How Language Influences Thought: The Case of Multiplying Fractions

This study addresses the question of whether and how language influences mathematical cognition. Canadian students in Grades 4–7 (N = 348) were asked fraction multiplication questions in one of the two ways. In one condition, students were asked a series of standard multiplication questions (e.g. What’s ½ × ½?). In the other condition, children were asked the same multiplication questions but the word “of” replaced the “×” symbol (e.g. “What’s ½ of ½?”). We hypothesized that the “of” condition would lead to better performance due to its familiar use to signify a proportion of a quantity or amount, encouraging children to interpret fraction multiplication as a “fraction of a fraction.” Contrary to our predictions, children in the “×” group answered more questions correctly and made fewer errors than children in the “of” group. While the word “of” prompted more diagrammatic reasoning, the “×” symbol prompted higher use of purely symbolic reasoning. Thus, diagrammatic reasoning did not help make fraction multiplication more intuitive and accurate. These findings suggest that changing the question format alone is insufficient to improve the comprehension of fraction multiplication. Given the poor performance of both groups, more research is needed on effective ways to improve the teaching and learning of fraction multiplication.