In the attempt to account for striking differences between learning activities of immigrant mathematics students from the former Soviet Union and of their native Israeli classmates, the authors introduce the notions of "actual" and "designated identities." These identities are subsequently presented as important factors that mold learning and influence its effectiveness. Since designated identities may be seen as personalized, "customized" versions of people's cultural heritages, the authors present a story of the wider culture making its way into individual learning processes. (Contains 4 tables.) [For complete proceedings, see ED496845.]