Using Cluster Analysis to Solve Real Problems in Schooling and Instruction.

N

44

National Inst. of Education (ED), Washington, DC.

Cluster Analysis; Cluster Grouping; Computer Software; Correctional Education; Evaluation Methods; Instructional Improvement; Mathematics Skills; Quantitative Tests; Remedial Mathematics; Research Design; Secondary Education; Statistical Studies; Student Evaluation

This report describes cluster analysis methodology and illustrates its potential merits for educational research by describing a study designed to identify the natural subgroups existing among students beginning a secondary level remedial mathematics course. Cluster analysis forms groups of relatively homogeneous subjects represented in large data blocks that contain several different observations for each subject. While recently developed software packages make the computation more manageable, identifying the optimal number of clusters, and making sense out of them, requires considerable knowledge of the subjects and variables being clustered. Cluster analysis was applied to data from the two Prealgebra surveys of the Training and Employment Prerequisites Survey given to almost 1,500 wards of the California Youth Authority enrolled in remedial mathematics classes. The Prealgebra Surveys cover the skills and concepts most common to mathematics instruction up through grade 7. Results indicate that even fairly well prepared students will be unsuccessful in traditional remediation programs which focus first on mastery of all types of complicated computational skills. Instead, general mathematics instruction should consist of one course that redevelops basic concepts and skills for handling fractions and decimals, and another course on more advanced topics in general mathematics applications or an introduction to algebra where the requirements for complicated forms of computation are carefully controlled. (BS)

1985

ED251506