Curriculum-based measurement of basic arithmetic competence: Do different booklets represent the same ability?

Abstract

An important prerequisite of progress monitoring as one source to support instructional decision-making is the existence of equivalent booklets. This study assesses this prerequisite with respect to a German elementary school math curriculum-based measurement instrument (LVD-M 2-4; Strathmann & Klauer, 2012). Every second week of a 19-weeks period, n = 108 third and n = 109 fourth graders (regular instruction) completed one of ten parallel booklets, each containing 24 arithmetic tasks. Analyses with (generalized) linear mixed models showed that in both grades the between-booklet variance was so small in relation to the between student variance that it was practically irrelevant. This corresponds to the key assumption of the binomial model that equivalent scores from different booklets reflect the same ability. While item difficulty varied within some of the tasks, the effect was insubstantial in comparison with the variance between students. These findings were replicated in two intervention samples of an RTI study. The parallel booklets can therefore be regarded as equivalent for typical applied purposes. Implications of these findings for curriculum-based measurement and booklet design are discussed.