Discriminant Analysis of Achievement Characteristics for Multi-Grade Grouping of Students

THE GROUPING of students in e le m entary and secondary schools has traditionally been accom plished on the basis of age-grade criteria. This practice has been modified somewhat in recent years by the grouping of students on the basis ofintelli gence, aptitudes, and achievement across several grade levels (4). Multi-grade grouping of students with common ability or achievement back grounds represents one major change from the traditional practices. These latter variations, however, have raised new problems in the identification of hetero geneous and homogeneous groups as well as addi tional problems concerning the purposes and effi ciency of certain aspects of the curriculum. Intelligence and achievement tests have been used widely in the classification and placement of pupils for various purposes and their use will probably in crease as traditional age-grade curricular stand ards become supplemented more and more by special programs. One type of program in high schools and colleges may involve a sequence of courses, suchas in professional or vocational studies, in which the discipline requires the student to complete one course prior to another; in this case, the aptitude or capacity to complete the entire sequence becomes the important variable, and the placement of a stu dent in the sequence generally de pends on the cour se s completed by the student. Another type of m u 11 i grade grouping (viz., cluster grouping) seen in the intermediate grades and junior high schools requires a homogeneity of abilities and interests but does not involve a fixed sequence of learning over a series of courses. With the advent of teaching machines, pro grammed instruction, and other concentrated rou tines, further applications of multi-grade grouping has become possible throughout all grades. The in itial achievement levels of students and their accel eration rate have become important for the place ment, or classification, of students into these pro grams as well as the evaluation of programmed in struction. The efficient classification of students for in structional purposes poses several problems to ed ucators and guidance personnel. One major prob lem pertains to the use of test information in the planning and conduct of the educational program. The various aptitude, achievement, and intelligence test data must be combined in some form for an op timum grouping of students. The grouping of stu dents with similar achievement and intelligence characteristics from several grade levels requires reliable measures of their educational development and potential, and much of the information available from existing standardized tests should prove to be of value. The California Achievement Test (CAT) is one of the most widely used achievement tests in the Unit ed States. The grade placement scores, derivable from the raw scores on each of the six subjects, in dicate the grade level commensurate with students' achievement, and some estimate ofastudent's grade qualification is immediately available from an over-all average of the subtest grade placement scores (9). The subtests have been used success fully in the prediction of course grades (2,3), but several problems are involved in the combination of the subtest scores for purposes of grouping stu dents. The subtests are known to correlate signi ficantly at most grade levels (3), and the subtest variances differ in magnitude. These fact materi ally affect any combination of the subtest scores and suggest that a differential weighting of scores is