Comparative studies aim to identify and explain differences of homologous
phenomena in two or more contexts. Comparative studies of mathematics
teaching and learning are undertaken with a variety of purposes and methods,
and their results and interpretations remain the subject of fierce debates,
especially in the case of large-scale quantitative surveys such as PISA. Even if
the measurement of student performance is not its central preoccupation,
didactic research is certainly concerned with these debates. This paper first
proposes a model for clarifying the levels at which comparison is done, based
on the anthropological theory of didactics. Using this model, we then propose
a synthetic analysis of a selected body of international comparative research
on mathematics education (from large-scale surveys to small-scale binary
comparisons in doctoral projects) with the particular aim of understanding
how the different studies differ and relate.