Working Memory and ‘‘Choking Under Pressure’’ in Math

We examined the relation between pressureinduced performance decrements, or ‘‘choking under pressure,’’ in mathematical problem solving and individual differences in workingmemory capacity. In cognitively based academic skills such as math, pressure is thought to harm performance by reducing the working memory capacity available for skill execution. Results demonstrated that only individuals high in working memory capacity were harmed by performance pressure, and, furthermore, these skill decrements were limited to math problems with the highest demands on working memory capacity. These findings suggest that performance pressure harms individuals most qualified to succeed by consuming the working memory capacity that they rely on for their superior performance. For many people, the desire to perform their best in academics is high. Consequences for suboptimal performance, especially in examinations, include poor evaluations by mentors, teachers, and peers; lost scholarships; and relinquished educational and employment opportunities. However, in comparison to research examining the cognitive processes underlying skill learning and execution (e.g., Anderson, 1993; Ericsson & Charness, 1994; Rosenbaum, Carlson, & Gilmore, 2001), little work has addressed the causal mechanisms by which high-stakes situations result in disappointing performances. Even less is known about the characteristics of those individuals most likely to experience unwanted skill failures. Recently, researchers in cognitive and social psychology have begun to address these issues. Three recent studies have focused specifically on failure in mathematics. Ashcraft and Kirk (2001) examined how math anxiety undermines the performance of individuals who, in non-anxiety-provoking task domains, are highly competent. Schmader and Johns (2003) examined the cognitive mechanisms responsible for stereotype threat in math. Stereotype threat occurs when awareness of a negative stereotype about a social group in a particular task results in less-than-optimal performance by members of that group (Steele, 1997). And we (Beilock, Kulp, Holt, & Carr, 2004) explored the cognitive processes governing ‘‘choking under pressure. ’’ Choking, or performing more poorly than expected given one’s skill, occurs in situations in which the desire for high-level performance is maximal (Beilock & Carr, 2001). Surprisingly, these studies of diverse phenomena yielded similar conclusions concerning how suboptimal performance arises in mathematical problem solving. All involved working memory, a short-term memory system that maintains, in an active state, a limited amount of information with immediate relevance to the task at hand while preventing distractions from the environment and irrelevant thoughts (Hasher, Zacks, & Lustig, in press; Kane & Engle, 2000, 2002). If the ability of working memory to maintain task focus is disrupted, performance may suffer. Ashcraft and Kirk (2001), and other anxiety researchers (Eysenck & Keane, 1990), have suggested that anxiety generates intrusive worries about the situation that occupy part of the working memory capacity normally devoted to skill execution. Moreover, research by Gray (2001; Gray, Braver, & Raichle, 2002) indicates a ‘‘double whammy,’’ because anxiety is an unpleasant emotion, and unpleasant emotional states reduce the working memory capacity available for any verbal information, whether necessary task information or situational worries. Schmader and Johns (2003) argued that stereotype threat also interferes with performance by consuming or reducing the working memory capacity that individuals need to perform successfully. Finally, we (Beilock et al., 2004) found support for distraction theories of choking, according to which, like anxiety, pressure creates mental distractions that compete for and reduce working memory capacity that would otherwise be allocated to skill execution. Together, this work suggests that compromises of working memory cause failure in tasks that rely heavily on this system. However, knowledge of the causal mechanisms governing Address correspondence to Sian L. Beilock, Department of Psychology, Miami University, Room 202, Benton Hall, Oxford, OH 45056; e-mail: beilocsl@muohio.edu. PSYCHOLOGICAL SCIENCE Volume 16—Number 2 101 Copyright r 2005 American Psychological Society suboptimal performance is only part of the key to understanding failure. To truly understand unwanted skill decrements, and to engineer training regimens to alleviate them, one must also identify characteristics of those individuals most likely to fail. Toward this end, the current experiment explored how individual differences in working memory capacitymight be involved in susceptibility to choking under pressure in mathematical problem solving. An obvious hypothesis is that individuals low in working memory capacity (LWMs) are more prone to choke under pressure than are individuals high in working memory capacity (HWMs) because LWMs have limited capacity to compute problem solutions to begin with. Consequently, pressure-induced consumption of working memory might shrink available capacity below the minimum needed to solve a problem successfully. However, another possibility exists: HWMs might be more prone to pressure-induced failure than are LWMs. Suppose HWMs rely more than do LWMs on strategies that load working memory during problem solution—‘‘if you’ve got it, flaunt it. ’’ If so, under normal conditions, HWMs should perform better than LWMs on difficult tasks, as HWMs should have more resources to devote to problem solving. However, HWMs’ usual working memory advantage may be just what makes them susceptible to failure when pressure is added, if pressure-induced consumption of working memory denies them the capacity they normally rely on to produce their superior performance. A similar argument has been made concerning working memory and the performance of attention-demanding verbal fluency and proactive-interference tasks. Under single-task conditions, HWMs outperform LWMs on such tasks. However, adding a secondary task essentially makes HWMs perform like LWMs by reducing the capacity that HWMs normally rely on to deal with the extra attention demands of difficult tasks (Kane & Engle, 2000, 2002). If pressure and anxiety target individuals high in working memory capacity, this would carry significant implications for interpreting performance in high-pressure situations (e.g., college entrance exams). First, it would suggest that individuals most equipped to handle difficult situations that are working memory intensive (i.e., HWMs) are the ones most likely to ‘‘blow it’’ under pressure. Second, as working memory capacity is known to mediate and predict higher-level functions from comprehension to learning (Engle, Kane, & Tuholski, 1999), such results would call into question the ability of performance in high-pressure situations to differentiate persons most qualified to succeed from those with less capacity-related potential. THE CURRENT EXPERIMENT We chose Gauss’s (1801) modular arithmetic (MA) task (cited in Bogomolny, 1996) to explore these hypotheses. The object of MA is to judge the truth value of problem statements such as ‘‘51 19 (mod 4). ’’ The problem is solved by subtracting the middle number from the first number (i.e., 51 19) and then dividing this difference by the last number (i.e., 32 4). If the dividend is a whole number (here, 8), the statement is true. MA is similar to real-world math, as it is based on subtraction and division procedures. However, because MA is novel, even to most people highly experienced in math, it is advantageous as a laboratory task. In the current study, individuals performed MA problems under both low-pressure and high-pressure conditions. The problems were manipulated to be either low or high in working memory demands. If pressure consumes the working memory capacity available for MA, then problems that depend heavily on working memory should suffer most when the problem solver is under pressure. Furthermore, if individual differences in working memory capacity are related to performance, this relationship should be most evident for MA problems that make the heaviest demands on working memory. For present purposes, higher versus lower working memory demand was determined by whether the first step in solving the MA problem did or did not have a large number (> 20) or require a borrow operation. For example, ‘‘5 3 (mod 2)’’ involves small numbers in the first step (5 3) and no borrow operation, so it was considered to have a low working memory demand. In contrast, ‘‘45 27 (mod 4),’’ involves both large numbers (45 27) and borrowing in the first step, so it was considered to have a higher working memory demand. Large numbers and borrow operations involve longer sequences of steps and require maintenance of more intermediate products, thereby placing heavy demands on working memory (Ashcraft, 1992; Ashcraft & Kirk, 2001).