Two Factors Involved in Successful Individualized Mathematics Programs

Abstract

The past decade has witnessed a tremendous growth in individualized instruction at the community college level. And for better or worse, the greatest growth seems to have occurred in the area of mathematics. Rare indeed is the community college mathematics department which has not at least considered the implementation of an individualized program for some of its course offerings. Unfortunately, it has been the experience of this author that the effectiveness of these programs usually fails to reflect the effort imvested in the program by the faculty involved. However, this lack of success, with few exceptions, is not reflected in the popular literature. A consideration of only those articles in the most frequently read teacher journals would lead one to believe that individualized instruction at the community college level has been an overwhelming success. This should not be surprising, for as a general rule only those programs which are successful are submitted for publication. The great many failures go unreported. But understandable as it might be not to report one's own unsuccessful program, it makes it very difficult to assess the overall effectiveness of individualized instruction. Thus, we must turn to the more scholarly literature, such as doctoral dissertations and research journals, where results of both a positive and negative nature are more apt to be reported. And rather than simply tabulating how many individualized programs were successful and how many were not, this paper will attempt to show a relationship between program structure and success in individualized mathematics programs at the community college level. This would seem to be the most useful approach, since the question is not really whether or not individualized instruction is successful or not, for obviously some programs are, but rather, what can be done to make individualized programs more successful. It should be noted, here, that a successful individualized program is defined as one which has proven to be at least as effective as the traditional program to which it was compared. For the purposes of this paper, program structure will be defined as the restrictions placed upon the student by the design of the program. The two extremes of program structure would be simply turning a student loose in a room full of instructional materials and devices and leaving him on his own; and requiring that a student perform certain specific actions at certain specific times every day, and every minute of every day. That is, a highly structured program would give a student no freedom to choose his own actions, and a loosely