Within the research on bilingual learning, first studies have revealed that content learned in one language is retrieved more slowly when participants have to switch language from instruction to testing (i.e., language-switching costs, LSC). These costs are attributed to language-dependent knowledge representations. However, the cognitive mechanisms underlying LSC are still largely unknown. We investigated these mechanisms by using strategy as well as translation self-reports and by analysing oscillatory parameters in the electroencephalogram (EEG). Thirty-six university students learned arithmetic facts of three different operations over four days either in English or in German. Afterwards, they were tested in both languages with concurrent assessments of self-reports and electrophysiological activity. As expected, LSC in response latencies were observed in all arithmetic tasks. More importantly, analyses of self-reports and EEG revealed that both translation processes and calculation procedures contribute to LSC, with translation processes being the main cognitive mechanism underlying LSC. These results corroborate previous findings of language-dependent knowledge representations in arithmetic fact learning and shed new light on the cognitive mechanisms underlying LSC and possible educational consequences.