Models of individual trajectories in computer-assisted instruction for deaf students.

In this report we present a new approach to evaluation of curriculum. Many of us who have been engaged in curriculum reform efforts have been dissatisfied with the wait-ahd-see approach required when classical evaluation of a new curriculum is used. We have in mind evaluation by comparing pretests and posttests, with an analysis of posttest grade-placement distributions as a function of pretest distribution and exposure in some form to the new curriculum. In line with approaches used in other parts of science, it is natu-ralto ask if a more predictive-control approach could be used and made an integral part of the curriculum to ensure greater benefits, especially for the disadvantaged or handicapped student. The approach discussed in this report is aimed precisely at this question. The strategy is to develop a theory of prediction for individual student progress through the curriculum, to use this predictive mechanism as a means of control by regulating the amount of time spent on the curriculum by a given student, and to "bhereby achieve set. objectives ·for the grade~placement'gains of a student. Such an approach also calls for individualization in the objectives of a course, for it is unrealistic to expect all students to make the same gains in the same amount of time, or to expect that the slowest students can cover as much material as the best students simply by 1 spending additional time in a course. Consequently, even with a differential approach to the amount of time each student may spend in the curriculum , it is still not reasonable to impose a uniform concept of grade-placement gain on all students. Another important feature of our approach to the prediction of student progress is to separate the global features of the curriculum (described in the next section) by a simple differential equation from the global individual parameters characteristic of the individual student. lnmany respects, the estimation of the global individual parameters corresponds to the fixing of boundary conditions in the solution of differential equations in physics. In our case the boundary conditions correspond to the characteristics of the individual student and the differential equation itself to the structure of the curriculum. We do not know if the differential equation that fits the structure of the elementary-mathematics computer-assisted instruction (CAl) curriculum developed at Stanford over a number of years will be the characteristic differential equation of other curriculums. The generality of the qualitative …