Item Relational Structure (IRS) graphs analysis is presented as a means for hierarchical structuring of test items. IRS graphs can be prepared from student performance scores obtained from pre-/post-tests, formative tests, and so on. This paper, based upon actual examples, discusses methods for construction and utilization of IRS graphs. In the first part, methods for construction of IRS graphs, expressed as a form of digraphs, are proposed. Manual construction methods are also shown. In the second part, a number of ways of using IRS graphs are presented. IRS graphs may be applied to (1) pretest analysis for courseware implementation, (2) instructional design, (3) formative evaluation, (4) analysis of the process of concept formation, and (5) analysis of the structure of the curriculum. Finally, four examples of actual application-each of them based upon an analysis of elementary school arithmetic instruction-are given. These clearly show the effectiveness of IRS graphs as an analysis technique and that they are applicable not only to diagnostic and formative evaluation but to curriculum evaluation as well.
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