A stage-sensitive written measure of multiplicative double counting for grades 3-8

We report on a written measure of multiplicative double counting (mDC), form children’s reasoning. Our aim is to apply theory students’ cognition validate for grade 3–8 students as proxy interviewing. The 4-item consists hint-free and hint-containing word-problems, following the fine-grain method that distinguishes prompt-dependent from prompt-independent stage. Using mixed methods, we analyzed individual, cognitive interviews conducted with fourth ( n = 37); administered third in three schools serving large proportions multilingual learners 406), Rasch modeling determine unidimensionality, item difficulty, person ability levels. found validly approximated interview-inferred stage distinctions, thus quick, stage-sensitive mDC discuss contributions our design validation processes practice.