A stage-sensitive written measure of multiplicative double counting for grades 3-8. (September 2022) - Tzur, Ron; Johnson, Heather Lynn; Davis, Alan; Hodkowski, Nicola M.; Jorgensen, Cody; Wei, Bingqian; Norton, Anderson
Abstract: We report on a written measure of multiplicative double counting (mDC), a form of children's multiplicative reasoning. Our aim is to apply theory of students' cognition to validate a written measure for grade 3–8 students as a proxy of interviewing. The 4-item measure consists of hint-free and hint-containing word-problems, following the fine-grain measure method that distinguishes a prompt-dependent from a prompt-independent stage. Using mixed methods, we analyzed individual, cognitive interviews conducted with fourth grade students ( n  = 37); administered the measure to third and fourth grade students in three schools serving large proportions of multilingual learners ( n  = 406), and conducted Rasch modeling to determine unidimensionality, item difficulty, and person ability levels. We found that the written measure validly approximated interview-inferred stage distinctions, thus serving as a quick, stage-sensitive measure of mDC reasoning. We discuss contributions of our design and validation processes to theory and practice. Highlights: Written assessment – a proxy for cognitive interviews. Initial form of multiplicative reasoning (grades 3–8). Stage distinction: prompt-dependent vs prompt-independent. Rasch modeling for validation.