The present paper questions the validity of Macnamara's (1966) finding that teaching arithmetic through a bilingual's weaker language leads to retardation in problem arithmetic. By comparing the performance of immersion pupils on an Irish (as a second language) version of the problem arithmetic test with the performance of non-immersion pupils on an English (as a first language) version, Macnamara's study confounds bilinguals' competence in arithmetic with their ability to demonstrate this competence when tested through their weaker language. Macnamara's attempt to demonstrate the equivalence of Irish and English versions of the problem arithmetic test fails to take account of probable differences in Irish competence between the immersion pupils in the pretest and those in the main study. Macnamara rejects Cummins' criticism in a brief reply. Cummins' reply to Macnamara's reply is also provided. (Author/CFM)