The Relationship between State Math Anxiety. and Working Memory Capacity. ERIN E. SOVANSKY B.A., Albion College, 2013 THESIS

Transcription

1 The Relationship between State Math Anxiety and Working Memory Capacity BY ERIN E. SOVANSKY B.A., Albion College, 2013 THESIS Submitted as partial fulfillment of the requirements for the degree of Master of Arts in Psychology in the Graduate College of the University of Illinois at Chicago, 2016 Chicago, Illinois Defense Committee: Stellan Ohlsson, Chair and Advisor Susan Goldman James Pellegrino

2 This thesis is dedicated to my husband, Marc, for his patience, love, and encouragement. ii

3 Acknowledgements I would like to thank my advisor, Stellan Ohlsson for his support and guidance. I would like to thank my committee, Susan Goldman, and James Pellegrino, as well as Jennifer Wiley and Eric Leshikar for their contributions and feedback. I would like to also thank my undergraduate advisor, Mareike Wieth, who encouraged me to pursue a graduate degree in cognitive psychology. Lastly, I would like to thank my family and friends for their unwavering support and encouragement throughout the years. iii

4 CHPATER TABLE OF CONTENTS PAGE I. INTRODUCTION...1 A. Math Anxiety...2 B. Math Anxiety and Working Memory Capacity...3 C. Theories of how Anxiety Relates to WMC...4 D. Trait and State Math Anxiety...6 E. Induction of Math Anxiety...7 F. Current Study...9 G. Predictions...9 II. METHOD...11 A. Participants...11 B. Materials Anxiety Measures Working Memory Capacity Measures Math Test Filler Problem Solving Task Demographic Information...16 C. Procedure...16 III. RESULTS...19 A. Baseline Measures...19 B. Demographic Information...19 C. Word Task...20 D. Did Operation Span Affect Anxiety Score?...20 E. Effect of the Test Manipulation Anxiety Measures Working Memory Capacity Measures...21 F. Interaction of Trait Math Anxiety and the Test Manipulation Anxiety Measures Working Memory Capacity Measures...23 IV. DISCUSSION...25 A. Follow-up Experiments...26 B. Conclusion...27 V. REFERENCES...29 VI. APPENDICES...33 A. Appendix A...33 B. Appendix B...34 C. Appendix C...36 D. Appendix D:...37 E. Appendix E...39 iv

5 CHAPTER Table of Contents (continued) PAGE F. Appendix F...44 G. Appendix G...48 H. Appendix H...51 I. Appendix I...52 VII. IRB APPROVAL...65 VIII. CURRICULUM VITAE...71 v

6 TABLE LIST OF TABLES PAGE 1. Order of tasks for each condition Math ability by condition Anxiety measure scores by condition WMC proportion scores by condition Regressions of trait anxiety and condition on anxiety measures Regressions of trait anxiety and condition on WMC measures...58 vi

7 FIGURE LIST OF FIGURES PAGE 1. Overview of running span, symmetry span, and operation span SMARS score as a function of AMAS split by condition State anxiety as a function of AMAS split by condition Ospan score as a function of AMAS split by condition Symspan score as a function of AMAS split by condition Runspan2 score as a function of AMAS split by condition...64 vii

8 Summary Previous work has found that math-anxious individuals perform more poorly on math-related working memory capacity (WMC) measures (Ashcraft & Kirk, 2001).However, based on previous work it is unclear whether having trait math anxiety causes deficits specific to mathrelated working memory capacity, or if instead math-related tasks trigger a state of math anxiety in math anxious individuals that lowers WMC in general. To test whether reduction in WMC is due to being in a state of math anxiety, this study attempted to induce a state of math anxiety by providing participants with a warning that they will have to perform math, by having participants complete a math test, or a combination of both. Participants then completed verbal, spatial, and math-related WMC measures. The anxiety manipulations did not appear to induce a state of math anxiety, and did not lead to poorer performance on any WMC measure. Additionally, this study failed to replicate previous work and did not find that math-related WMC performance decreases with increasing math anxiety. viii

9 1 I. INTRODUCTION The use of mathematics is ubiquitous in modern society. Students are taught math through all grade levels of elementary and secondary school, and math is a main subject on many standardized tests that students take through their educational career, making proficiency in math important for academic success (Miller & Bichsel, 2004). Additionally, many careers require some level of proficiency in math, with high proficiency predicting better earning potential (Rivera-Batiz, 1992). Even though understanding mathematics is beneficial to educational and career success, there is a large portion of the population who struggle with math, who avoid having to perform math, and may even experience negative feelings, thoughts, and physical sensations in relation to performing math (Richardson & Suinn, 1972). This negative reaction to math is called math anxiety. The goal of this study was to explore how math anxiety relates to working memory capacity (WMC), which is a person s ability to control attention toward taskrelevant information (Engle, 2002). Some previous research has found that math anxious individuals perform worse on WMC measures involving math compared to their non-math anxious peers (Ashcraft & Kirk, 2001; Ashcraft & Krause, 2007; Miller & Bichsel, 2004). This performance decrement also extends to other types of dual tasks involving math computation as one of the tasks (Ashcraft & Kirk, 2001). Even though several studies have reported this relationship between math anxiety and math related WMC measures, the reason why this WMC decrement happens is not clear. Do math anxious individuals have decreased attentional control specifically when performing math? Or, is it possible that, for math anxious individuals, the presence of math triggers a state of math anxiety that lowers attentional control more generally? If the latter is true, then individuals who are currently experiencing a state of math anxiety may show a reduction in performance on WMC measures regardless of whether they involve

10 2 performing math. In order to test whether math anxiety leads to specific or general WMC decrements, this study examined how inducing a state of math anxiety affects performance on several measures of WMC. A. Math Anxiety Math anxiety is a specific type of anxiety in which people experience negative feelings such as fear, worry, or dread in relation to performing mathematics (Richardson & Suinn, 1972). People with math anxiety generally have negative attitudes toward math, and tend to avoid math in school as well as later in life, thereby reducing their potential career opportunities (Hembree, 1990). Math anxiety not only leads to negative feelings toward math, but also decreased math performance compared to those who do not have math anxiety (Ashcraft & Krause, 2007; Hembree, 1990; Miller & Bichsel, 2004). Because math anxiety relates to lower math performance, some researchers have suggested that people with math anxiety may simply be less competent in math and the anxiety stems from being aware of their incompetence (Tobias, 1985). However, other research suggests that this is not likely (Hembree, 1990). Math anxious individuals perform as well as everyone else when completing simple math problems, and performance deficits only begin to happen as math problems get more complex (Ashcraft & Faust, 1994; Ashcraft & Krause, 2007). Ashcraft and Faust (1994) took this finding to suggest that math anxiety is not caused by being incompetent at math, and instead math anxiety prevents people from being able to solve problems that involve mentally processing and maintaining larger amounts of information, such as problems requiring carry functions or multiple operations. Because math anxiety hurts math performance only when problems are more complex, it is likely that math anxiety negatively relates to WMC (Ashcraft & Kirk, 2001).

11 3 B. Math Anxiety and Working Memory Capacity Ashcraft and Kirk (2001) conducted one of the first studies to examine the relationship between working memory capacity and math anxiety. In Experiment 1, Ashcraft and Kirk examined correlations among self-reported math anxiety measured by the Short Mathematics Anxiety Rating Scale (SMARS) and performance on two measures of working memory capacity: the verbal listening span (L-span) and the math-related computation span (C-span; Salthouse & Babcock, 1990) tasks. Participants completed the SMARS, C-span, and L-span in a randomized order. They found that math anxiety correlated negatively with performance on both L-span and C-span, as well as number of math classes taken, and grades received in high school math courses. After performing a regression analysis in order to partial out the common variance between L-span and C-span scores, it was found that math anxiety much more strongly predicted C-span score. C-span and L-span were performed again during experiment 3, and this time C- span performance decreased with increasing math anxiety, but L-span performance did not relate to math anxiety. In Experiments 2 and 3, Ashcraft and Kirk additionally found that people with higher self-reported math anxiety had longer response times and more errors on a dual task involving mathematical computation compared to people with medium or low levels of math anxiety. These effects were strongest when the math task involved a carry function or the transformation task required multiple transformations. Ashcraft and Kirk s (2001) study provides evidence that math anxiety is related to lower working memory capacity when math is involved in the task. Following Ashcraft and Kirk s 2001 study, Miller and Bichsel (2004) examined correlations among self-reported math anxiety measured by the math anxiety rating scales (MARS), state and trait general anxiety measured by the state-trait anxiety inventory (STAI),

12 4 gender, math performance, reading span performance, and performance on a spatial problem solving task (paper folding). Order of tasks was counterbalanced across participants. They found that math anxiety was more common in females than males, correlated positively with scores on both the state and trait anxiety inventories, and correlated negatively with performance on the paper folding task, as well as both math performance measures. Math anxiety did not relate to performance on the reading span. This study did not find evidence that math anxiety relates to verbal WMC, but found that higher math anxiety leads to poorer performance on a paper folding task, which Miller and Bichsel argue involves math-like processes. In summary, Ashcraft and Kirk (2001) found that math anxiety can lead to a reduction in WMC. The effect is strongest when tasks involve mathematical computation. Miller and Bichsel (2004) found that math anxiety negatively correlates with spatial problem solving, which involves processes that are similar to math. Additionally, both studies found that math anxiety did not strongly relate to performance on working memory capacity measures involving verbal processing. The results of both studies suggest that math anxiety leads to a reduction in WMC, only when performing tasks that involve math or math-like processing. However, these results stand at odds with several theories of how anxiety relates to WMC (e.g. Eysenck & Calvo, 1992). These theories of anxiety would instead predict that anxiety leads to a more general deficit in WMC. C. Theories of how Anxiety Relates to WMC There are several competing theories describing how anxiety affects cognition. These theories include the hemispheric asymmetry hypothesis (Shackman, Sarinopoulos, Maxwell, Pizzagalli, Lavric, and Davidson, 2006), the two-component model (Vytal, Cornwell, Arkin, & Grillon, 2012), and the processing efficiency theory (Eysenck & Calvo, 1992), which evolved

13 5 into the attentional control theory (Eysenck, Derakshan, Santos, & Calvo, 2007). The hemispheric asymmetry hypothesis predicts that anxiety specifically affects visuospatial WMC because anxious arousal uses right prefrontal cortex resources that would normally be used for processing visual information. This theory, however, is flawed because other studies have found performance decrements on other measures of WMC, suggesting that anxiety does not uniquely affect visuospatial WMC (e.g. Ashcraft & Kirk, 2001; Vytal, Cornwell, Letkiewicz, Arkin, & Grillon, 2013). The two-component model instead suggests that in addition to disrupting visuospatial WMC, anxiety also leads to anxious apprehension and worry, which affects verbal WMC (Vytal, et al., 2012). Support for the two-component model comes from threat of shock studies finding that being under threat of shock decreases performance on all difficulty levels of a visual n-back task, but only easy and medium levels of a verbal n-back task. Similarly, the processing efficiency also predicts a more general effect of anxiety on WMC. The processing efficiency theory states that worry and anxious apprehension expend some of a person s limited working memory resources, decreasing their overall processing ability, possibly having a stronger effect on verbal WMC due to the verbal nature of worries (Eysenck & Calvo, 1992). The processing efficiency theory has evolved into the attentional control theory of anxiety (Eysenck, Derakshan, Santos, & Calvo, 2007), which further specifies that anxiety affects the attentional control component of working memory, specifically, the ability to inhibit distractions to focus on task relevant information. Support for the processing efficiency and attentional control theories come from research finding that high anxiety is related to poorer performance on tasks measuring inhibition and ability to shift between tasks (see Derakshan and Eysenck, 2009 for review).

14 6 Ashcraft and Kirk described their (2001) study as support for Eysenck and Calvo s (1992) processing efficiency theory because the mathematical processing component of the c- span put high math anxious individuals into a state of math anxiety, which then decreased their performance on the task. From this point of view, math anxiety uniquely affects performance on math related WMC tasks because the math anxious individuals only experience anxiety during tasks involving math. However, it is possible that for math anxious individuals, the presence of math could trigger a state of math anxiety lasting longer than the math task itself. If that is the case, the theories described above would predict that being in a state of math anxiety would affect performance on WMC measures beyond those involving math. All theories would predict decreased performance on a spatial WMC measures. In addition, the two-component model would predict some performance decrement on verbal WMC measures, and the processing efficiency model would predict stronger decrements on verbal WMC measures. D. Trait and State Math Anxiety In predicting that math anxiety could lead to performance decrements on non-math measures of WMC, a distinction is being made between math anxiety as a type of trait anxiety and a type of state anxiety. When describing how some individuals are more or less math anxious than others, math anxiety is being described as a trait. When describing how people experience the effects of math anxiety, it is instead being described as a mental state. Previous studies of math anxiety and working memory capacity have failed to make a distinction between trait math anxiety and state math anxiety (Ashcraft & Kirk, 2001; Miller & Bichsel, 2004), interchangeably using language describing math anxiety as a trait and a state. Individuals vary in their levels of trait math anxiety, meaning that some are more prone to math anxiety than others. However, to experience math anxiety, a state of anxiety must be induced by a triggering event,

15 7 such as performing math problems or being asked about feelings toward math. Because previous studies (Ashcraft & Kirk, 2001; Miller & Bichsel, 2004) presented tasks in randomized or counterbalanced orders, this presents a problem in trying to understand their results. First, it is unclear whether the self-reported anxiety scores represent trait levels of math anxiety or a combination of trait and state math anxiety. Similarly, if completing a math anxiety questionnaire could induce a state of math anxiety, completing the questionnaire immediately before WMC measures might affect performance on those measures. In order to better distinguish between trait and state math anxiety on a self-report measure, participants would need to report their math anxiety twice, once before the study in a separate session to get a baseline trait measure, and another measure toward the end of a study to see any increase in anxiety that happened during the study. The goal of the current study is to explore the effects of inducing a state math anxiety on WMC. In order to do this, this study will vary whether a state of math anxiety is induced prior to completing the WMC measures. E. Induction of Math Anxiety In order to test whether inducing a state of math anxiety will lead to a more general reduction in WMC, the first step is figuring out how to induce a state of math anxiety. Because math anxiety is anxiety in relation to performing math, the seemingly obvious way to induce math anxiety would be to have participants perform math. However, a couple studies suggest that anticipation of an anxiety-triggering event might be enough to induce a state of anxiety (Coy, O Brien, Tabaczynski, Northern, & Carels, 2011; Lyons & Beilock, 2012). Lyons and Beilock (2012) used functional magnetic resonance imaging (fmri) to examine the neural correlates of math anxiety. In their study, high- and low-math-anxious

16 8 participants completed a word puzzle task and a math problem-solving task while neural activity was being measured using fmri. The tasks were presented in random order, using a colored shape to indicate which task was about to start. They found that high-math-anxious individuals experienced neural activity associated with pain in anticipation of the math task, which decreased upon performing the math task. The results of this study suggest that math anxiety is experienced most acutely, not when performing math, but in anticipation of having to perform math. Similarly, Coy, O Brien, Tabaczynski, Northern, and Carels (2011) examined whether warning participants that they were about to take a difficult test induced a state of evaluation anxiety, and whether that led to poorer performance on various cognitive measures. In their study, one group received this warning and another group was told that they were about to take tests of memory and attention, but performance did not matter because the researchers were piloting materials for a future project. After receiving instructions, participants completed a test anxiety questionnaire followed by several measures of working memory capacity and executive functioning, including the forward and backward digit spans, forward and backward visual memory spans, and color-word interference Stroop tasks. After these measures, participants completed a cognitive interference inventory and a final test anxiety questionnaire. Heart rate was also measured and recorded in 15 second intervals throughout the completion of the study. Coy and colleagues found that participants in the test expectation condition reported higher anxiety, had higher increases in heart rate, and had lower performance on both digit span tasks compared to the pilot-test condition. Taken together, these studies show that warning participants that they are about to perform math is sufficient for inducing anxiety.

17 9 F. Current Study The current study examined the effects of an induced state of math anxiety on spatial, verbal, and math-related measures of WMC. Previous studies, which did not control induction of state math anxiety, found that high-math-anxious individuals score lower than low-math-anxious individuals specifically on WMC measures involving math. This could be either because WMC deficits are specific to math, or because the math-related task was the only time when participants experienced a state of math anxiety. The three theories of anxiety and WMC listed above would all predict that inducing a state of math anxiety would lead to decreases in WMC on at least one of the two non-math WMC measures. Two manipulations were used for inducing a state of math anxiety. One was providing a warning that the study involved taking an additional math test, and the other was actually having the participant perform a math test. This led to the creation of four conditions, a control condition with no anxiety manipulation, a warning manipulation condition, a test manipulation condition, and a condition, which received both manipulations. The purpose of having multiple manipulations was to have three chances for inducing a state of anxiety. G. Predictions First, it was predicted that having participants perform a math test toward the beginning of the study will induce a state of math anxiety. Participants in the math test condition were predicted to report higher anxiety than the control group at the end of the study. Second, because the likelihood of experiencing math anxiety may be based on trait math anxiety, the math test was predicted to increase math anxiety more strongly in participants with higher baseline (trait) math anxiety.

18 10 Based on the work of Ashcraft and Kirk (2001), it was predicted that this study would replicate the finding that higher math anxiety is related to lower performance on the math-related measure of WMC. Because math anxiety is already expected to relate to the math-related WMC measure, group differences were not predicted. For the spatial and verbal WMC measures, math anxiety is not expected to relate either measure for the control condition. For the test condition, the predicted results depend on the theory. The hemispheric asymmetry hypothesis (Shackman, et al., 2006), would predict that induced anxiety would lead to lower performance on the spatial WMC measure, but not the verbal WMC. The two-component model (Vytal, et al., 2012) would predict that inducing math anxiety would decrease spatial WMC and possibly verbal WMC depending on the load of the task. The processing efficiency theory (Eysenck & Calvo, 1992) or the attentional control theory (Eysenck, Derakshan, Santos, & Calvo, 2007) would predict that induced anxiety would decrease performance on both spatial and verbal WMC measures, most strongly affecting the verbal. The effect of the math test on WMC measures may also depend on trait math anxiety.

19 11 II. Method A. Participants The sample consisted of 95 female undergraduate students from the University of Illinois at Chicago Introductory Psychology subject pool. There were four conditions: a control condition (n = 23), a warning condition (n = 27), a math test condition with warning (n = 24), and a math test condition without warning (n = 21). 34 additional participants were run, but removed from analyses because they did not complete all anxiety and WMC measures. Females were chosen as participants because they are more likely to have math anxiety, and because some studies have found gender differences in the effects of math anxiety (Hembree, 1990; Miller & Bichsel, 2004). If males were included, gender would have to be included as a factor, doubling the number of participants required for the studies. B. Materials 1. Anxiety Measures. Three separate measures of anxiety were used during this study. To obtain a baseline measure of trait math anxiety, participants completed the 9-item Abbreviated Math Anxiety Scale (AMAS; Hopko, Mahadevan, Bare, & Hunt, 2003) as part of the mass testing session (Appendix A). Possible scores ranged from 9-45 with higher scores indicating higher math anxiety. Another measure of math anxiety was collected during the study session using the 25-item Short Mathematics Anxiety Rating Scale (SMARS; Alexander & Martray, 1989; Appendix B). Possible scores ranged from with higher scores indicating higher anxiety. For both questionnaires, participants were presented with mathematics-related scenarios, such as receiving your final math grade, to which they responded how anxious they felt on a 5-point Likert scale. Because this study involved inducing a state of math anxiety, state anxiety was measured using the state anxiety portion of the State Trait Anxiety Inventory

20 12 (STAI; Spielberger, Gorsuch, Lushene, Vagg, & Jacobs, 1984; Appendix C). The state portion of the STAI had 20 items. Participants were presented with statements such as I feel calm and they answered how true this statement was at the moment on a 4-point Likert scale. Possible scores ranged from with higher scores indicating higher anxiety. 2. Working Memory Capacity Measures. Three different measures of working memory capacity were used during this study: Automated running span (Runspan), automated symmetry span (Symspan), and automated operation span (Ospan) tasks. An overview of the three tasks is shown in Figure 1. All three tasks were run on computers using E-prime software (Schneider, Eschman, & Zuccolotto, 2001). Runspan is a WMC measure in which participants are asked to remember the last several letters in a list that is continuously updating (Broadway & Engle, 2010). Exact instructions and an overview of the procedure can be found in Appendix D. For each set of trials, participants are informed by the program how many letters they will have to remember (3-7). A series of letters (1-3 letters longer than the number to be remembered) then appears on the screen one at a time for 500 ms per letter. When the letters stop appearing, a response window appears where participants are asked to click on only the most recent letters corresponding to the set size they were told at the beginning of the trial. The response window has no time limit. There are 4 practice trials in which participants are asked to remember the last 2 letters, followed by a total of 30 trials (3 trials of each length), with a total possible score of 75. The different trial lengths appear in a randomized order, with all three trials of the same length appearing in a block. Strings of letters are randomly selected without replacement from 72 possible series of letters, and because there are 3 possible series lengths per trial length, and 5 different trial lengths, there are 3240 different possible stimuli that can be generated. A participant s score is computed as the

21 13 total number of letters they remember in the correct order, which includes partial credit when some, but not all letters were remembered in the correct order. Conway and colleagues (2005) suggested using partial credit scoring because the scores approximate a normal distribution more closely than all-or-nothing scoring. Total scores were converted to proportion correct to allow comparison with Ospan and Symspan. Participants completed this task twice. It was administered once as a baseline measure of working memory capacity at the start of the study (Runspan1), and a second time after the anxiety manipulation (Runspan2). Because there are over 3000 possible sets of stimuli, it is highly unlikely that a participant received the exact same stimuli both times completing the task. The automated Symspan is a working memory capacity task in which participants make judgments of symmetry of images while simultaneously remembering the locations of red squares in a 4 x 4 grid (Redick, et al., 2012). Exact instructions and an overview of the procedure can be found in Appendix E. First, participants are shown a design in a rectangular grid and they are asked to judge whether the object is symmetrical across a vertical axis (equal to average practice RT plus 2.5 times the SD of practice RT). Then a screen appears with two boxes labeled YES and NO, and participants answer YES if the previous image was symmetrical, and NO if it was not (no time limit). Following that participants are shown a grid with one box highlighted in red that they need to remember (650 ms). After 2-5 items, participants are shown an empty 4 x 4 grid and are asked to click on the location of each red square in the correct order. The response window does not have a time limit. Following Redick and colleagues (2012), a participant s score is computed as the number of squares remembered in the correct order, including partially completed sets. There are 12 trials total, with 3 trials of each length (2-5),

22 14 with a total possible score of 42. Different trial lengths appear in a randomized order. Like the Runspan, scores were converted to a proportion correct out of the total. The automated Ospan is a working memory capacity task in which participants solve math problems while simultaneously remembering strings of letters (Unsworth, Heitz, Schrock, & Engle, 2005). Exact instructions and an overview of the procedure can be found in Appendix F. Participants are first shown a math problem (e.g., (9/9) + 1) with a duration tailored to participant (1000 ms longer than average time per problem in practice trials), then on the next screen they are shown a number and two boxes labeled TRUE and FALSE. If the number is the correct solution to the equations, participants should respond TRUE and they should respond FALSE if the number is not the solution (no time limit). Then participants are presented a letter to remember for 1000 ms. After 3-7 items, participants presented with a response screen and are asked to click on the letters in the order in which they were presented. The response window has no time limit. There are 15 trials in total, with 3 trials of each length, with a total of 75 points. Different trial lengths are presented in a randomized order. Following Unsworth and colleagues (2005), a participant s score was computed as the number of letters that are remembered in the correct order, including credit for partially complete sets of letters. Ospan scores were converted to a proportion correct out of the total. In both Ospan and Symspan tasks, it is common practice to remove participants who score less than 85% on the processing component of the tasks, because these people may be ignoring the processing component in order to do better on the memory component (Conway, et al., 2005). However, sometimes this is not the case and those with more processing errors do not have higher span scores (Kane, et al., 2004). Because this study is particularly interested in mathanxiety-related decrements in span task performance, it is important to ensure that participants

23 15 with high math anxiety are not unnecessarily being removed from analyses because they may be more likely to have poor math performance on the Ospan processing component. Because of this, correlation analyses were performed to test if there is a relationship between processing performance and span score, and if so which direction. Symmetry span score and number of processing errors were not correlated, r(93) =.07, p =.51; and Ospan score negatively correlated with the number of errors on the processing component, r(93) = -.31, p <.01; suggesting that participants did not sacrifice performance on the processing component in order to do better on the memory component for either task. Additionally, for the Ospan, those who performed worse on the processing component had lower span scores. Correlation analyses testing the relationship between math anxiety and Ospan processing errors were also performed to test whether those with higher processing errors also have higher math anxiety. Processing errors had a marginally significant correlation with SMARS score, r(93) =.18, p <.09; and state anxiety, r(93) =.19, p =.07; but not AMAS,r(93) = -.02, p =.86. Because two of the anxiety measures had marginally significant correlations with Ospan processing errors, there is a chance that removing those with low processing performance could disproportionately remove math anxious participants. Because there was no evidence that the participants in this sample ignored the processing component to do better on the memory component, and there was evidence that Ospan processing errors increase with higher math anxiety, participants with low processing performance were not removed from the sample. 3. Math Test. The math test consisted of 12 problems taken from the applied mathematics subtest of the Woodcock-Johnson Tests of Achievement (Woodcock & Johnson, 1990; Appendix G). Problems were presented on a computer using E-prime software, and participants were able to work through the problems with a pencil and paper if needed, but did

24 16 not have access to a calculator. Problems were presented one at a time in order of increasing difficulty, and participants could not return to a problem once it had been presented. Participants performance on the task was timed in E-prime, and the task automatically ended after completing the current problem once 10 minutes had passed. 4. Filler Problem Solving Task. The problem solving task was a word task based on the task used in Lyons and Beilock (2012). In this task, participants were presented with a string of letters, and were asked to verify if the letters spell a real word if reversed. Strings of letters were four letters in length, and half had real word solutions. Words were presented on the computer using E-prime in order to keep the task as similar as possible to the math task. Participants were asked to press t for true if the letters form a word and f for false if they do not. This task was chosen because it is a verbal, non-math-related task that has been previously used as a filler task in a study related to math anxiety (Lyons & Beilock, 2012). Words were presented in a randomized order and there was no time limit to respond. The list of stimuli and instructions can be found in Appendix H. 5. Demographic Information. Participants completed a questionnaire asking basic demographic questions. It includes questions about language background as well as scores on the ACT and SAT to assess participant s math background to screen out outliers and test for similarity across conditions. The demographic questionnaire can be found in Appendix I. C. Procedure Prior to the study, participants completed the AMAS during at the beginning of the semester during a mass testing session, in which members of the subject pool completed prescreening surveys for various studies. The remaining tasks were completed during an experimental session. An overview of the procedure for each condition is presented in Table 1.

25 17 Participants in all conditions first completed an initial Runspan task in order to get a baseline measure of working memory capacity. In the no-math-test conditions (control and warning), participants completed the word problem solving task, followed by a second Runspan, then the Symspan, Ospan, SMARS, and STAI. They completed the math test and the demographic questionnaires as the final tasks. In the math-test conditions, participants completed the math test, followed by a second Runspan, then the Symspan, Ospan, SMARS, and STAI. They completed the word task and the demographic questionnaires as the final tasks. In all conditions, approximately half of the participants completed the SMARS and STAI before completing the Ospan in order to assess whether self-reported anxiety changed depending on whether the measure was taken before or after the Ospan. This was done to ensure that selfreported math anxiety was not being inflated in participants who completed the Ospan immediately before the anxiety measures. In the warning conditions, participants will receive a warning that they will perform a difficult math test during the study adapted from Coy, O Brien, Tabaczynski, Northern, and Carels (2011). This instruction will come after completing the initial Runspan and prior to the math test or word problem solving task: During this study, you will perform a test that assesses your math ability. This test has been shown to be highly related to your intelligence and your ability to do college-level work. During this test you will be timed and notes will be taken regarding your performance. It is important that you do well because your results will be reviewed and compared to the performance of other college students. Any questions?

26 18 At the end of the study, participants were debriefed and dismissed. The study lasted approximately 70 minutes.

27 19 III. Results A. Baseline Measures In order to determine whether randomized assignment resulted in matched conditions, 1 X 4 ANOVAs were run to test whether the groups differed on the baseline measures of math anxiety (AMAS) and WMC (Runspan1). Because these are baseline measures, no difference was expected between groups. For AMAS, the control group had an average score of (SD = 5.38), the warning group had an average score of (SD = 6.26), the test group had an average score of (SD = 6.14), and the warning with test group had an average score of (SD = 6.28). There was not a significant difference between groups on the AMAS, F(3, 91) =.08, p =.97. For Runspan1, the control group had an average proportion score of.51 (SD =.14), the warning group had an average score of.45 (SD =.14), the test group had an average score of.51 (SD =.12), and the warning with test group had an average score of.47 (SD =.13). There was not a significant difference between groups on Runspan1, F(3, 91) = 1.16, p =.33. These results indicate that groups did not differ from each other on either baseline measure. B. Demographic Information Some information regarding math ability and attitudes were collected from the demographic survey. This included their perceived math ability (on a scale of 1 7), importance of math (on a scale of 1 7), and math ACT score (for those who took the ACT; out of 36). Group information for these demographic questions can be found in Table 2. There were no group differences in perceived math ability F(3, 91) = 1.16, p =.33, importance of math F(3, 91) =.38, p =.77, or math ACT scores F(3, 62) =.59, p =.62. Overall, the groups were matched for math ability and attitudes.

28 20 C. Word Task Although the word task was used as a filler task, results were still recorded. The total possible score was 108. The control group had an average score of (SD = 12.74), the warning group had an average score of (SD = 5.30), the test group had an average score of (SD = 12.80), and the warning with test group had an average score of (SD = 10.73). There was a significant difference in performance between groups, F(3, 91) = 3.23, p =.03, and Tukey s HSD post-hoc tests revealed that the warning group had a marginally higher score than the three other groups. D. Did Operation Span Affect Anxiety Score? Next, t-tests were run in order to determine whether there were differences in selfreported anxiety depending on whether the Ospan was performed immediately before or after the anxiety measures. For the purposes of these analyses, t-tests were run to compare the two orders. For SMARS, the Ospan before group had an average score of (SD = 18.08), and the Ospan after group had an average score of (SD = 15.63). For the state anxiety portion of the STAI, the Ospan before group had an average score of (SD = 10.93), and the Ospan after group had an average score of (SD = 7.67). There were not significant order effects for either SMARS, t(93) = -.65, p =.52, or the state anxiety portion of STAI, t(93) = -1.59, p =.12. Based on these analyses, it does not appear that completing the Ospan immediately prior to the anxiety measures leads to higher anxiety compared to those who completed Ospan after the anxiety measures. Ospan performance may have also been affected by manipulating the task order. The Ospan before group had an average Ospan proportion score of.71 (SD =.22), and the Ospan after group had an average proportion score of.62 (SD =.23). There was a marginally significant

29 21 effect of order on Ospan performance, t(93) = 1.89, p =.06, in which those who completed the Ospan after the anxiety measures trended toward poorer performance. In summary, completing the Ospan prior to the anxiety measures, did not affect anxiety score, but performing Ospan after the anxiety measures led to a trend toward lower Ospan performance. E. Effect of the Test Manipulation 1. Anxiety Measures. Group differences on the SMARS and state anxiety portion of the STAI were examined to test whether the test manipulation led to an overall increase in anxiety. If the test manipulation led to higher anxiety, it would be expected that the test group would report higher scores on both anxiety measures. SMARS and state anxiety score for each group are presented in Table 3. There were not significant group differences on either the SMARS, F(3, 91) =.53, p =.66; or the state anxiety portion of the STAI, F(3, 91) =.607, p =.61. The test manipulation did not lead to group differences in post-manipulation math anxiety or state anxiety. 2. Working Memory Capacity Measures. Group differences on the Ospan, Symspan, and Runspan2 were examined to test whether the anxiety manipulations led to overall performance decrements on the WMC measures. WMC proportion scores for each group are presented in Table 4. Because the Ospan is a math-related WMC measure, math anxiety related performance decrements could be expected even in the control condition, so no difference was expected. Ospan did not significantly differ by group, F(3, 91) =.69, p =.56. Because the Symspan and Runspan2 did not already include math, if any of the manipulations induced a state of anxiety, it could have resulted in performance decrements compared to the control condition. Symspan scores did not significantly differ by group, F(3, 91) =.326, p =.81. Runspan2 scores

30 22 did not significantly differ by group, F(3, 91) =.063, p =.98. The test manipulation did not lead to an overall decrease in WMC on any of the measures. The test manipulation did not lead to overall group differences in self-reported anxiety or on any WMC measure. However, it may be possible that the effect of the anxiety manipulations depends on an individual s trait math anxiety. More specifically, a manipulation to trigger a state of math anxiety may only work on those who already have high trait math anxiety, and may have no effect or even an opposite effect on those with low trait math anxiety. If that is the case, the anxiety manipulations may interact with trait math anxiety, and affect anxiety and performance on WMC measures differently depending on trait anxiety. F. Interaction of Trait Math Anxiety and the Test Manipulation Regression Analyses were run in order to test whether trait math anxiety interacted with the test manipulation on the SMARS, State anxiety portion of the STAI, and the WMC measures. The manipulations were dummy coded with control group as a reference group. This led to the creation of three dummy codes, one in which warning group was labeled as 1 and all other groups were labeled as 0, a second in which the test group was labeled 1 and other groups were labeled 0, and a third in which the warning with test group was labeled 1 and other groups were labeled 0 (Tabachnick & Fidell, 2013). AMAS was transformed into a z-score, and manipulation by AMAS interaction terms were created by was created by multiplying the dummy codes by standardized AMAS (Aiken & West, 1991). This regression design allows the intercept and slope of each manipulation to be compared against the control group. All factors were simultaneously entered into the regression model. 1. Anxiety Measures. To test whether post manipulation math anxiety depended on the interaction of the test manipulation and trait math anxiety, a regression model was run using

31 23 SMARS as a dependent variable. The overall regression model was significant, and it was found that only AMAS was a significant predictor of SMARS (see Table 5). None of the manipulations or manipulation by AMAS interaction terms were significant predictors of SMARS. As trait anxiety increased, SMARS score increased regardless of manipulation (see Figure 2). To test whether state anxiety depended on the interaction of the test manipulation and trait math anxiety, a regression model was also run using the state anxiety portion of STAI as a dependent variable. The overall regression model was marginally significant, but there were no significant predictors of state anxiety (see Table 5). As shown in Figure 3, AMAS score did not relate to state anxiety, and none of the anxiety manipulations led to results that were different from the control condition. From these results, it did not appear that any of the anxiety manipulations increased state anxiety. 2. Working Memory Capacity Measures. To test whether math-related WMC depended on the interaction of trait math anxiety and test manipulation, a regression model was run using Ospan as a dependent variable. The overall regression was not significant, and AMAS scores, the anxiety manipulations, and their interactions did not significantly predict performance for Ospan (see Table 6). Ospan performance did not relate to AMAS, none of the anxiety manipulation conditions performed differently than the control condition (see Figure 4). To test whether spatial WMC depended on the interaction of trait math anxiety and test manipulation, a regression model was also run using Symspan as a dependent variable. The overall regression was not significant, and AMAS scores, the anxiety manipulations, and their interactions did not significantly predict performance for Symspan (see Table 6). Symspan performance did not relate to trait math anxiety and none of the anxiety manipulations were different from the control group (see Figure 5).

32 24 To test whether verbal WMC depended on the interaction of trait math anxiety and test manipulation, a regression model was also run using Runspan2 as a dependent variable. The overall regression was not significant, and AMAS score, the anxiety manipulations, and their interactions were not significant predictors of Runspan2 (see Table 6). Symspan performance did not relate to trait math anxiety and none of the anxiety manipulations were different from the control group (see Figure 6).

33 25 IV Discussion Math anxiety has already been found to be related to poorer performance on math-related measures of WMC (Ashcraft & Kirk, 2001). However, based on several theories of how anxiety relates to WMC, it was predicted that inducing a state of math anxiety could lead to poorer performance on spatial and verbal measures of WMC as well. The hemispheric asymmetry hypothesis (Shackman, et al., 2006), predicts that anxiety specifically reduces spatial WMC, the two-compnent model (Vytal, et al., 2012) predicts that anxiety reduces spatial WMC and sometimes verbal WMC, and the processing efficiency theory (Eysenck and Calvo, 1992) predicts that anxiety affects WMC as a whole, possibly affecting verbal WMC more strongly. The results of the current study did not support any of these theories. There was no evidence that the anxiety manipulations led to a heightened state of anxiety, and the anxiety manipulations did not lead to performance differences on any of the WMC measures. Additionally, this study also failed to replicate Ashcraft and Kirk s (2001) finding that having a high level of math anxiety is associated with decreased math-related WMC. One limitation of the current study is that it had a small sample size, which did not have high power to detect an effect, especially for the regressions. The regressions would have required at least 38 participants per group to have an 80% chance of detecting a medium effect size. This could be resolved in follow-up studies by increasing the sample size, and by focusing only on one anxiety manipulation to compare against a control in order to make collecting a large enough sample per group more feasible. Another limitation of this study is that Ospan performance may have been affected by the other WMC measures that were recorded prior to completing the Ospan because these tasks would have provided practice on WMC tasks. Practice effects could have reduced differences in

34 26 Ospan performance due to trait math anxiety. A future direction to address this issue would be to use Ospan as the baseline WMC measure to see if a relationship between Ospan and trait math anxiety can be found after removing potential practice effects. Another potential problem with the Ospan results is that changing the task order might have led to poorer Ospan performance for those who completed the Ospan after the anxiety measures. This may have also affected the ability to find a relationship between baseline math anxiety and WMC. This problem could be resolved in future studies by keeping the task order constant across participants. A. Follow-up Experiments Two follow-up experiments have been run since the current study. Both follow-up studies only used the control and test conditions, and kept task order constant. The first follow-up experiment used the same procedure as the current study, with a larger number of participants per group. This follow-up study did not find any differences in anxiety of WMC at the group level, but found an interaction effect in which the test manipulation increased state anxiety for those who already reported having high trait math anxiety. Those same participants also had marginally poorer performance on Runspan2. This study nevertheless failed to find a relationship between math anxiety and math-related WMC, but did find some evidence to suggest that being in a state of anxiety may lower verbal WMC. The second follow-up study used Ospan as the baseline WMC measure in order to determine whether a relationship between trait math anxiety and math-related WMC could be found when Ospan there were no other tasks completed prior to it. The order of WMC measures in the later block were also reversed from the current study in order for the second Ospan to be performed immediately after the test manipulation, and have a better chance of being affected by the manipulation. This study was unable to find a relationship between trait math anxiety and

35 27 math-related WMC on either Ospan measure, and the test manipulation did not affect Ospan performance. However, this study found that the test manipulation increased state anxiety, and decreased Runspan performance, and this effect was seen at the group level. Like the first follow-up study, this study failed to find a relationship between math anxiety and math-related WMC, but found that inducing anxiety decreased verbal WMC. B. Conclusion The current study did not find evidence that the anxiety manipulations induced a state of anxiety or led to more general reductions in WMC. However, follow-up experiments to address issues with the current study found evidence that the test manipulation increased state anxiety in at least some of the participants, and led to lower verbal WMC. The results of the follow-up experiments are consistent with the processing efficiency theory (Eysenck & Calvo, 1992) because verbal WMC was most strongly affected by anxiety. Neither the current study nor subsequent studies were able to replicate Ashcraft and Kirk s (2001) finding that high math anxiety is associated with lower math-related WMC. There are a few possibilities for why the studies failed to replicate this finding. One possible reason is that Ashcraft and Kirk used a different math-related WMC measure (c-span), which required remembering the last number in the mathematical operation instead of an unrelated letter. Because the math problems and memory component of the c-span were not separate stimuli, it is not clear if poorer performance on this task reflects lower WMC or differences in ability to process math problems. The failure to replicate these results using the Ospan suggests that the later might be the case. Another possible reason that the current study failed to find a relationship between trait math anxiety and Ospan performance is that the relationship between math anxiety and math-related WMC might depend on other factors such as motivation or academic

36 28 achievement. This possibility is supported by a recent study which found that low achieving students show a decrease in math performance with increasing math anxiety, whereas high achieving students show an increase in math performance with increasing math anxiety (Moore, Allred, An, & Ashcraft, 2015). It is possible that academic achievement affects the relationship between math anxiety and math-related WMC in a similar way. The current study may have included both high and low achieving students, masking any potential relationship between math anxiety and WMC. In summary, the current study and subsequent studies found that when a state of math anxiety is successfully induced via a math test, only verbal WMC was reduced. These results suggest that being in a state of math anxiety triggers off-task thoughts and worries that reduce available WMC, and additionally call into question the previously found relationship between math anxiety and math-related WMC. Because inducing a state of math anxiety was found to reduce verbal WMC, but not math-related WMC, it suggests that interventions to help individuals with math anxiety may want to focus the most attention on addressing off-task thoughts and worries associated with math anxiety.

37 29 V References Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park, CA: Sage. Alexander, L., & Martray, C. (1989). The development of an abbreviated version of the Mathematics Anxiety Rating Scale. Measurement and Evaluation in Counseling and Development, 22, Ashcraft, M. H., & Faust, M. W. (1994). Mathematics anxiety and mental arithmetic performance: An exploratory investigation. Cognition and Emotion, 8, Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130, Ashcraft, M. H., & Krause, J. A. (2007).Working memory, math performance, and math anxiety. Psychonomic Bulletin & Review, 14, Broadway, J. M., & Engle, R. W. (2010). Validating running memory span: Measurement of working memory capacity and links with fluid intelligence. Behavior Research Methods, 42, Conway, A. R. A., Kane, M. J., Bunting, M. F., Hambrick, D. Z., Wilhelm, O., & Engle, R. W. (2005). Working memory span tasks: A methodological review and user s guide. Psychonomic Bulletin & Review, 12, Coy, B., O Brien, W. H., Tabaczynski, T., Northern, J., & Carels, R. (2011).Associations between evaluation anxiety, cognitive interference, and performance on working memory tasks. Applied Cognitive Psychology, 25, Derakshan, N., & Eysenck, M. W. (2009). Anxiety, processing efficiency and cognitive performance: New developments from attentional control theory. European Psychologist, 14,

38 30 Engle, R. W. (2002). Working memory capacity as executive attention. Current Directions in Psychological Science, 11, Eysenck, M. W., & Calvo, M. G. (1992). Anxiety and performance: The processing efficiency theory. Cognition and Emotion, 6, Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21, Hopko, D. R., Mahadevan, R., Bare, R. L., & Hunt, M. A. (2003). The abbreviated math anxiety scale (AMAS): Construction, validity, and reliability. Assessment, 10, Kane, M. J., Hambrick, D. Z., Tuholski, S. W., Wilhelm, O., Payne, T. W., & Engle, R. W. (2004). The generality of working memory capacity: A latent-variable approach to verbal and visuo-spatial memory span and reasoning. Journal of Experimental Psychology. General, 133, Lyons, I. M., & Beilock, S. L. (2012). When math hurts: Math anxiety predicts pain network activation in anticipation of doing math. PLoS ONE, 7(10): e Miller, H. & Bichsel, J. (2004). Anxiety, working memory, gender, and math performance. Personality and Individual Differences, 37, Moore, A. M., Allred, G. A., An, W., & Ashcraft, M. H. (2015). Pupillary response and mental multiplication: Problem size and individual differences. Poster presented at the annual meeting of the Psychonomic Society, Chicago, IL Redick, T. S., Broadway, J. M., Meier, M. E., Kuriakose, P. S., Unsworth, N., Kane, M. J., et al. (2012). Measuring working memory capacity with automated complex span tasks. European Journal of Psychological Assessment, 28,

39 31 Richardson, F. C., & Suinn, R. M. (1972). The mathematics anxiety rating scale. Journal of Counseling Psychology, 19, Rivera-Batiz, F. L. (1992). Quantitative literacy and the likelihood of employment among young adults in the United States. The Journal of Human Resources, 27(2), Salthouse, T. A., & Babcock, R. L. (1990). Computation span and listening span tasks. Unpublished manuscript, Georgia Institute of Technology, Atlanta. Schneider, W., Eschman, A., & Zuccolotto, A. (2001). E-Prime user s guide. Pittsburgh: Psychology Software Tools. Shackman, A. J., Sarinopoulos, I., Maxwell, J. S., Pizzagalli, D. A., Lavric, A., and Davidson, R. J. (2006). Anxiety selectively disrupts visuospatial working memory. Emotion 6, Spielberger, C. D., Gorsuch, R. L., Lushene, R., Vagg, P. R., & Jacobs, G. A. (1984). State Trait Anxiety Inventory. Consulting Psychological Press, Inc. Tabachnick, B. G., and Fidell, L. S. (2013). Using multivariate statistics, 6th ed. Boston: Pearson. Tobias, S. (1985). Test anxiety: Interference, defective skills, and cognitive capacity. Educational Psychologist, 20, Unsworth, N., Heitz, R. P., Schrock, J. C., & Engle, R. W. (2005). An automated version of the operation span task. Behavior Research Methods, 37, Vytal, K., Cornwell, B., Arkin, N., and Grillon, C. (2012).Describing the interplay between anxiety and cognition: From impaired performance under low cognitive load to reduced anxiety under high load. Psychophysiology 49,

40 32 Vytal, K. E., Cornwell, B. R., Arkin, N. E., Letkiewicz, A. M., and Grillon, C. (2013). The complex interaction between anxiety and cognition: insight from spatial and verbal working memory. Frontiers in Human Neuroscience, 7:93. Woodcock, R.W., & Johnson, M.B. (1990). Woodcock Johnson Psycho-Educational Battery Revised. DLM Teaching Resources, Allen, TX.

41 33 VI APPENDICES Appendix A: Abbreviated Math Anxiety Scale (Hopko, Mahadevan, Bare, & Hunt, 2003) Please rate each item in terms of how anxious you would feel during the event specified. Use the following scale and record your answer in the space to the left of the item: Scale: 1 = Low Anxiety 2 = Some Anxiety 3 = Moderate Anxiety 4 = Quite a bit of Anxiety 5 = High Anxiety 1. Having to use the tables in the back of a math book. 2. Thinking about an upcoming math test one day before. 3. Watching a teacher work an algebraic equation on the blackboard. 4. Taking an examination in a math course. 5. Being given a homework assignment of many difficult problems which is due the next class meeting. 6. Listening to a lecture in math class. 7. Listening to another student explain a math formula. 8. Being given a pop quiz in a math class. 9. Starting a new chapter in a math book.

42 34 Appendix B: Short Mathematics Anxiety Rating Scale (Alexander & Martray, 1989) Not at A little A fair Much Very all amount much 1. Studying for a math test. 2. Taking math section of a college entrance exam (ACT/SAT). 3. Taking an exam (quiz) in a math course. 4. Taking an exam (final) in a math course. 5. Picking up math textbook to begin working on a homework assignment. 6. Being given homework assignments of many difficult problems that are due the next class meeting. 7. Thinking about an upcoming math test 1 week before. 8. Thinking about an upcoming math test 1 day before. 9. Thinking about an upcoming math test 1 hour before 10. Realizing you have to take a certain number of math classes to fulfill requirements. 11. Picking up math textbook to begin a difficult reading assignment. 12. Receiving your final math grade. 13. Opening a math or statistics book and seeing a page full of problems. 14. Getting ready to study for a math test.

43 Being given a pop quiz in a math class. 16. Reading a cash register receipt after your purchase. 17. Being given a set of numerical problems involving addition to solve on paper. 18. Being given a set of subtraction problems to solve. 19. Being given a set of multiplication problems to solve. 20. Being given a set of division problems to solve. 21. Buying a math textbook. 22. Watching a teacher work on an algebraic equation on the board. 23. Signing up for a math course. 24. Listening to another student explain a math formula. 25. Walking into a math class.

44 VERY MUCH SO MODERATELY SO SOMEWHAT NOT AT ALL 36 Appendix C: State -Trait Anxiety Inventory (Spielberger, Gorsuch, Lushene, Vagg, & Jacobs, 1984) A number of statements which people have used to describe themselves are given below. Read each statement and then circle the appropriate number to the right of the statement to indicate how you feel right now, at this moment. There are no right or wrong answers. Do not spend too much time on any one statement, but give the answer which seems to describe your present feelings best. 1. I feel calm I feel secure I am tense I feel strained I feel at ease I feel upset I am presently worrying over possible misfortunes I feel satisfied I feel frightened I feel comfortable I feel self-confident I feel nervous I am jittery I feel indecisive I am relaxed I feel content I am worried I feel confused I feel steady I feel pleasant

45 37 Appendix D: Running Span Instructions and Procedure Overview (Broadway & Engle, 2010) Instruction Page 1 In this task, you will see letters one after the other. The length of each series of letters will be different and unpredictable each time. Your job will be to remember a certain number of the most recent letters in the same order as presented. Instruction Page 2 For example, you might see a series of FIVE letters, but you will need to recall the LAST TWO. Other times, you might see a series of four letters, but your job will still be to remember the last TWO letters in the same order as presented. You will get a chance to practice the task before the real trials. Instruction Page 3 For example, you could see this list, one letter at a time: J Q S R K The last 2 letter in the order presented are R K. After the end of each list of letters you will see a screen containing possible letters with a check box beside each one. Click on the box for each letter that you remember in the order it was presented. The letters will appear at the bottom of the screen as you click. Instruction Page 4 Click NEXT when you have selected the letters in the correct order. If you forget one or more letters, click BLANK to leave a spot for each missing letter. It is very important to give the letters in the presented order! Click CLEAR if you make a mistake and want to start over.

46 38 Instruction Page 5 After this screen, you will get four practice trials. The length of each sequence of letters will be unpredictable. The letters will appear at a rate of about 2 per second. Do your best to remember the LAST TWO letters from each list in the order presented. Please ask the experimenter any questions you may have at this time. Practice Trials Instruction Page 6 That is the end of the practice. In the following blocks of real trials, sometimes you will need to remember DIFFERENT numbers of letters. Sometimes, you will need to remember the last 4 letters, or sometimes the last 5 letters, and so on. You will always be told at the start of a block of trials how many of the last letters you will need to remember during that block. Please ask the experimenter any questions that you may have at this time. Real Trials End of Task

47 39 Appendix E: Symmetry Span Instructions and Procedure Overview (Redick, et al., 2012) Instruction Page 1 In this experiment you will try to memorize the position of colored squares you see on the screen while you also make judgements about other pictures. In the next few minutes, you will have some practice to get you familiar with how the experiment works. We will begin by practicing the "square" part of the experiment. Instruction Page 2 For this practice set, squares will appear on the screen one at a time. Try to remember where each square was, in the order it was presented in. After 2-5 squares have been shown, you will see a grid of the 16 possible places the squares could have been. Your job is to select each square in the order presented. To do this, use the mouse to select the appropriate boxes. The squares you select will turn red. Instruction Page 3 When you have selected all the squares, and they are in the correct order, hit the EXIT box at the bottom right of the screen. If you make a mistake, hit the CLEAR box to start over. If you forget one of the squares, click the BLANK box to mark the spot for the missing square. Remember, it is very important to get the squares in the same order as you see them. If you forget one, use the BLANK box to mark the position. Do you have any questions so far? When you are ready, click the mouse button to start the square practice. Square Practice Trials Instruction Page 4 Now you will practice doing the symmetry part of the experiment. A picture will appear on the screen, and you will have to decide if it is symmetrical. A picture is symmetrical if you can fold

48 40 it in half vertically and the picture on the left lines up with the picture on the right. On the next screen you will see a picture that IS SYMMETRICAL. Example Page 1 Notice that this picture is symmetrical about the red line. In the real pictures the red line will not be present. Example Page 2 Here, the picture is NOT symmetrical. If you folded this across the red line, the boxes would NOT line up.

49 41 Example Page 3 This is another example of a picture that IS symmetrical. If you folded it vertically, the two sides would line up. Example Page 4 Here is another example of a picture that is NOT symmetrical. Notice that if folded, the two sides would not line up. If you have any questions about how symmetry works, please ask them now. Instruction Page 5 Once you have decided if the picture is symmetrical, click the mouse. On the next screen a YES and NO box will appear. If the picture you saw was symmetrical, click the YES box. If it was not symmetrical, click the NO box. After you click on one of the boxes, the computer will tell you if you made the right choice.