two roots. Thus for an equation whose roots are 12, have the pupils 1+1 2, and r2 1-12, or in decimal form r1 2.414+ and .414+. Obviously this practice will aid in maintaining and increasing the pupil's efficiency in arithmetic. This device at once enforces the idea that there are two roots and gives meaning to the irrational roots. Often, children will say glibly that the roots are 112 without realizing either of the two essential facts involved. write: r1 98 To make somewhat clear the meaning of imaginary roots, the graphical illustration seems to be the most helpful device. Pupils should learn three methods of solving a complete quadratic: the factoring, the method by completing the square and the formula method. The factoring method is easy. The second method may be made unnecessarily difficult. One method of completing the square is sufficient; unnecessarily complicated coefficients, both numerical and literal, should be avoided; the problems should be carefully graded, starting with such as have 1 for the coefficient of x2 and an even coefficient of x, and gradually becoming a little more difficult. This method of solution must be looked upon as only a means of ultimately getting the formula, by solving the standard quadratic ax2 + bx + c = 0. Pupils should learn to use the formula in solving quadratics. Under the last two methods, the greater part of the problems should have irrational roots, as the pupils should be taught that, when possible, a quadratic is to be solved by factoring. It is of course desirable to have the first few in each list possess rational roots so that the pupils may check their solutions by substitution. When the roots are irrational, though it is possible to check them by substitution, few experienced teachers will recommend it. There is much more opportunity for error in making the substitution than in solving the original problem. A short device for checking such roots is to find their algebraic sum, either in radical or decimal form; this, according to a well known theorem, should equal the negative of the coefficient of x divided by the coefficient of x2. A few equations containing imaginary roots should be included. The theory of quadratics, with discussion of the character of the roots and the formation of quadratics having given roots, should all be left for the advanced course. In the concrete problems, many pupils find it distinctly easier to use two unknowns, getting as a rule one linear equation and one quadratic. This suggests the desirability of teaching the solution of a system of one linear and one quadratic with two unknowns. By the substitution method, this offers no difficulty and is a distinct. help in the solution of problems. Pupils will often introduce it of their own accord. The Second-hand School Book Evil Wisconsin has set the pace for systematic and continuous warfare on contagious diseases. The work of the Anti-Tuberculosis Association has attracted nation-wide notice. The deadly common drinking cup and the filthy common towel have received their just deserts. Is it not time. that a propaganda be instituted against another great conveyer of contagious disease-the dirty schoolbook? It has been proved many times that filthy schoolbooks have been responsible in certain. localities for a periodic recurrence of epidemics of contagious diseases. A book is one of the most obstinate carriers. Medical authorities agree that a book cannot be effectively disinfected. It is impracticable separately to fumigate each leaf, and yet nothing short of this is safe. A book in use in a school where there is not individual ownership is handled on the average by a dozen different children. It is bad enough where children have access to only their own books or those of the members of their family; but in promiscuous use the danger is increased by the almost universal habit of children of moistening their fingers in turning the leaves and thus introducing the disease germs directly into the mouth. Undoubtedly the apparently inexplainable apparence of an epidemic of scarlet fever or diphtheria among school children could be traceable very frequently to germ-laden books. With all the recent agitation resulting in much legislation to prevent the spread of contagious diseases it is natural that attention is now being directed in may states to the question of eliminating or modifying the danger resulting from the use of second-hand text-books. In one state at least (Maine) prohibitive legislation has been enacted. In Toronto the medical authorities, after a searching inquiry, decided that the situation was so grave and the dangers so imminent that there was but one way to treat filthy books, and ordered them burned. In free text-book territory it is an easy problem, for the books are all owned by the board and they can confine the purchase to new books and destroy the old books whenever in their |