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.