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

ABSTRACT

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.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Sources: search.crossref.org – www.researchgate.net – scholar.google.com – data updated at 9th June 2022.

2 “Lire” was the name of the currency in Italy before the introduction of the Euro in 2002.

3 “Ability” is a technical term used within the framework of the Rasch analysis to refer to the latent trait that the instrument used to collect data purports to measure. In this study, students’ ability thus refers to their mathematical attainment.

4 A detailed description of the procedure employed to construct the SC-index has been provided in Cascella (2019) along with a description of the procedure to deal with missing values and data imputation.

5 INVALSI collects data at grade 2 and 5 (primary school), grade 8 (lower secondary), and at grade 10 and 13 (secondary school). No data are collected in any other grade. Nonetheless, since lower secondary school spans from grade 6 to grade 8, and since our sample units are schools (instead of students), information collected at grade 8 by INVALSI can be considered reliable to acquire the information we need (to construct the SC-index).

6 Just a few differences between results from our study and the original one were found. The presence of differences between the results of the original study and our replication could depend on many causes (included the different samples, the changes in Italian curriculum during the last 35 years, and so on) that could be researched. In any case, the available data do not allow us to conjecture any interpretation and questioning the nature of those differences is beyond the scopes of this article.