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PROBLEMS OF THE SCHOOL LAW

School Clerks and Teachers Are Privileged to Use These Columns Freely in the Discussion of School Law Questions

District Transporting Its Pupils Receives Special the district and not to any one or more schoolState Aid

If the electors of a district having a small school, vote at the annual or a special meeting to transport their children to another school and pay tuition, do they receive special state aid and if so how much?

Special state aid amounting to $150 will, if the conditions are observed, be paid to a district. so closing its school and transporting its children.

Is Election by Acclamation Legal?

The electors at the annual meeting elected a director by acclamation. He had no opposition. Will his acts as director be valid and binding upon the district?

They will be most certainly. He is an officer de facto and his acts within the scope of the law are as binding between the district and third parties as are the acts of an officer de iuri.

School District May Have More Than Thirty-Six Square Miles

Is it within the power of the board of supervision to create a district having more than thirty-six square miles of territory within its boundaries?

Yes, the legislature of 1911 removed this restriction in order that a town heretofore operating under the township system of government could be entitled to organize under the independent system of school government.

Limit of Appropriation for Equipment

In many of our northern districts we have several schools. The law provides that electors at the annual meeting may apportion seventy-five dollars ($75.00) for the purpose of equipping the schools. In our town we have five schools and consequently will need more than seventy-five dollars ($75.00). Can this law be interpreted to mean that each school shall be allowed seventy-five dollars?

No. The law in this case relates merely to

houses. It would seem also that if the five schools in this district had been in existence for some little time that the additional equipments might be provided for the sum of one hundred dollars which can be levied under this statute. This is the only interpretation that can be placed upon the statute as it stands at present. Must Attend the Nearest School

A family lives four miles from the district school house, at a railroad station. The train can carry them to a station seven miles distant-taking them in the morning and returning in the evening. Question: If the children attend the school at the station seven miles distant is the district in which they live compelled to pay tuition to the other district?

No. It is not the nearest school. It is worth while to have a special meeting in the district in which you live asking them to enter into an agreement with the school board at Z as to the amount of tuition to be paid and then agree to pay this tuition-also the carfare if any is charged.

Manitowoc's Rule on Smoking

"Smoking anywhere outside of the students' homes will be considered a wrong by school authorities. Any one guilty of this wrong cannot accept or receive any honor, favor or recognition from his class or the school. Accepting any of these is evidence that the student is not guilty. A violation will be referred to the City Superintendent and the Board of Educatiou for final action."

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The Big State Meeting at Milwaukee

The Sixtieth Annual Meeting of the Wisconsin Teachers'
Association Meets at Milwaukee
November 7-8-9

Last year 5,883 teachers enrolled at the anWhat nual meeting. That's quite a bunch! does it mean? that in numbers Just this: there is strength, to say nothing of inspiration; that in this strength that united band has within its power the making and shaping of educational policies which shall determine the future educational welfare of Wisconsin. A handful of pedagogs could not do this. Then let's get together in large numbers and show the people and their law-making representatives in the legislature this winter what a power we are in mere numbers. They will respect numbers more than any other force.

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Mrs.

There is a splendid program ready. Bradford, the Queen of Wisconsin's teachers, has worked incessently to make these three days at Milwaukee days of inspiration for the teachers of the commonwealth. From outside the state are coming many of the greatest educators of the nation. The best of Wisconsin's educational talent will be there, too. Milwaukee's local members are ready to receive the outside teachers and to give them such entertainment as is due the representatives of the greatest profession on earth.

You'll be there! Sure! And so will all the teachers who are working with you in the same system. The county superintendents will be there and hundreds of their teachers. All the normal school presidents, most of the college presidents, city superintendents, members of the college and normal faculties, principals of all sorts they will all be there. What a crowd to get mixed up with! Dont you want to get in touch with all? Then be there. Look at this

Partial List of Speakers from Abroad William H. Allen, Director of the Bureau of Municipal Research, New York City.

Earnest Burnham, Teacher of Agriculture, State Normal School, Kalamazoo, Mich.

Hon. P. P. Claxton, U. S. Commissioner of Education, Washington, D. C.

Maurice Irvin Flagg, Director of School of Design and Hadicraft, Minneapolis, Minn.

Prof. C. A. Fullerton, Director of the Music Department of the Iowa State Normal College, at Cedar Falls, Iowa.

Dr. C. F. Hodge, Head of Department of Biolgy, Clark College, Worcester, Mass. Author of well known book, "Nature Study and Life."

James F. Hosic, Department of English, Chicago Teachers' College, Secretary of National Council of Teachers of English.

Charles H. Judd, Direttor of School of Education, University of Chicago.

Margaret Lennan, Principal of McKinley School, St. Paul, Minn.

Anna E. Logan, of Miami University, Oxford, Ohio. Mrs. H. K. Scroff, Philadelphia, President of National Congress of Mothers and Parent Teachers' Association.

Theodora Sexauer, High School, Albert Lea, Minn. Henry Suzzalo of Teachers' College, Columbia University, New York.

And there are some other things going to be pulled off at Milwaukee which will make a hit.

On Thursday evening banquets and alumni reunions of the normals and colleges of the

state.

On Frday evening an address by the United States Commissioner of Education - Hon. P. P. Claxton.

Free sight seeing tours conducted by the teachers of Milwaukee.

Music of all kinds including an organ recital by Louis Vantine.

The book-men with their parlors in the Plankinton and all their wares. What would an association be without them?

But the whole story can not be told within the limits of these pages.

Write to Secretary M. A. Bussewitz, State Normal School, Milwaukee, for the completed program.

And best of all, come yourself and see for yourself what is there!

CONSCI

Inductive Instruction in Mathematics

Professor W. W. Hart, University of Wisconsin

YONSCIENTIOUS teachers, superintendents, and principals are constantly endeavoring to improve methods of teaching. Among teachers, this desire often finds expression in the requests they make of their colleagues for a hint on how to teach this or that particular topic in the course. Thus it is no uncommon thing for a teacher of mathematics to ask another, "How do you teach long division?" or, in high school, "How do you teach negative number?" They seek and often find a way out of a present dfficulty by getting a device which is successful in that particular situation. It is obvious that the teacher who seeks this sort of assistance has to face each new topic as a new problem, and that for each particular device offered she has only the word of some one else that it is helpful. There is another possibility, the advantage of which all will admit, namely to seek some general method of procedure which will serve as a guide in the teaching of any new idea, whether it be in arithmetic, algebra, or geometry. The possession of such a guide frees the teacher from slavish adherence to either text or colleague, and provides a means of testing out a proposed teaching device before trying it on the pupils. Inductive instruction provides exactly. that general mode of procedure, and it is unfortunate that conscious use of it is not more general.

The Underlying Psychology

In arithmetic the first idea of number grasped by children is that of the positive integer; at that time "number" means integer to them. Later they have fractions and then number means not only integer, but integers and fractions. Still later they learn about negative number, and again the concept number is widened. Continuing thus, for those who go on into mathinto mathematics farther and farther, the concept number is made to include ever newer kinds of numbers, the irrational number, the complex number and even other realms of number, of which the majority of people never obtain any idea. These successive classes of number are each in turn a particular kind of number; but

when sufficient maturity has come to enable the individual to speak of "number" as including all of them, then the individual has what is called the general concept of number. This example is an illustration of the manner in which the mind acquires its store of ideas. The raw material of our thinking is the product of sense and mental perception. The actual objects, facts, and relations perceived are called individual notions. From earliest infancy there is an association of things perceived with previously assimilated things with which they are connected. This process of associating new individual notions with previously acquired stores of related notions is called apperception, and the resulting store of related notions is called the apperceptive mass. It is to be noted that after repeated observation of related particular notions, we find ourselves analyzing them, ignoring their individual peculiarities and building up out of their common characteristics a more general idea called the general notion. Thus, reverting to our example, it is a peculiarity of integers that they may be used in counting, whereas this is not a characteristic which is common to all numbers; so in the general idea of number, there is no implication that they may all be used in counting, for example, the negative numbers. This general notion is a mental product formed by a process of reflection. This general notion in turn is subject to modification as new particular instances of it are encountered in life; this fact also is typified in the constantly changing idea of number outlined above. The habit of forming these general ideas is one of the distinguishing characteristics of the human race, and is one of the particular products expected from the training given children in school. For convenience the essentials of the process are:

1. The possession of a store of previously acquired notions, the apperceptive mass. 2. The perception and apperception of individual notions by a process of observation. 3. The formation of a general notion out of these individual notions by a process of reflection. 4. The elaboration of this general notion

through use of it in the observation and perception of new particular instances.

Teachers will recognize in this the elaboration of the familiar dictum, teach the particular before the general, the simple before the complex, the concrete before the abstract. The object in making this elaborate statement is to call attention to the elements of the process. Corresponding to this psychological theory, there is the general policy of instruction to which we shall now turn.

The Essentials Of Method

Five stages of instruction on a new idea will be indicated. For convenience these will be labeled "Preparation," "Presentation," "Generalization," "Formulation," and "Application." These will be taken up in order.

Preparation. Thorough comprehension of an individual notion is conditioned upon success in associating itwith the appropriate apperceptivemass. It is obvious that in the child's mind the apperceptive mass upon any subject may be dormant and so in poor condition for the reception of a new idea. Here the experienced teacher finds her first opportunity to show her skill in rousing properly that portion of the previous experiences of her class which will aid them in assimilating the new thought of the coming lesson. She brings into the fore ground of their conciousness those facts, processes, truths, and relations which in her experience are necessary to enable her pupils to have a feeling of security, of familiarity in dealing with the new idca and which will enable them to grasp it with the least strain. For example, in developing the law for squaring a binomial, it is wise to recall, at the begining of the lesson, the meaning of binomial and of the square of a number; in teaching how to add two columns of numbers, it will be well to make certain, in the beginning of the lesson, that the pupils recall the meaning of "tens" and units." The advantage of this preparation for the lesson is that the teacher guards against the disastrous interruptions in the presentation of a new idea involved in going back to recall some realatively more elementary idea necessary in the develop

ment.

In this stage of preparation may properly come an attractive statement of the object of the lesson, designed to get the interest of the class.

It is important to keep in mind that this is only the preparation for the real business of the day. This stage should take only such time as is necessary to accompolish the end in view. It is worth repeating that in this stage of the lesson, the skillful teacher often shows her great superority over her less skillful colleagues in the manner in which she prepares her class for the reception of the new idea the preparation being shown by the lack of strain which attends the apperception of the new idea by her pupils.

Presentation. The next step in the lesson is that of presenting to the class particular instances of the general notion. These individual notions need to be selected with discrimination in order to bring out the essential characteristics of the general notion. There must be sufficient variety in order that the pupils may not get the idea that the general notion is limited to any special form; and there must be sufficient repetition so that the essential characteristics may stand out prominently. Variety in presentation also makes for interest, but that must, for the present, be considered only an incident. The experienced teacher will be watching for the opportunity to pass to the general notion, for the presentation of these particular notions is only a means to that end. Here there is often waste, in that too many particular cases are given; but more commonly there is even greater waste in that too four cases are given, with the result that the pupils are forced to pass on to the general idea before they are prepared for it. Here, again, the teacher of experience shows her skill. She encourages the mentally alert to generalize as soon as they can, and continues to assist the slow with additional special cases. This is the place for sympathetic, careful teaching. In passing, it may be said that objective work and concrete illustrations have their place especially in this stage of the lesson.

Generalization. We have now arrived at the most important part of the whole lesson; it is the goal-namely, the formation of the general idea. This is the place where the previous parts of the lesson are tested. Generalization calls for the simultaneous contemplation of the individual notions presented, analysis of them to determine their common characteristics,

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