Math Performance in Stressful Situations

Whether because individuals are made aware of negative stereotypes about how they should perform or are in a high-stakes testing situation, a stressful environment can adversely affect the success people have in solving math problems. I review work examining how unwanted failure in math occurs and individual differences in those most likely to fail. This work suggests that a high-stress situation creates worries about the situation and its consequences that compete for the working memory (WM) normally available for performance. Consequently, the performance of individuals who rely most heavily on WM for successful execution (i.e., higher-WM individuals) is most likely to decline when the pressure is on. KEYWORDS—pressure; stereotype threat; math anxiety; working memory; math problem solving Solving a math problem like ‘‘(32 18) 7 5 ?’’ in one’s head involves several steps. First, one must compute the answer to ‘‘32 185 ?’’ Second, one must hold this answer in memory and divide by 7. Although the attention, memory, and computational processes that support these types of calculations have been investigated, less work has addressed how such calculations are affected by common types of real-world situations in which mathematical thinking takes place. How might being in an important testing situation affect performance of the above problem? What about working through the problem at the chalk board while an entire class looks on? Or, what if a female student performed this calculation after being told ‘‘everyone knows girls can’t do math’’? Although individuals may be motivated to perform well in such stress-laden situations, these circumstances often cause individuals to perform at their worst. The expression ‘‘choking under pressure’’ is used to describe what happens when people perform more poorly than expected given their skill level precisely because there are large incentives for optimal performance and highly negative consequences for poor performance (Beilock & Carr, 2001). And, the term stereotype threat (ST) describes situations in which awareness of a negative stereotype about how one’s social group should perform (e.g., ‘‘girls can’t do math’’) produces less-than-optimal execution (Steele, 1997). Studies of choking and ST have yielded similar conclusions about how suboptimal performance in math arises. My colleagues and I are interested in understanding why these performance decrements occur and for whom they are most likely. Our goal is to leverage this knowledge to devise training regimens, performance strategies, and testing environments that alleviate math failure. WHY DOES FAILURE IN MATH OCCUR? For several decades, researchers have investigated why individuals who are overly anxious about math perform poorly at it, despite often showing competency in other domains. One explanation is that math-anxious individuals were never math proficient to begin with. However, while there is usually a negative relation between math anxiety and math skill, this is not the entire story. Ashcraft and Kirk (2001) have shown that part of highly math-anxious individuals’ poor performance stems from anxiety-induced depletion of the cognitive resources that support complex math tasks. The work described here focuses on how situation-induced feelings of pressure can undermine math performance in anyone, not just why dispositionally math-anxious individuals perform poorly. Nonetheless, similar to the idea that math anxiety robs one of the cognitive capacity needed to successfully execute math tasks, our findings suggest that suboptimal math performance in stress-laden situations arises because worries about the situation compete for the working memory (WM) available for performance. WM is a short-term system involved in the control, regulation, and active maintenance of a limited amount of information immediately relevant to the task at hand (Miyake & Shah, 1999). If the ability of WM to maintain task focus is disrupted, performance may suffer. We refer to this as the Address correspondence to Sian L. Beilock, Department of Psychology, 5848 South University Avenue, The University of Chicago, Chicago, IL 60637; e-mail: [email protected]. CURRENT DIRECTIONS IN PSYCHOLOGICAL SCIENCE Volume 17—Number 5 339 Copyright r 2008 Association for Psychological Science distraction account of failure because we believe that stress-laden environments essentially place individuals in a dual-task situation: Task execution and performance-related worries vie for the WM capacity that, in less-stressful circumstances, could be devoted solely to math. To understand how situation-induced pressures undermine math performance, my colleagues and I have created a highstakes testing environment in our laboratory. We have used the mathematician J.C.F. Gauss’s modular arithmetic (MA) as a test bed. MA involves judging the truth value of equations [e.g., 34 18 (mod 4)]. To do this, one subtracts the second number from the first number (‘‘34 18’’). This difference is then divided by the last number (‘‘16 4’’). If this division step results in a whole number (here, 4), the statement is true. Problems with remainders are false. Problem validity can also be determined by dividing the first two numbers by the mod number. If the same remainder obtains (here, 34 4 and 18 4 both have remainders of 2), the equation is true. We usually teach participants the first method mentioned above for solving MA problems in our studies. It is important to understand how pressure compromises performance on tasks like MA because careless mistakes on the types of computations inherent in MA contribute to less-thanoptimal performance in many standardized math testing situations. Moreover, even problems that go beyond the conceptual demands of MA (at least, as we use MA) often require mental calculations similar to those needed to compute MA answers. Thus, understanding how stressful situations compromise even relatively simple calculations will shed light on unwanted performance decrements. In an initial study (Beilock, Kulp, Holt, & Carr, 2004), individuals solved MA problems that varied as a function of whether the first problem step (i.e., the initial subtraction step) involved large numbers (greater than 10) and borrowing from the tens column (a borrow operation; e.g., ‘‘45 27’’). Larger numbers and borrow operations involve longer sequences of steps and require maintenance in memory of more intermediate products, placing greater demands on WM (Imbo, Vandierendonck, & Verguewe, 2007). If pressure impacts WM, then performance should be more likely to decline on high-WM-demanding problems [e.g., 51 29 (mod 4)] in comparison to low-WMdemanding problems [e.g., 6 3 (mod 3)]. To test this, some individuals (assigned to a low-pressure group) were simply told to try their best. Others were given a scenario based on common pressures (e.g., monetary incentives, peer pressure, social evaluation). Participants were informed that if they performed at a high level on the math task, they would receive some money. Participants were also told that this award was dependent on the good performance of both themselves and a partner they were paired with—a ‘‘team effort.’’ Participants were then informed that their partner had completed the experiment and improved. Thus, the current participant was entirely responsible for winning (or losing) the money. Participants were also told that their performance would be videotaped and that teachers and students would watch the tapes. Not surprisingly, this scenario increased participants’ reported feelings of pressure and reduced their math accuracy relative to individuals in the low-pressure group. However, performance decrements were limited to problems highest in WM demands. This suggests that pressure exerts its impact by taxing WM resources necessary for demanding computations. Although this work implicates WM in math failure, it does not tell us what exactly pressure-filled environments do to WM to produce suboptimal performance. As previously mentioned, the distraction account suggests that situation-related worries reduce the WM available for performance. If so, then math problems heavily reliant on the resources that worries also coopt should be most susceptible to failure. Thus far, we have conceptualized WM as a general-capacity system—meaning that it supports cognitive operations regardless of the type of information involved. However, there is also work suggesting that certain components of WM may be devoted more to either verbal processes (e.g., inner speech and thinking) or visuospatial processes (e.g., holding a visual image in memory). If worries tax verbal components of WM, and if math problems can be differentiated by the demands they make on verbal versus visuo-spatial resources, then performance on problems heavily reliant on verbal resources should be especially compromised under stress. Of course, this does not mean that tasks with spatial demands (e.g., mental rotation) will show no signs of failure (especially if, for example, one concocts visual images of feared consequences). Rather, if verbal ruminations and worries are a key component of stress-induced failure, then performance decrements should be most pronounced in tasks that depend heavily on WM and especially verbal aspects of this system. Beilock, Rydell, and McConnell (2007) examined this hypothesis using a different type of stress, negative-performance stereotypes. We asked whether women at a selective Midwestern university who were reminded of the stereotype that men are better at math than women would perform worse on MA than women who did not receive this information (i.e., whether negative stereotype presentation would elicit ST). With respect to gender and math, sex differences in problem solving have been shown to emerge most strongly at higher age levels and in highly select samples (e.g., college-bound high-school students; Hyde, Fennema, & Lamon, 1990). Thus, a high-achieving college population seemed especially appropriate to study. We were particularly interested in whether performance on math problems that relied more heavily on verbal resources than visuo-spatial resources would be differentially harmed. Although all arithmetic problems involve general WM resources, Trbovich and LeFevre (2003) demonstrated that math problems presented in a horizontal format (Fig. 1) depend heavily on phonological or verbal resources, because individuals maintain problem steps in memory verbally (e.g., repeating them in their head). Math problems presented in a vertical 340 Volume 17—Number 5 Math Performance