Invited Paper



Many children in the U.S. initially come to understand the equal sign operationally, as a symbol meaning “add up the numbers” rather than relationally, as an indication that the two sides of an equation share a common value. According to a change-resistance account (McNeil & Alibali, 2005), children's operational ways of thinking are never erased, and when activated, can interfere with mathematics learning and performance, even in educated adults. To test this theory, undergraduates practiced unfamiliar multiplication facts (e.g., 17-times table) in one of three conditions that differed in terms of how the equal sign was represented in the problems. In the operational words condition, the equal sign was replaced by operational words (e.g., "multiplies to"). In the relational words condition, the equal sign was replaced by relational words (e.g., "is equivalent to"). In the control condition, the equal sign was used in all problems. The hypothesis was that undergraduates' fluency with practiced facts and transfer problems would be hindered in the operational words condition compared to the other conditions. Results supported this hypothesis, indicating that the activation of operational thinking is indeed detrimental to learning and transfer, even in educated adults.