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Procedures for grouping students into homogeneous subsets have long interested educational researchers. The research reported in this paper is an investigation of a set of objective grouping procedures based on multivariate analysis considerations. Four multivariate functions that might serve as criteria for adequate grouping are given and discussed; a method for optimizing these functions is also described. The set of procedures is illustrated through application to data from two samples of students, each student with scores on either ten or eleven subtests of a criterion referenced mathematics inventory. The results indicate that the procedures discussed provide a promising means for grouping students to minimize classroom heterogeneity. (Author)

This paper describes the development of a criterion-referenced test. The Prescriptive Mathematics Inventory (PMI) was developed to measure 400 stated behavioral objectives. The test consists of three overlapping levels with the objectives chosen to cover 90 to 95 per cent of the mathematics curriculum nominally taught in grades 4 through 8. Each of the 400 items was designed to measure one of the 400 objectives, the criterion of mastery of each objective being that the student find the correct answer to the corresponding item. Two types of errors can be made when responding to each item: (1) by marking the correct answer when in fact the criterion behavior has not been mastered, and (2) by missing the item even though the criterion behavior has been mastered. To cope with these two types of errors the PMI provides a unique answer grid for the recording of answers to items. The PMI was tested with a group of fifth and seventh graders and it was noted that the students appeared to become bored or tired because of the length of the PMI. (CK)