Many mathematics problems can be solved in different ways or by using different strategies. Good knowledge of arithmetic principles is important for identifying and using strategies that are more sophisticated. For example, the problem "6 + 38 - 35" can be solved through a shortcut strategy where the subtraction "38 - 35 = 3" is performed before the addition "3 + 6 = 9," a strategy that is derived from the arithmetic principle of associativity. However, both children and adults make infrequent use of this shortcut and the reasons for this are currently unknown. To uncover these reasons, new sensitive measures of strategy identification and use must first be developed, which was one goal of our research. We built a novel method to detect the time-point when individuals first identify an arithmetic strategy, based on trial-by-trial response time data. Our second goal was to use this measure to investigate the contribution of one particular factor, attention, in the identification of the associativity shortcut. In two studies, we found that manipulating visual attention made no difference to the number of people who identified the shortcut, the trial number on which they first identified it, or their accuracy and response time for solving shortcut problems. We discuss the theoretical and methodological contribution of our findings and argue that the origin of people's difficulty with associativity shortcuts may lie beyond attention.
Keywords: Associativity; arithmetic; attention; conceptual understanding; measurement; strategy.