inhibiting attention towards intrusive or worrisome thoughts. Inhibition theory (Hasher & Zacks, 1988; Connelly, Hasher & Zacks, 1991) proposes that there is a mechanism for suppressing, or inhibiting, task-irrelevant distracters. If this mechanism is not working adequately then task-irrelevant information may interfere with working memory processes and consequently result in poor performance. Indeed, Hopko et al., 1998) demonstrated that high and medium math anxious groups took significantly longer than a low math anxious group to read through text that included irrelevant information, suggesting poor inhibitory control. Similarly, Hopko, McNeil, Gleason and Rabalais (2002) found that response times of high math anxious individuals were longer on a card counting task with numeric stimuli, compared to a card-counting task involving letters, again implicating inhibitory mechanisms related to working memory. Whilst previous math anxiety research has made reference to worrisome or irrelevant thoughts, surprisingly little research has attempted to examine the influence of worrisome thoughts on arithmetic performance. In an early study, Hunsley (1987) measured math anxiety, test anxiety, performance appraisals, performance attributions and internal dialogue amongst 96 university students before and after midterm statistics examinations. Participants’ negative internal dialogue was measured using the Cognitive Interference Questionnaire (CIQ, Sarason, 1978), which required participants to rate (on a five-point scale) the frequency with which they experienced negative thoughts during the exam. Math and test anxiety accounted for 15% and 10% of the variance in CIQ scores, respectively. Further, Beilock, Kulp, Holt and Carr (2004) found that students performing arithmetic in a high pressure condition (involving carry operations) had significantly increased perceptions of performance pressure and reported thoughts and worries about the high pressure situation and its consequences, compared to students in a low pressure condition. More recently, DeCaro,
impeded calculation, and the amount of effort used to stop/reduce the thoughts. A final question asked participants to indicate whether they had experienced intrusive thoughts that were non-math-task related, for example relationship problems or health problems. The study also included a measure of trait anxiety, taken from the State-Trait Anxiety Inventory (Spielberger, Gorsuch, Lushene, Vagg & Jacobs, 1984) but, the zero-order correlations showed no relationship between trait anxiety and error rates and response time, so analyses including trait anxiety are not presented here (these are available from the first author). Experimental stimuli and procedure Using the experiment-building software E-prime, 80 two-digit addition problems were presented using a verification task, for example ‘37 + 18 = 52’. Sixty of these problems had a solution that was true; 20 had an incorrect solution. Of the 60 true problems, 30 involved a carry operation, for example “17 + 18 = 35”, and 30 involved no carry, for example “17 + 12 = 29”. Addends were randomly taken from a range of 10-89. Problem-size was counterbalanced across addends and carry/no-carry conditions so that performance could be attributed to factors other than the size of the problems. Problems where both addends ending in zeros, for example ‘20 + 30’, or fives, for example ‘25 + 35’, were not included. Incorrect problems were divided approximately equally with splits of +/- 1, +/- 3, and +/- 5, counterbalancing the number of positive and negative splits. Participants gave informed consent and completed the mathematics anxiety scale. Stimuli were presented in the centre of a VDU, in Times New Roman, size 40, bold font. Following the on-screen instructions and five practice trials, participants were asked to respond ‘true’ or ‘false’ to the proposed answers. This was achieved by pressing the ‘z’ and
were an antecedent to response time or whether they occurred following response time. The present study is limited by the extent to which maths anxiety is manipulated. However, experimental designs could be used to examine the importance of particular thoughts in math anxious individuals by manipulating them; for example regular reminders of a time limit (c.f. Kellogg, Hopko & Ashcraft, 1999) or the use of a flashing camera light to increase awareness that performance is being observed. It would also be interesting to investigate the relationship between math anxiety and arithmetic performance, and the importance of intrusive thoughts about previous math experiences, as previous research has emphasised the importance of negative math experiences as antecedents to math anxiety (Trujillo & Hadfield, 1999). In conclusion, math anxiety was shown to be a significant predictor of response time to both carry and no-carry problems. In addition, math anxiety was related to a higher error rate on problems involving a carry operation. Importantly, the extent to which intrusive thoughts impeded calculation mediated this relationship. These findings provide support for an inhibition theory account of math anxiety effects on performance. Intrusive thoughts should be the focus of future research that investigates the relationship between math anxiety and performance. References Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11, 181–185. Ashcraft, M. H., & Faust, M. W. (1994). Mathematics anxiety and mental arithmetic performance: An exploratory investigation. Cognition and Emotion, 8, 97–125. doi: 10.1080/02699939408408931 Ashcraft, M. H., & Moore, a. M. (2009). Mathematics anxiety and the affective drop in performance. Journal of Psychoeducational Assessment, 27, 197–205. doi:10.1177/0734282908330580
Carry problems No-carry problems Step Variables Entered Beta R2 change Model R2 Beta R2 change Model R2 1 Math anxiety .251** .063** -.004 <.001 2 Math anxiety .131 .069* .132** -.078 .014 .014 Frequency -.069 -.028 Difficulty in removing -.018 .147 Impeding calculation .331** .016 3 Math anxiety .141 .002 1.33** -.078 <.001 .014 Frequency -.052 -.028 Difficulty in removing .012 .147 Impeding calculation .347** .016 Effort to reduce thoughts -.074 .002 *p ≤.05 **p ≤.01 Table 2. Results of hierarchical regression with percentage of errors as the outcome variable
Carry problems No-carry problems Step Variables Entered Beta R2 change Model R2 Beta R2 change Model R2 1 Math anxiety .299*** .090*** .302*** .091*** 2 Math anxiety .262* .034 .124** .213 .033 .124** Frequency .105 .114 Difficulty in removing -.198 -.127 Impeding calculation .166 .179 3 Math anxiety .249* .002 1.26** .207 .001 .125** Frequency .085 .104 Difficulty in removing -.234 -.144 Impeding calculation .146 .170 Effort to reduce thoughts .089 .042 *p ≤.05 **p ≤.01 **p ≤.001 Table 3. Results of hierarchical regression with response time as the outcome variable
Thought occurrence Yes No Frequency Maths anxiety Frequency Maths anxiety T (& p) value Effect size (d)* Nature of thought Making mistakes 109 (89.3%) 52.72 (16.51) 13 (10.7%) 43.00 (11.11) 2.06 (.04) 0.61 Time pressure 60 (49.2%) 56.03 (16.67) 62 (50.8%) 47.47 (14.82) 3.00 (.003) 0.54 Method of problem solving 58 (47.5%) 53.29 (17.08) 64 (52.5%) 50.22 (15.48) 1.04 (.30) 0.19 What people might think 48 (39.3%) 59.58 (16.53) 74 (60.7%) 46.55 (13.96) 4.68 (<.001) 0.87 Panicking 26 (21.3%) 65.08 (19.01) 96 (78.7%) 48.05 (13.40) 5.22 (<.001) 1.15 Previous maths experiences 49 (40.2%) 55.67 (16.97) 73 (59.8%) 49.00 (15.32) 2.26 (.03) 0.42 Physical changes 36 (29.5%) 60.97 (17.84) 86 (70.5%) 47.79 (13.92) 4.38 (<.001) 0.87 Non 51 (41.8%) 56.43 (15.25) 71 (58.2%) 48.27 (16.22) 2.81 (.006) 0.52 Table 4. Frequency of intrusive thoughts and maths anxiety level as a function of specific thoughts. *Based on a pooled standard deviation