Linear Equation Flexibility Test-4 (LEFT-4): Introducing and empirically validating a short measure for procedural flexibility in multinational samples

Procedural flexibility is a key-component of mathematical knowledge and is commonly assessed by solving linear equations using the Tri-Phase Flexibility Assessment. Although well established, the Tri-Phase Flexibility Assessment is time-consuming for students to complete, and for researchers and practitioners to score. Given this background, we set out to introduce and empirically validate a short version, the Linear Equation Flexibility Test-4 (LEFT-4). We designed the LEFT-4 to be an ecologically valid assessment tool that can be administered in 20 minutes while retaining the long version’s psychometric properties for accuracy, flexibility, adaptivity, and potential flexibility. The LEFT-4 is based on multinational samples of secondary-school students, that is archival data from Finland, Spain, and Sweden (n = 791), China (n = 121) and Austria (n = 186). Short test versions were tested for unidimensionality, reliability, and representation of heterogeneous equation transformations and cross-validated in the other samples. On a psychometrical note, we showcase a novel method for reducing test lengths which exploits readily available computational powers. Furthermore, as an additional contribution to the field and to preclude jingle-jangle fallacy in the research on procedural flexibility, we provide a terminological synthesis of ambiguously used terminology on what Tri-Phase Assessments using linear equations assess. The existence of this shortened assessment is intended to encourage researchers and practitioners to assess and to study students’ accuracy, flexibility, adaptivity, and potential flexibility in solving linear equations. We provide the LEFT-4 in a ready-to-print and openly accessible version in Chinese, English and German.