Language and the algebraic mind

Natural language is often depicted as the sine qua non of mathematical thinking, a view buttressed by findings of language-of-training effects among bilinguals. These findings, however, have been limited to studies of arithmetic. Here, we asked whether algebraic thinking differs. We trained Chinese–English bilinguals and English monolinguals to solve arithmetic and algebra problems in either Chinese or English and tested them on new and old problems in both languages. In Experiments 1 and 2, bilinguals solved arithmetic problems faster in their trained than untrained language, and old arithmetic problems were solved faster than new ones. However, both the language-of-training and novelty effect were reduced or eliminated when learning algebraic rules. Strikingly, when English monolinguals were given Chinese problems, they successfully learned to solve the algebraic—but not arithmetic—problems. Together, the findings suggest that—unlike rote arithmetic—algebraic rules need not be encoded in natural language.