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educational sleep thinking that mathematics will always be the mathematics of Euclid, and that Euclidean geometry will always hold the place of eminence it has held since the days of the Greeks. But the truth is that mathematicians have drastically changed their concept of mathematics during the past few decades and that, in a sense, they have changed their concept of how to attack mathematical problems. This changed concept has caught our schools and colleges in a deep curricular sleep. They were not anticipating the change and were not ready to cope with any change in their concept of the goals of mathematicians. As a result, staffs are not adequately prepared for the needed changes.

The lesson the educational world must learn from our present experience is that we must always be ready for a change in the mathematician's concept of his subject and, with the rapid rate of growth of the subject, it might well happen that in the next 50 or 100 years schools will again be called upon to bring their teaching up to new standards. Knowing that this is likely to occur, the schools must not be caught unprepared a second time. To avoid this, there can be but one answer, namely, adequate inservice education provisions for the teachers. In effect, the schools must provide schools for their teachers and make the necessary expenditures of money and time to encourage teachers to attend them. It has often been said that learning is a never-ending activity for the human being. Most certainly, the good teacher and the good teaching staff will never cease learning; in particular, they will never cease learning mathematics. It cannot be otherwise, for how can a teacher instill the love of learning if the teacher does not know what it means to love learning sufficiently to pursue it constantly?

Group Work Sessions

Promising Practices in Inservice Education of Mathematics Teachers

Promising Practices in Small Schools and Small School Systems

Chairmen for the Session:

DR. MILTON W. BECKMAN

DR. JAMES H. ZANT

HIGHLIGHTS OF THE REPORT

1. Regional conferences of high school mathematics teachers should be organized in order to examine and discuss the evolving new content of the subject.

2. Some military officers who have strong backgrounds in mathematics might be prepared through inservice programs and engaged to teach in the public schools. The same applies to mothers whose children have grown up.

3. Teaching machines, tape-recorded lessons, and television-film lessons are useful teaching aids.

4. As a means for improving teachers' competence, they could be sent to graduate schools and teacher institutes, with the tuition paid by the teachers' school.

5. Local colleges and State departments of education should be called upon for assistance in formulating and conducting inservice education programs.

6. State-approved colleges and universities should be encouraged to establish appropriate correspondence courses to meet the particular needs of mathematics teachers who cannot attend campus classes.

INTRODUCTION TO THE REPORT

This discussion group decided to report according to the following plan:

1. Identify the problem situations which small schools face in establishing and conducting inservice programs for teachers of mathematics.

2. Suggest possible ways and means by which small schools can develop inservice mathematics programs and/or strengthen and improve those already in operation.

The problems on inservice education encountered by small schools or small school systems may also be encountered, to a lesser extent, by medium-size or large schools systems. Such matters as the lack of adequate funds, sufficient personnel, program flexibility, proximity to area colleges, and other factors are present to a greater degree in

small schools than they appear to be in medium size or large schools. With this in mind, the group has focused on problems as they exist in small schools, and has given illustrations of possible solutions geared to problem situations in these schools. The problems identified, and the solutions suggested do not necessarily preclude some applicability to the larger schools.

THE REPORT

Problem Situation 1.-Lack of understanding by teachers and administrators that there is an imperative need for extensive reeducation and that additional content covering the newer concepts of mathematics must be learned.

Suggested Solutions.-The group's discussion on the first problem situation which they identified resulted in the following suggested solutions:

1. Identify knowledgeable persons in the field of mathematics to present the nature of the problem, data, and materials to mathematics teachers and other faculty members, including superintendents and principals. 2. Establish regional conferences sponsored by such organizations as State mathematics associations, National Council of Teachers of Mathematics, Mathematical Association of America, American Mathematical Society, State colleges and universities, and State departments of education, in order to examine and discuss the evolving new content in mathematics. 3. Promote programs which provide for the study of the evolving new courses in mathematics at professional institutes, State conventions, and meetings of school administrators.

4. Read and circulate among mathematics teachers the newsletters and pamphlets issued by groups now sponsoring curriculum revisions.

5. Provide mathematics teachers with adequate supplies and equipment for inservice programs.

6. Urge the establishment of a clearinghouse at the area college to provide services and faculty resources to assist school mathematics teachers in finding solutions to their professional problems. A college staff member should be assigned by the college to discharge this responsibility. Problem Situation 2.-Absence of a well-defined mathematics curriculum K-12, designed approximately according to content and grade placement.

Suggested Solutions.-Five suggested solutions came out of the discussions on the second problem situation:

1. Reexamine local mathematics arriculums in light of current proposals by groups such as the Commission on Mathematics (College Entrance Examination Board, Box 592, Princeton, N.J.), University of Illinois Committee on School Mathematics (University of Illinois Press, Urbana), School Mathematics Study Group (Drawer 2502-A, Yale Station, New Haven, Conn.), University of Maryland Mathematics Program (College of Education, University of Maryland, College Park, Md.), and

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