Percentages versus Rasch estimates: alternative methodological strategies for replication studies in mathematics education

We present an external close replication of the 1985 Fischbein et al. study about intuitive models of multiplication and division. We administered two batteries of mathematics items developed in the original study, via a spiralling process, to a quota sample of 903 students attending grade 7. Compared with the analytic strategy based on the count of correct answers employed in the original research, our study goes a step further as we propose a methodological approach that guarantees measurement invariance, thus allowing for the direct comparison of different groups of students and/or items. The advantages of Rasch estimates compared to percentages of correct answers over the total are critically discussed to show why the former should be considered as more robust than the latter.