This article examines whether the way that PISA models item outcomes in mathematics affects the validity of its country rankings. As an alternative to PISA methodology a two-parameter model is applied to PISA mathematics item data from Canada and Finland for the year 2012. In the estimation procedure item difficulty and dispersion parameters are allowed to differ across the two countries and samples are restricted to respondents who actually answered items in a mathematics cluster. Different normalizations for identifying the distribution parameters are also considered. The choice of normalization is shown to be crucial in guaranteeing certain invariance properties required by item response models. The ability scores obtained from the methods employed here are significantly higher for Finland, in sharp contrast to PISA results, which gave both countries very similar ranks in mathematics.