ADMINISTRATIVE PROBLEMS Under the administrative problems five seem of great importance: Those of time, money, personnel, location, and supervision. First, time must be found for the teachers to take courses and time for the supervisors or instructors to prepare them. The solution suggested here is that this time be made a permanent part of a planned program within a school or school system and that teachers and administrators accept the principle that inservice education shall continue indefinitely in the future and always be part of the work of the school and the teachers in it. Second, the problem of money. Obviously, it costs something to provide books for teachers, salaries for instructors, or payment for preparing special TV programs. This fact will require local budgets to accept such a responsibility permanently. Third, personnel. Both people to teach and people to attend these programs must be found. There are a few college people who have the right combination of interest and background in both content and methods to be able to appeal to the teachers. Using poor instructors has hurt inservice education programs in the past. Teachers who choose to take classes not required for every teacher in the system must be motivated to the hard intellectual activity involved. Not only their natural human inertia, but also their traditional practical viewpoint, must be overcome. Teachers must realize that although inservice education may be of no immediate application in the classroom, it may still be very valuable. The solution to the personnel problem may well be that active leadership must come more and more from those within the school system. People must be selected to teach with this purpose in mind. They must be educated by the school system and much of their regular time must be alloted for the workthis rather than that such responsibilities be given as an additional load. Also, these people must be provided with a budget to carry out their work. Fourth, the location of courses and conferences. In many parts of the country the location must be considered carefully, since teachers cannot be expected to travel long distances to take courses and attend conferences. As long as such an activity is considered an emergency, teachers will put forth great effort, but if it is to be a permanent part of their re-education, the opportunity must be brought closer to them. Fifth, the supervision of inservice education must be in the hands of a person trained in mathematics. Supervisors must not be nonspecialists and they must not share their time with other duties, as happens sometimes when a person who is given responsibility for a mathematics inservice program is one whose whole education and background are in other areas. PROCEDURAL PROBLEMS After the technical details of time, money, etc. have been taken care of, the person in charge of an inservice education program for teachers must decide what methods to use. Let use summarize very briefly 10 categories abstracted from all the foregoing details which apply to content and three which apply to methods of teaching. As far as increasing the background in mathematical content which teachers know, we have mentioned the following: Individual reading by teachers, study groups with no outside help, discussion groups with an outside leader, classes conducted for the teachers, conferences and lectures, cooperative programs with nearby colleges, published bulletins and bibliographies, consultation with the teachers, work on the curriculum, institutes, and workshops. With regard to methods of teaching it certainly seems as though general conferences will continue for motivation and inspiration. Also the following will doubtless continue: visits of supervisors to techers followed by individual conferences, intervisitation among teachers, and finally, but to a less extent, formal courses in methods of teaching provided within the school system. Characteristics of a Desirable Inservice Education DR. HENRY VAN ENGEN HIGHLIGHTS OF THE ADDRESS 1. In mathematics we are experiencing a rejection of the traditional approach in favor of a modern one. 2. In order to prepare teachers for presentation of the new mathematics, the first efforts were directed only to teaching more subject matter. Those efforts are now somewhat discredited. 3. School administrators should provide leadership for modernizing mathematics instruction. 4. Supervisors should carry active responsibility for inservice education of teachers. 5. School system should provide on-the-job courses for its teachers. These courses should concentrate on the specific needs of the school curriculum. 6. Summer institutes and summer schools offer opportunities for inservice education. 7. Television and radio programs provide opportunities for inservice education in some communities. 8. Teachers need careful conditioning before being asked or permitted to teach the new mathematics. 9. School corporations should bear the cost of the teachers' inservice education. THE ADDRESS Archibald MacLeish opened a recent television play entitled "The Secret of Freedom" with the words, "Ours is a strange time in America." MacLeish was referring to political, economic, and religious thought in America. His words apply equally well, however, to many other phases of American life. The technological explosion that has taken place since World War II has caused us to reevaluate our usual way of life and to seek other, and still better, ways to preserve that which we hold even dearer than life. In many instances, brute facts have caused us to do things which are strange in the sense that they are not usual. Problems in education have much in common with problems in Government or problems in family life. It is only in details that things are different. In mathematics and science we are experiencing a rejection of a traditional approach for one needed by the contemporary mathematician and scientist in order to work on pressing social problems. In view of the problems confronting our society, there can be no excuse for teaching mathematics in the schools unless it encourages our youth to think like mathematicians. Of course, a similar statement could be made about art, music, social science, science, and any other subject taught in the schools. Schools do have their utilitarian objectives, but above all they are working with the intellect of the young people and this intellect must be so developed as to enable today's youth to understand tomorrow's mathematics. This is a primary function of the schools. Today's mathematics is somewhat different from yesterday's mathematics. Today there is a greater emphasis on solving problems in the large, a more intense search for related structures in various branches of mathematics, a desire to solve groups of problems rather than seek a solution for a particular instance. Since mathematics has changed during the past few decades, it goes without saying that the mathematics of our schools and colleges must change. In the schools, many staff members have been prepared to teach the old mathematics. Such preparation is not suitable for today's teachers. This raises a problem for those whose responsibility it is to provide leadership for an educational program. How does one encourage a staff to keep up to date, to rethink a mathematics program, and to build a new program? The first reaction of many people who became concerned about mathematics in our schools was to teach the teachers more mathematics. As a result, institutes were established whose emphasis was on teaching mathematics to teachers. It soon became clear that some of these institutes were overshooting their mark. The advanced mathematics courses offered were not suitable for teachers and in many instances had little or no bearing on the mathematics taught in the schools. The institute courses bore no fruit in terms of the ultimate objective: to change the attitudes of the teacher and the way he teaches in the classroom. This does not mean that teachers should not be taught more mathematics. Indeed, more mathematics for the teacher is a necessary step toward improving teaching and the curriculum, but it is not sufficient. As evidence, one need only cite many recent college programs whose spirit was not much different from that of the high school programs. College staffs know more mathematics than high school staffs, but the spirit, and sometimes the content, was not much different from that offered in the high schools. Now we come to an important question: What are some of the desirable characteristics of a good inservice program in mathematics for teachers of grades 1 through 12? Leadership The schools cannot improve either the curriculum or the inservice program without adequate leadership. Superintendants and principals set the intellectual atmosphere in which a staff must work, and this atmosphere will condition the attitudes, the working habits, and the instructional goals of the staff. No staff can do effective work in an educational atmosphere which is inimical to the spirit of education itself. Creating the proper intellectual atmosphere is one of the most important tasks of an administrator. It is particularly important in schools where the drive for academic excellence, social responsibility for education, and continued learning is not so strong as in colleges and universities. Once having established the proper climate for study and learning, the administrator is faced with the task of selecting someone to do the detail work and provide specialized leadership. No inservice program can function effectively without adequate leadership from the supervisory staff. In positions of this type the schools need vision as well as adequately trained personnel. The supervisor must know mathematics thoroughly in addition to vital facts about children, curricula, teachers, administrators, and administration. The supervisor must know the school system and the mathematics staff with all of its strengths and weaknesses. Without a knowledge of mathematics he is in the position of leading a staff without a certain knowledge of where to go. The supervisor must be able to make independent judgments concerning the value of certain mathematical topics. These judgments cannot be made without an understanding of the nature of the subject itself. Schools should not underestimate the amount of mathematical knowledge required of a supervisor of secondary mathematics. Although one should never underestimate the value of a knowledge of such things as basic principles of psychology and philosphy, and the basic techniques of supervision, it is also important not to underestimate the need for a knowledge of mathematics. All the values that one expects from the mathematics classroom rest on a sound mathematical program. Such a program cannot be developed by one who is insecure about the mathematical principles to be taught. On-the-Job Courses A program for the improvement of teaching and the development of a sound course of mathematical instruction will have as one of its |