Math Teacher 

Abstract: THE mathematical curriculum in our elementary and secondary schools faces a serious dilemma when it comes to geom etry. It is easy to find fault with the tra ditional course in geometry, but sound advice on how to remedy these difficul ties is hard to come by. The Commission on Mathematics of the CEEB, the School Mathematics Study Group, the Illinois Project, and many other curricular reform groups at home and abroad have tackled the problem, but with singular lack of success or agreement. On the other hand, the "new math" has made great strides in arithmetic and algebra that seem to be acceptable to all except the congenital standpatters who resist change of any kind. We are, therefore, under pressure to "do something" about geometry; but what shall we do? In this article I shall discuss the reasons for the present state of confusion and make suggestions for mod est first steps toward clearing it up.

Abstract: THE advent of the computer has served as a catalyst to the turmoil in mathematics and mathematics education during the past decade Mathematicians have run the gamut from 1950 when only a few innova tive souls ventured to use computers to explore solutions of mathematical rela tionships to the present time when a majority of those who make extensive use of mathematics do so by means of a com puter Debates over whether the computer influences the essence of mathematics would not be difficult to locate, but there is no debating that the use of mathematics, now and in the future, is directly related to computer technology And how is so formidable a tool related to teaching students both the essence and use of mathematics? That question has created a considerable dilemma for mathe matics educators The pure mathematician is very likely to contend that the essence of mathe matics can be explored without appeal to the computer But to the mathematics educator that contention may be some what academic and esoteric with respect to his responsibility to students, the vast majority of whom are likely to be users of mathematics rather than creators of mathematics in any pure sense Can the computer assist a greater num ber of students to grasp basic principles? Can the computer strengthen and broaden students' understanding of basic prin ciples? Can mathematics teachers afford not to utilize so formidable a mathematical device when motivation poses a major problem? Will the mathematics learned by our students be more functional if they also know the role computers play in its use? Should small computers be as integrated into mathematics programs as the slide rule has been in the training of engineering students? Early attempts to use the computer with secondary mathematics students have generally treated it in isolation from ex isting programs Indeed, until more was known about the availability of teachers to work with computers, the ability of students to master computers, the acces sibility of computers, specific ideas that can be illuminated by the use of compu ters, etc, experimentation necessarily had to be conducted in a manner that avoided the fragmentation of existing programs It now appears that in school districts that have explored those questions, the next move will be to explore ways of using the computer to strengthen existing mathematics courses One must be careful to recognize that with any innovative de vice as new as this there exist schools all along the continuum, from those that ig nore the device completely to those that see it as the basis for their entire program Computers do have a role to play in mathematics education, but there is un

Abstract: NOW that programmed instruction has gained some acceptance in the schools, various questions concerning its format, applicability, etc, are being investigated in doctoral research studies Not only are some earlier questions being answered by the growing body of research, but addi tional areas have been indicated as neces sary and fruitful for study The purpose of this paper is to examine recent research in the use of programmed instruction in mathematics