Mathematics is useful for many aspects of everyday living. Its use ranges from basic arithmetic, such as calculating change in a shop, through to advanced mathematics involved in, for example, physics and engineering. Success in mathematics also has wider reaching consequences in terms of improved reasoning and problem solving skills (Attridge & Inglis, 2013; Nisbett, Fong, Lehman, & Cheng, 1987; Smith, 2004) as well as enhanced employability and earning potential (Bynner, 1997; RiveraBatiz, 1992). Individual differences in mathematics are underpinned by a range of different domainspecific and domaingeneral factors, as specified in multicomponent models of mathematical cognition (Fuchs et al., 2010; Geary, 2004, 2011; LeFevre et al., 2010).
A key domaingeneral skill linked to individual differences in mathematics is working memory, the ability to temporarily store and manipulate information in mind (Baddeley, 1992). Individuals who perform well in tests of mathematics have been consistently found to also possess good working memory skills (e.g. Gathercole, Pickering, Knight, & Stegmann, 2004; Holmes & Adams, 2006; Imbo & LeFevre, 2010; Leikin, PazBaruch, & Leikin, 2013; Raghubar, Barnes, & Hecht, 2010; Wilson & Swanson, 2001). The vast majority of this research has focused on arithmetic, most often with children, and there has been comparatively little focusing on the cognitive skills associated with the performance of advanced mathematics in adults (Wei, Yuan, Chen, & Zhou, 2012).
Relationships between working memory and mathematics may differ for adults and children however. Firstly, working memory has been found to play a larger role in the procedural strategies favored by children, as compared to the greater use of retrieval strategies and more efficient use of procedural strategies in adults (Imbo & Vandierendonck, 2008). Secondly, research involving children might also reflect the role of working memory in learning mathematics rather than the proficient performance of mathematics, and finally, working memory may play a larger role in the arithmetic that dominates early mathematics, rather than the wider range of areas encountered later in study.
A further question concerns the type of working memory that best predicts mathematics outcomes. The model of working memory typically adopted in this field comprises verbal (phonological loop) and visuospatial (visuospatial sketchpad) storage components and an executive component (central executive) that coordinates them (Baddeley, 2003). While the central executive is considered a domaingeneral resource, most executive working memory tasks involve the storage of information in either the verbal or visuospatial domain. There is mixed evidence concerning whether mathematics performance is more strongly related to verbal or visuospatial storage. Some studies, particularly those carried out with children, suggest verbal working memory shows a stronger link with mathematics (Bayliss, Jarrold, Gunn, & Baddeley, 2003; Frisovan den Bos, van der Ven, Kroesbergen, & van Luit, 2013; Östergren & Träff, 2013). Moreover, there is some evidence that the role of verbal working memory may increase between the ages of 7 and 12 years, while the role of visuospatial working memory may decrease (Van de WeijerBergsma, Kroesbergen, & Van Luit, 2015; but see Geary, Nicholas, Li, & Sun, 2017).
In contrast, other studies find a stronger relationship between visuospatial working memory capacity and mathematics (e.g. David, 2012; Leikin et al., 2013) and suggest that the role of visuospatial working memory may increase with age between 6 and 15 years (Li & Geary, 2013, 2017). Szűcs, Devine, Soltesz, Nobes, and Gabriel (2014) examined a wide range of cognitive abilities linked to mathematics in 100 seven to ten year old children and found that whilst visuospatial working memory predicted arithmetic performance, verbal working memory did not. To our knowledge, only two studies to date have directly compared the contribution of verbal and visuospatial working memory in arithmetic in adults, one finding a greater role for verbal as compared to visuospatial working memory (Logie, Gilhooly, & Wynn, 1994), and the other a greater role for visuospatial as compared to verbal working memory (Clearman, Klinger, & Szűcs, 2017). However, no studies have directly compared the role of verbal and visuospatial working memory in more general advanced mathematics in adulthood.
One established method of studying the relationship between advanced mathematics and other cognitive skills in adults is to compare students who study mathematics with those who do not (e.g. Attridge & Inglis, 2013; Inglis & Simpson, 2009). While this cannot tell us about causality, it can indicate the presence or absence of relationships. Dark and Benbow used a similar approach to compare the role of working memory in mathematically and verbally gifted adolescents (1214yearsold) across a series of studies (Dark & Benbow, 1990, 1991). They found that mathematically gifted adolescents had greater capacity for the simple storage of digits and spatial information in memory than verbally gifted adolescents as well as greater ability to update paired associations between letters and digits in working memory. Greater ability to update paired associations between letters and spatial locations was found in one study (Dark & Benbow, 1990) but not another (Dark & Benbow, 1991). Taken together, these findings suggest that general advanced mathematics may be associated with enhanced shortterm and working memory, however it remains to be seen whether this relationship is present in adults.
In this paper we present three experiments which investigate differences in both verbal and visuospatial working memory capacity between adult mathematics and humanities students^{i}. Examining the working memory performance of skilled adult mathematicians will help inform models of which working memory resources are associated with the proficient solving of mathematical problems, and how these associations are influenced by age, skill level and type of mathematical knowledge. It is yet to be shown whether adults who are proficient at mathematics have superior working memory capacity to those who are less skilled at mathematics, and if so, whether this depends on the type of material to be stored. If working memory plays a critical role in mathematics, as suggested by literature investigating both verbal and visuospatial working memory (e.g. Dark & Benbow, 1990, 1991, 1994; Szűcs et al., 2014), we would expect to see greater working memory capacity in skilled mathematicians compared to an equivalent group who are not skilled in mathematics in both verbal and visuospatial domains.
Experiment 1 [TOP]
Experiment 1 investigated differences between the working memory storage capacity for number, word and visuospatial stimuli of adult mathematics and humanities students. Individuals with good visuospatial working memory have been shown to have higher levels of mathematics achievement (David, 2012; Leikin et al., 2013; Li & Geary, 2013; Szűcs et al., 2014). Previous research with adults (Fürst & Hitch, 2000; Imbo & Vandierendonck, 2007; Logie et al., 1994) and children (Adams & Hitch, 1997; Gathercole et al., 2004; Jarvis & Gathercole, 2003; Passolunghi, Vercelloni, & Schadee, 2007; Purpura & Ganley, 2014) has also suggested verbal working memory capacity is linked to mathematics achievement. Therefore, we predicted that mathematics undergraduates would have greater working memory capacity for both verbal and visuospatial information than humanities undergraduates.
Traditionally, span tasks used to measure working memory capacity have included a processing element, such as reading, performing arithmetic or judging the symmetry of pairs of objects, interweaved with toberemembered storage items, such as numbers, words or the orientation of arrows (Friedman & Miyake, 2004; Unsworth & Engle, 2007). At the end of each set, the toberemembered items have to be recalled, in correct serial order. However, the format of verbal and visuospatial processing elements, and whether they are combined with storage items from the same or different domain, impacts the number of items remembered. It can also affect the strength of correlations between working memory and higherlevel cognitive tasks (Jarrold, Tam, Baddeley, & Harvey, 2011; Shah & Miyake, 1996; Vergauwe, Barrouillet, & Camos, 2010). Therefore, choice of the type and format of the processing element in a working memory span task is extremely important. To reduce the impact of the processing element on the storage capacity for different types of material, we used the same novel facematching task (Burton, White, & McNeill, 2010) for the processing element in all conditions. This was a basic visual comparison involving no spatial transformation (Miyake, Friedman, Rettinger, Shah, & Hegarty, 2001) or verbal processing and was therefore chosen because it was as neutral as possible with regard to the storage stimuli used.
Method [TOP]
Participants [TOP]
55 participants were recruited from undergraduates at the University of Nottingham: 27 (10 male) to a mathematics students group and 28 (8 male) to a humanities students group. All participants gave written informed consent and received an inconvenience allowance of £6. The study was conducted in accordance with the British Psychological Society’s (BPS) Code of Human Research Ethics. The mathematics students group comprised 19 students studying for a Mathematics degree and 8 students studying for an Economics degree^{ii}. Their ages ranged from 18.33 to 30.58 years (M = 20.43; SD = 2.29). Economics students were included because degree modules for this subject contain substantial mathematics elements and all economics undergraduates had studied mathematics at A level (advanced standard examinations completed by UK students at 18 years of age). The humanities students group comprised English, History and Sociology undergraduates, who were not studying mathematics modules at University. Their ages ranged from 18.67 to 28.92 years (M = 20.72; SD = 2.35). Five of the humanities students group were later discovered to have studied mathematics at A level and their data was therefore discarded. The remaining participants in this group had not studied mathematics for a mean of 4.29 years (SD = 2.71). All experiments received ethical approval from the ethics committee of the School of Psychology, University of Nottingham.
Equipment and Materials [TOP]
A Viglen Pentium D computer, running Windows XP and PsychoPy2 version 1.73.06 (Peirce, 2007), was used to present stimuli and record latencies and accuracy. Participants’ responses were collected via keyboard, numeric keypad or USB mouse depending on the task.
Working Memory Tasks [TOP]
There were three working memory span tasks which had the same processing element interweaved with different storage elements.
For the processing element, participants were presented with two photographs of faces (8.5 cm x 9.5 cm high) side by side on screen and had to make a judgement as to whether they were different pictures of the same person or not, responding with the ‘y’ or ‘n’ key on the keyboard. The pictures were all taken from the Glasgow Unfamiliar Face Database, which shows a high internal reliability when used in a facematching task (Burton et al., 2010). Faces presented were all white, Western, with neutral expressions and matching pairs were presented in approximately 50% of the trials.
The storage element of each span task consisted of numerical, word or visuospatial items presented in the center of the screen (size 2cm). Items were taken from a group of nine possible stimuli in each condition. Numerical items included the digits 1 to 9. Word items were animal words (fly, cow, dog, bat, ape, fox, elk, hen, ram). Visuospatial items employed a black 3 x 3 grid (each square 6cm wide x 6cm high) with a red dot (diameter 3 cm) placed in one of the nine possible locations on the grid.
Each trial comprised an interweaved series of processing elements and storage items (see Figure 1). Each pair of faces (processing element) was presented on screen for 3 seconds, although participants were still able to respond after this time. Storage items were presented for 500 ms, commencing 500 ms after a response had been given to the preceding pair of faces. The next pair of faces was presented 500ms after the storage item disappeared from screen. Once all storage items had been presented, a “ ? ” appeared in the center of the screen that prompted the participants to recall the storage items, in their order of presentation. In the number condition, participants said the numbers aloud and the experimenter keyed the response into the USB numeric keypad. In the word condition, participants said the words out loud, the experimenter coded them and then entered them via the USB numeric keypad. In the visuospatial condition, a black 3 x 3 grid appeared on screen immediately after the “ ? ” and participants recalled the serial order of the red dot by clicking on the grid, using the USB mouse. Once recall was completed, the participant pressed the space bar to begin the next trial. Each of span lengths 2 to 7 was presented three times, giving 18 span sets (trials) in each of the three conditions. Each of the nine possible items within each set was presented approximately equally.
Additional Materials [TOP]
The Matrix Reasoning and Vocabulary subtests from the Wechsler Abbreviated Scale of Intelligence (WASI; Psychological Corporation, 1999) were administered, using the standard procedures and scores, to enable comparison of the IQ of the two groups. The WoodcockJohnson Calculation Test (Woodcock, McGrew, & Mather, 2001) was also administered. Questions ranged from arithmetic, fractions and long division through to items such as matrices, integration and trigonometry.
Procedure [TOP]
All participants were tested individually by the same experimenter and each session lasted around one hour. After initial instructions, participants practiced 6 trials of the facematching task. All three span tasks commenced with a practice of one 2span set and one 3span set comprising both processing and storage tasks, before the 18 experimental sets were administered. The order in which the three span tasks were presented was counterbalanced across participants and the order of presentation of span sets and the presentation of items within each set was randomized. Participants then completed the Matrix Reasoning and Vocabulary tests, the order of which was counterbalanced across participants. Finally, participants completed the Calculation Test.
Results [TOP]
Seven participants (3 mathematics group; 4 humanities group) were excluded from the current analyses for having an unacceptably high (>15%) error rate in the processing task. One influential outlier was detected in the humanities students group in the visuospatial condition, with a Cook’s Distance score > 1, and this male participant’s data was discarded for analysis purposes.
This left data for 24 (10 male) participants in the mathematics students group and 18 (7 male) in the humanities students group. For all three experiments in this paper, controlling for age and gender had no significant impact on analyses, so age and gender were not included in any analyses reported. Also, for all three experiments, degrees of freedom were corrected using GreenhouseGeisser estimates of spherity where necessary and Bonferroni corrections for multiple comparisons were used. For all analyses other than ANCOVA or correlations involving nonnormal distributions, Pearson’s correlations coefficient, r, is used as a measure of effect size. We have employed this measure rather than other measures of effect sizes, such as Cohen’s d, as it is easily interpreted and compared because its value ranges from 0 to 1. Values for r are widely interpreted as follows: r = .10 (small effect); r = .30 (medium effect); r = .50 (large effect) (Field, 2009, p. 57)
Standardized Tests [TOP]
An independent ttest to compare the two groups’ Calculation Test scores confirmed that the mathematics students group (M = 36.83, SD = 2.91) were significantly better at mathematics than the humanities students group (M = 24.61, SD = 3.57), t(40) = 12.22, p < .001, r = .89. Independent ttests also showed that there was no significant difference between the two groups for Matrix Reasoning (mathematics students: M = 29.42, SD = 2.47; humanities students: M = 28.72, SD = 2.78), t(40) = 0.86, p = .398, r = .13 or for Vocabulary, (mathematics students: M = 61.83, SD = 6.27; humanities students: M = 65.17, SD = 5.73), t(40) = 1.77, p = .085, r = .27.
Storage Element [TOP]
Proportion correct scores were first calculated for each participant for the number of storage items recalled in their correct serial position (Conway et al., 2005). Descriptive statistics by group are shown in Figure 2a. A 2(group: mathematics, humanities) x 3(working memory storage type: number, visuospatial, word) mixed Analysis of Variance (ANOVA) was then performed on these scores. There was no main effect of group, F(1,40) = 3.57, p = .066, r = .29. There was a significant main effect of storage type, F(1.57,62.93) = 51.01, p < .001, r = .67. Pairwise comparisons showed participants were significantly more accurate in the number condition than the visuospatial condition, p < .001, or the word condition, p < .001. Participants were also more accurate in the visuospatial condition than the word condition, p = .003.
There was a significant group x working memory storage type interaction, F(1.57,62.93) = 6.01, p = .007, r = .30. Tests of Bonferronicorrected simple main effects showed that the mathematics students group had significantly greater scores than the humanities students group in the visuospatial condition, F(1,40) = 19.10, p < .001, r = .57, but there was no significant difference in performance between the two groups in the verbal domain, either for word span F(1,40) = 0.01, p = .921, r = .02 or number span F(1,40) = 0.08, p = .783, r = .04. Word span and number span scores were significantly correlated, r = .59, p < .001, but neither were significantly correlated with visuospatial span scores: word span r_{s} = .16, p = .312; number span r_{s} = .12, p = .434.
There was a significant correlation between WoodcockJohnson Calculation scores and visuospatial span performance, r_{s} = .56, p < .001, but neither storage types in the verbal domain correlated with mathematics scores: word span r_{s} = .18, p = .264; number span r_{s} = .07, p = .681.
To further explore the presence or lack of group differences for spatial, word and number storage span scores we conducted a series of Welch’s ttests (allowing for unequal variance due to unequal group sizes) to test for differences between and equivalence of group mean scores (Lakens, 2017). To test for group equivalence, we used the two onesided test (TOST) procedure and set equivalence bounds of raw score differences of .05 and .05 (i.e. groups means were treated as equivalent if mathematicians’ scores were less than 5% above or below nonmathematicians’ scores). For visuospatial span scores, Welch’s ttest for group difference was significant, t(38.42) = 4.40, p < .001, and Welch’s equivalence ttest was nonsignificant, t(38.42) = 1.39, p = .913. For word span scores, Welch’s ttest for group difference was nonsignificant, t(38.06) = 0.08, p = .940, and Welch’s equivalence ttest was significant, t(38.06) = 1.82, p = .038. For number span scores, Welch’s ttest for group difference was nonsignificant, t(35.71) = 0.25, p = .807 and Welch’s equivalence ttest was significant, t(35.71) = 3.85, p < .001. In other words, there is evidence that the groups differed in their visuospatial span scores and there is evidence that the groups were equivalent in their word span and number span scores.
Bayesian analysis was also conducted to examine the presence or lack of group differences for number, word and visuospatial storage span scores. The analysis was conducted using default prior in JASP to conduct simple Bayesian ttests for group differences in correct scores for the different conditions. There was moderate evidence for the null hypothesis that the mathematics and humanities groups were the same in the number (BF_{10} = 0.323) and word (BF_{10} = 0.303) conditions. There was, however, very strong evidence for the alternative hypothesis, that the mathematics and humanities groups were different in the visuospatial condition (BF_{10} = 46.724).
Processing Element [TOP]
Mean accuracy and median RT on the facematching task were calculated for each participant in each of the three working memory span conditions and analyzed with separate 2(group: mathematics, humanities) x 3(working memory storage type: number, visuospatial, word) mixed ANOVAs (see Table 1 for descriptive statistics).
Table 1
Group  Experiment 1

Experiment 2



Accuracy (Pc)

Reaction Time (ms)

Accuracy (Pc)

Reaction Time (ms)


M  SE  M  SE  M  SE  M  SE  
Storage Condition: Number  
Mathematics  .94  .01  1264  63  .95  .01  1304  56 
Humanities  .95  .01  1326  72  .94  .01  1252  59 
Storage Condition: Visuospatial  
Mathematics  .94  .01  1287  50  .95  .01  1311  50 
Humanities  .96  .01  1421  86  .95  .01  1129  48 
Storage Condition: Word  
Mathematics  .93  .01  1323  63  
Humanities  .93  .01  1403  76 
Note. Pc = Proportion correct.
For accuracy, there was no main effect of group, F(1,40) = 2.47, p = .124, r = .24 or group x span type interaction, F(2,80) = 0.34, p = .716, r = .09. There was a significant main effect of storage type, F(2,80) = 5.57, p = .005, r = .42. Pairwise comparisons showed no significant difference in facematching accuracy for the number and visuospatial storage conditions, p = 1.00, but greater facematching accuracy for both the number (p = .034) and visuospatial (p = .016) storage conditions than the word storage condition.
Facematching latencies showed no main effect of group, F(1,40) = 1.03, p = .316, r = .16 or group x storage type interaction, F(2,80) = 0.90, p = .411, r = .15. There was a significant main effect of storage type. F(2,80) = 3.52, p = .034, r = .21. Pairwise comparisons revealed facematching latencies in the number condition were faster than in the word condition, p = .035. There was no significant difference in facematching latencies between the visuospatial and word conditions p = 1.00, or between number and visuospatial conditions, p = .099.
Discussion [TOP]
We found that mathematics students have superior working memory capacity within the visuospatial, but not the verbal domain. There was a large difference between groups for the visuospatial storage condition, where mathematics students were around 10% more accurate than the humanities students. This was underlined by the strong correlation between visuospatial span and WoodcockJohnson Calculation scores, which revealed visuospatial working memory capacity has a significant association with mathematics achievement. Contrary to predictions, there were no differences between the groups of mathematics and humanities students in either the word or numerical conditions. The predictions were based on results of previous studies that involved young children (Adams & Hitch, 1997; Gathercole et al., 2004; Passolunghi et al., 2007; Purpura & Ganley, 2014) and adolescents (Dark & Benbow, 1990, 1991, 1994; Jarvis & Gathercole, 2003) and therefore may reflect a role for verbal working memory resources in learning rather than doing mathematics. Dual task studies with adults (Fürst & Hitch, 2000; Imbo & Vandierendonck, 2007; Logie et al., 1994) have shown that verbal working memory resources are involved in mathematics, but this does not necessarily mean that mathematicians are better at using these resources. Overall, these findings suggest that visuospatial working memory may be linked to advanced mathematics in adults.
There were no group differences on the processing element of the task. In both groups, there was a mediumsized effect of storage condition on the facematching task where accuracy was slightly worse in the word condition than in the number and visuospatial conditions. This is consistent with previous findings that performance on the processing element of a working memory span task usually positively correlates with performance on the storage element (Conway et al., 2005) and performance for word storage was worse than for numbers and visuospatial storage, as shown in Figure 2a. Similarly, a small effect of storage condition indicated that processing latencies were faster in the number condition than in the word and visuospatial conditions, reflecting the greater performance for number storage items. Descriptive statistics in Table 1 show longer processing times for the humanities students compared to the mathematics students in each of the three conditions in Experiment 1, suggesting processing latencies may have been affected by the cognitive load of the storage tasks. However, none of the betweengroup differences for processing latencies were significant.
In Experiment 2 we investigated potential mechanisms to account for our finding that mathematics students had a greater working memory capacity for visuospatial information than humanities students. We explored whether differences in visuospatial shortterm memory (with no processing) or controlled spatial attention could account for this effect. Research has found that the shortterm storage of information is required when solving mathematical problems (Adams & Hitch, 1997; Trbovich & LeFevre, 2003) and that the visuospatial sketchpad may be used during calculation (Lee & Kang, 2002; Logie et al., 1994; Trbovich & LeFevre, 2003). Visuospatial shortterm memory performance, with no processing element present, has been linked to mathematics in adults (Wei et al., 2012). It may therefore be that mathematics students simply have a superior ability to store information within the visuospatial sketchpad.
An alternative explanation for mathematics students’ superior visuospatial working memory capacity could be better endogenous spatial attention. Endogenous attention is believed to be important for refreshing items in memory and for ensuring items remain available for further processing and/or recall (e.g. Barrouillet, Bernardin, Portrat, Vergauwe, & Camos, 2007; Cowan, 2001; Engle, 2002). Previous experimental research suggests an overlap between endogenous attention and visuospatial working memory (Astle & Scerif, 2011; Awh, Jonides, & ReuterLorenz, 1998; Awh, Vogel, & Oh, 2006; Chun & TurkBrowne, 2007; Gazzaley & Nobre, 2012).
Experiment 2 again compared the working memory storage capacity of undergraduate mathematicians and undergraduate humanities students for verbal and visuospatial information. Only the number condition was used in the verbal domain as, in Experiment 1, the number and word conditions showed similar patterns of association with mathematics scores and dissociation with the visuospatial condition. The visuospatial condition in Experiment 2 was identical to that used in Experiment 1 to see whether the result that mathematicians have superior visuospatial working memory storage capacity could be replicated in a new sample. In the number condition, the span lengths used were increased to spans 3 to 8 to investigate whether ceiling effects present in the number condition had impacted the results of Experiment 1.
Based on previous research, we predicted that visuospatial shortterm memory capacity would correlate with calculation skill (Wei et al., 2012). Mathematics students were also predicted to have superior endogenous spatial attention (Astle & Scerif, 2011; Awh et al., 1998; Awh et al., 2006; Gazzaley & Nobre, 2012). Finally, it was expected that mathematics students would still have greater visuospatial working memory capacity when shortterm memory and endogenous attention skills were controlled for because working memory measures that involve both processing and storage are generally deemed better predictors of mathematics achievement than more basic storageonly measures (Bayliss et al., 2003; St. ClairThompson & Sykes, 2010). In line with Experiment 1, no difference in working memory capacity for numbers was expected between the groups.
Experiment 2 [TOP]
Method [TOP]
Participants [TOP]
54 new participants were recruited from undergraduates at the University of Nottingham: 27 (9 male) to a mathematics students group and 27 (9 male) to a humanities students group. Participants gave written informed consent and received an inconvenience allowance of £6. The study was conducted in accordance with the BPS’ Code of Human Research Ethics.
The mathematics students group comprised 15 mathematics students and 12 economics students who had studied mathematics at A level. Their ages ranged from 18.66 to 36.89 years (M = 20.88, SD = 3.53). The humanities students group comprised English, History, Philosophy and Sociology students who had not studied mathematics at A level. Their ages ranged from 18.78 to 22.68 years (M = 20.33, SD = .99). On average, participants in the humanities group had not studied mathematics for 4.18 years (SD = 1.16).
Working Memory Tasks [TOP]
The working memory tasks in Experiment 2 were identical to those used in the number and visuospatial conditions of Experiment 1, with the exception that span lengths 3 to 8 were used for the number condition. Span lengths 2 to 7 were again used in the visuospatial condition.
ShortTerm Memory Task [TOP]
This task consisted of a series of sequentially presented visuospatial storage elements. The format and timings of the task were identical to those of the working memory tasks, except that it consisted solely of toberemembered storage items, with no processing element.
Endogenous Spatial Attention Task [TOP]
Endogenous spatial attention was measured via a basic Posner task (Posner, 1980) which recorded time taken to respond to the appearance of a target stimulus that was preceded by a central cue. The cue either indicated the position of the target (valid cue) or directed controlled attention in the opposite direction (invalid cue) (Doricchi, Macci, Silvetti, & Macaluso, 2010). Participants were expected to respond faster to valid than to invalid cues. The difference in RTs between responses to targets preceded by valid cues and those preceded by invalid cues was taken as a measure of endogenous spatial attention.
The onscreen display consisted of a central cueing stimulus (a diamond shape, 1.3cm wide) and peripheral squares to the left and right (1cm wide), centred at 7cm eccentricity, inside which a target ‘x’ appeared (size 1cm). Initial instructions told participants to stare only at the central cue and not to move their eyes, and to respond to the appearance of target stimuli in the peripheral squares as quickly and accurately as possible by pressing the space bar on the keyboard using their right index finger. On valid and invalid trials, one side of the central diamond cue was highlighted, acting as an arrow towards one of the boxes (valid: same side; invalid: opposite side). On neutral trials, both sides of the central cue lit up. Targets appeared on the right 50% of the time for each cue type. A total of 36 neutral trials, 36 invalid trials and 144 valid trials were used. The 216 trials were split into 3 identical blocks of 72 trials. The order of trials was random within each block and across participants. All cues lit up for 100ms and targets followed cue offsets at stimulusonset asynchronies (SOA) of 200, 400 or 800ms (Gitelman et al., 1999; Kim et al., 1999; Nobre et al., 1997). Targets were also displayed for 100ms. Each of the three SOAs was used in equal proportions within the neutral, valid and invalid trial types. All trials had a total duration of two seconds.
Additional Materials [TOP]
WASI Matrix Reasoning and WoodcockJohnson Calculation Test were administered as in Experiment 1.
Procedure [TOP]
All participants were tested individually by the same experimenter and each session lasted around one hour. After completion of the working memory span tasks, participants completed the shortterm memory task, followed by the attention task. For the shortterm memory task, after reading initial instructions, participants completed a practice of one 2span set and one 3span set, before the test sets were presented. For the endogenous spatial attention task, after initial instructions, participants practiced the task for 22 randomly presented trials. They then viewed a screen which repeated the initial instructions, before commencing the three blocks of experimental trials. A short break was allowed between blocks if required. At the end of the task, participants were asked to selfrate for what extent of the time they had kept their gaze fixed on the central cue as instructed, using the numeric keypad, on a scale of 1 to 5, where 1 was ‘hardly any’ and 5 was ‘almost all’. Finally, participants completed Matrix Reasoning followed by the Calculation Test.
Results [TOP]
Three participants (2 mathematics students group; 1 humanities students group) were excluded from the analyses for having an unacceptably high (>15%) error rate in the processing element of the working memory tasks leaving data for 25 (9 male) participants in the mathematics students group and 26 (9 male) in the humanities students group.
Standardized Tests [TOP]
An independent ttest to compare the two groups’ WoodcockJohnson Calculation Test scores confirmed that the mathematics students group (M = 35.80, SD = 3.50) were significantly better at mathematics than the humanities students group (M = 23.15, SD = 3.46), t(49) = 12.97, p < .001, r = .88.
An independent ttest showed that the mathematics students group (M = 28.92, SD = 2.41) had significantly higher scores for WASI Matrix Reasoning than the humanities students group (M = 26.88, SD = 3.25), t(49) = 2.53, p = .015, r = .34, suggesting a higher nonverbal IQ. All analyses were therefore initially run controlling for WASI Matrix Reasoning scores. This made no difference to main effects or interactions, therefore the results reported below do not control for WASI Matrix Reasoning scores.
Storage Element of Working Memory Tasks [TOP]
Proportion correct scores were calculated for each participant for the number of storage items recalled in their correct serial position. Before conducting the main ANOVA, scores were examined for the two groups in the number span condition for span lengths 3 to 8, to check for ceiling effects. Mean proportion correct scores (mathematics students: M = .88, SD = .08; humanities students: M = .87, SD = .05) clearly showed that neither group was performing at ceiling and showed no significant difference in proportion correct scores between the two groups, U = 323.00, Z = .04, p = .974. Only one participant in each group answered all items correctly.
A 2 (group: mathematics, humanities) x 2 (working memory storage type: number, visuospatial) mixed ANOVA was then performed on the proportion correct scores using span lengths 3 to 7 for both conditions. Descriptive statistics are shown in Figure 2b. There was a main effect of group, with mathematics students scoring higher overall, F(1,49) = 8.90, p = .004, r = .39. There was also a main effect of storage type, with performance for number span greater than that for visuospatial span, F(1,49) = 29.50, p < .001, r = .61. There was also a group x storage type interaction, F(1,49) = 24.09, p < .001, r = .57. Tests of simple main effects showed that the mathematics students group had significantly greater visuospatial span scores than the humanities students group, F(1,40) = 19.94, p < .001, r = .54, but there was no significant difference in performance between the two groups for number span F(1,49) = 0.07, p = .788, r = .04. Visuospatial span scores also did not correlate with number span scores, r_{s} = .17, p = .245.
There was a significant correlation between participants’ visuospatial span performance and their WoodcockJohnson Calculation scores r_{s} = .57, p < .001. Number span did not correlate significantly with Calculation scores r_{s} = .04, p = .763.
To further explore the presence or lack of group differences for spatial and number storage span scores we conducted a series of Student’s ttests to test for differences between and equivalence of group mean scores (Lakens, 2017). To test for group equivalence, we used the two onesided test (TOST) procedure and set equivalence bounds of raw score differences of .05 and .05 (i.e. groups means were treated as equivalent if mathematicians’ scores were less than 5% above or below nonmathematicians’ scores). For visuospatial span scores, the ttest for group difference was significant, t(49) = 4.49, p < .001, and the equivalence ttest was nonsignificant, t(49) = 2.72, p = .995. For number span scores, the ttest for group difference was nonsignificant, t(49) = 0.26, p = .799 and the equivalence ttest was significant, t(49) = 2.30, p = .013. In other words, there is evidence that the groups differed in their visuospatial span scores and there is evidence that the groups were equivalent in their number span scores.
Bayesian analysis was also conducted to examine the presence or lack of group differences for number and visuospatial storage span scores. The analysis was conducted using default prior in JASP to conduct simple Bayesian ttests for group differences in correct scores for the different conditions. There was moderate evidence for the null hypothesis that the mathematics and humanities groups were the same in the number (BF_{10} = 0.289) condition. There was, however, extreme evidence for the alternative hypothesis, that the mathematics and humanities groups were different in the visuospatial condition (BF_{10} = 424.547).
Processing Element of Working Memory Tasks [TOP]
Mean accuracy and median RT on the facematching task were calculated for each participant in each of the two working memory span conditions over span lengths 3 to 7, and analyzed with separate.2 (group: mathematics, humanities) x 2 (working memory storage type: number, visuospatial) mixed ANOVAs (see Table 1 for descriptive statistics). There was no significant difference in accuracy or RT for the facematching task between groups or across the different storage conditions (all F < 1.25, ns).
ShortTerm Memory Task [TOP]
Proportion correct scores were calculated for each participant for the number of storage items recalled in their correct serial position. There was no significant difference in performance between the mathematics students (M = .88, SD = .06) and the humanities students (M = .85, SD = .08), U = 234.00, Z = 1.72, p = .086, r = .25. A nonparametric test was used because both groups’ scores showed significant negative skew.
Endogenous Spatial Attention Task [TOP]
Median RTs were calculated for each participant for each of neutral, valid and invalid trials, before calculating the difference between their invalid and valid RTs (endogenous spatial attention). Participants reported they had kept their gaze fixed centrally, as required, on the majority of trials (mathematics group: M = 4.63, SD = 0 .74; nonmathematics group: M = 4.70, SD = 0.67). There was no significant difference between mathematics students (M = 326, SD = 40) and humanities students (M = 316, SD = 38) for reaction times to respond to valid trials, U = 25.50, Z = .74, p = .463. An independent ttest compared the endogenous spatial attention skills of the two groups (invalid RTs minus valid RTs: mathematics group: 25, SD = 24; humanities group: M = 28, SD = 23) and, again, no significant difference was found, t(49) = 0.91, p = .367, r = .13.
Group Differences in VisuoSpatial Working Memory When Controlling for ShortTerm Memory and Attention Skills [TOP]
An ANCOVA was run to investigate whether mathematics students had greater visuospatial working memory storage capacity when controlling for shortterm memory performance and endogenous spatial attention. Results showed the covariate visuospatial shortterm memory was significantly related to visuospatial working memory F(1,47) = 13.58, p = .001. The covariate endogenous spatial attention was not significantly related to visuospatial working memory, F(1,47) = 1.61, p = .210. When controlling for visuospatial shortterm memory and endogenous spatial attention, the mathematics students still had significantly greater visuospatial working memory scores than the humanities students, F(1, 47) = 15.54, p < .001, r = .50.
Discussion [TOP]
In a new sample of participants we replicated our finding of greater visuospatial working memory storage capacity in mathematics students compared with humanities students with an even larger effect size. Furthermore, visuospatial working memory storage scores again correlated strongly with WoodcockJohnson Calculations scores (r = .57). The results of both Experiments 1 and 2 suggest visuospatial working memory storage capacity is linked to mathematics.
As predicted, results of the ANCOVA showed that, when controlling for visuospatial shortterm memory scores and endogenous spatial attention, there was still a large difference between mathematics students and humanities students in the ability to store visuospatial information in working memory. This therefore suggests it is the ability to hold visuospatial information in mind whilst carrying out processing, rather than more simple storage or endogenous attention, that underlies the link with mathematics. This pattern of results supports the previous finding that working memory skills are more predictive than shortterm memory skills of complex cognitive processes (Bayliss et al., 2003; St. ClairThompson & Sykes, 2010).
Experiment 3 [TOP]
Experiments 1 and 2 involved working memory span tasks with a processing element that was as neutral as possible with regard to the storage elements. This enabled the examination of capacity for the verbal and visuospatial storage elements using a consistent processing element across the tasks in both domains. It also ensured that, as far as possible, the processing element did not interfere with storage in one domain more than in the other. However, previous research has shown that the domain of the processing element affects the number of verbal and visuospatial items that can be stored and the relationship between working memory capacity and more complex cognition (Jarrold et al., 2011; Shah & Miyake, 1996; Vergauwe et al., 2010). Experiment 3 therefore combined verbal and visuospatial processing with verbal and visuospatial storage. This allowed us to test whether mathematics students always have superior visuospatial storage ability while using working memory or whether this depends upon the type of processing being carried out. It also examined whether mathematics students’ apparent superior capacity for storing visuospatial information in working memory is simply due to a greater ability to deal with visuospatial information.
Experiment 2 ruled out the possibility that shortterm memory and endogenous spatial attention were driving group differences in visuospatial working memory. A further possibility is that the visuospatial working memory difference stems from differences in general ability for dealing with visuospatial information. Wei et al. (2012) found both visuospatial storage capacity and general visuospatial skills, measured by a 3dimensional spatial rotation task, correlated with mathematics performance in Chinese college students. However, they did not examine whether the relationship between visuospatial storage ability and mathematics could be explained by general visuospatial skills. Previous research has implicated the use of general visuospatial resources in the solving of mathematical problems (Delgado & Prieto, 2004; Friedman, 1995; Jiang, Cooper, & Alibali, 2014; Landy, Brookes, & Smout, 2014; Marghetis, Núñez, & Bergen, 2014; Pinhas, Shaki, & Fischer, 2014; Wiemers, Bekkering, & Lindemann, 2014). Casey, Nuttall, Pezaris, and Benbow (1995) and Casey, Nuttall, and Pezaris (1997) found links between mental rotation ability and scores on the SATM math test, whilst Geary, Saults, Liu, and Hoard (2000) found mental rotation was related to arithmetical reasoning ability. It is therefore plausible that a generally enhanced ability for dealing with visuospatial information could underpin mathematics students’ superior visuospatial working memory as well as drive the relationship between visuospatial storage ability and performance on the Calculation test.
To determine whether mathematics students possess greater visuospatial skills, participants’ performance was compared on the Revised Vandenberg & Kuse Mental Rotations Test: MRTA (Peters, Chisholm, & Laeng, 1995), which has been used across a range of subject literature as a measure of general visuospatial processing (e.g. Hausmann, Slabbekoorn, Van Goozen, CohenKettenis, & Güntürkün, 2000; Hedman et al., 2006; Langlois et al., 2009). Performance of the mathematics students and humanities students was also compared for the processing elements of the working memory span tasks, which provided another measure of general visuospatial processing skills.
On the basis of Experiments 1 and 2 we predicted that mathematics students would remember more items in their correct serial position in the two working memory span task conditions involving visuospatial storage, regardless of the domain of the processing. It was predicted that there would be no difference between the performance of the two groups in the verbal processing & verbal storage condition. No firm prediction was made regarding differences in the visuospatial processing & verbal storage condition. It was also expected that mathematics students would perform better than humanities students for general visuospatial skills as measured by scores for the MRTA, and faster and more accurately for the visuospatial processing elements of the span tasks (e.g. Delgado & Prieto, 2004; Wei et al., 2012). It was expected there would be no difference between the two groups for verbal processing. Finally, it was predicted that mathematics students would still have greater visuospatial working memory capacity than humanities students after controlling for visuospatial processing ability, because of the view that complex span tasks are better predictors of cognitive ability than measures of more basic skills (Bayliss et al., 2003; St. ClairThompson & Sykes, 2010).
Method [TOP]
Participants [TOP]
57 new participants were recruited from the undergraduate population at the University of Nottingham: 28 (11 male) to a mathematics students group and 29 (7 male) to a humanities students group. All participants gave written informed consent and received an inconvenience allowance of £9. The study was conducted in accordance with the BPS’ Code of Human Research Ethics. The mathematics students group comprised 20 mathematics students and 8 economics students who had studied mathematics at A level. Their ages ranged from 18.68 to 32.56 years (M = 20.83, SD = 2.68). The humanities students group comprised English, History, and Sociology students who had not studied mathematics at A level. Their ages ranged from 18.76 to 31.70 years (M = 20.63, SD = 2.51). On average, participants in the humanities students group had not studied mathematics for 4.22 years (SD = 1.39).
Equipment [TOP]
An Acer Aspire 5736Z laptop computer, running Windows 7 and PsychoPy2 version 1.77.01 (Peirce, 2007), was used to present stimuli and record latencies and accuracy.
Working Memory Tasks [TOP]
There were four span tasks. Each had a different combination of interweaved processing and storage elements: verbal processing & verbal storage; verbal processing & visuospatial storage; visuospatial processing & verbal storage; and visuospatial processing & visuospatial storage. Timings used were identical to those used in the working memory span tasks of Experiments 1 and 2.
The visuospatial processing task was adapted from one used by Miyake et al. (2001) and employed spatial visualization. Participants saw two pictures on screen, side by side. The picture on the left of each pair represented a piece of paper folded in half with a hole punched in it. Participants had to imagine opening out this piece of paper towards the dotted lines shown. They then indicated whether or not the unfolded paper would look like the picture on the right of the pair, by pressing the ‘y’ key on the laptop’s keyboard for yes or the ‘n’ key for no.
The verbal processing task was a word rhyming judgement task (e.g. Baldo & Dronkers, 2006; Gathercole, Alloway, Willis, & Adams, 2006). Participants saw two English words on screen, side by side. They had to indicate whether or not the two words rhymed, by pressing the ‘y’ key for yes or the ‘n’ key for no.
Two blocks of unique visuospatial processing items and verbal processing items were created. A pilot study was conducted to confirm no difference in difficulty of the four blocks of processing items. Each processing block was then assigned to one of the working memory span task conditions. The storage items of each span task consisted either of the same numbers or visuospatial items as in Experiment 2. Presentation of trials and recording of responses were the same as in the previous two experiments. Span sets, and items within them, were presented in a random order. In all four conditions, each span length from 3 to 8 was presented three times, giving 18 trials. Each of the nine possible storage items within each condition was presented approximately equally.
Additional Materials [TOP]
The WoodcockJohnson Calculation Test and WASI Matrix Reasoning were again administered. Participants also completed the Revised Vandenberg & Kuse Mental Rotations Test: MRTA (Peters et al., 1995) as a measure of general visuospatial skills.
Procedure [TOP]
All participants were tested individually by the same experimenter and each session lasted around 90 minutes. Participants completed the four working memory span tasks on the computer, for each span length 3 to 8. The order in which the four conditions were presented was counterbalanced. and it was ensured the same processing task was not presented in consecutive tasks.
For their first and second span tasks, each participant practiced the relevant processing task. After initial instructions, participants made yes or no judgements for six items, so they could familiarize themselves with the task. They then began the experiment. They commenced with a practice of one 2span set and one 3span set comprising both processing and storage tasks, before the 18 test sets were administered. For their third and fourth span tasks, participants followed the same procedure as described for the first and second span tasks, but omitting the initial practice of the processing element as they were already familiar with it. After completing all four span tasks, they completed the Matrix Reasoning and MRTA tests, the order of which was counterbalanced across participants. Finally, participants completed the Calculation Test.
Results [TOP]
One female participant in the humanities students group was excluded from the analyses due to software failure in one of the conditions. Six participants (1 mathematics group; 5 humanities group) were also excluded for having an unacceptably high (>15%) error rate in the processing task, leaving data for 27 (10 male) participants in the mathematics students group and 23 (7 male) in the humanities student group available.
Standardized Tests [TOP]
An independent ttest to compare Calculation Test scores confirmed the mathematics students group (M = 37.70, SD = 3.56) was significantly better at mathematics than the humanities students group (M = 25.57, SD = 4.86), t(48) = 12.14, p < .001, r = .87. Mathematics students (M = 12.30, SD = 4.83) performed better on the MRTA test of general visuospatial skills than the humanities students (M = 9.09, SD = 4.44), t(48) = 2.43, p = .019, r = .33. There was a significant correlation between MRTA scores and calculation scores, r = .46, p = .001. There was no significant difference between the two groups for Matrix Reasoning (mathematics: M = 29.04, SD = 3.60; humanities: M = 27.52, SD = 3.20), t(48) = 1.56, p = .125, r = .22.
Storage Element [TOP]
Proportion correct scores were calculated for each participant for the number of storage items recalled in their correct serial order. A 2 (group: mathematics, humanities) x 2 (working memory processing type: verbal, visuospatial) x 2 (working memory storage type: verbal, visuospatial) mixed ANOVA was performed on the proportion correct scores. Descriptive statistics are shown in Figure 2c. There was no main effect of group, F(1,48) = 1.08, p = .304, r = .15. There was, however, a main effect of storage type, F(1,48) = 31.21, p < .001, r = .63, with storage of verbal items more accurate overall than storage of visuospatial items. In contrast to Experiments 1 and 2 there was no storage type x group interaction, F(1,48) = 0.02, p = .882, r = .02. There was also a main effect of processing type, F(1,48) = 8.13, p = .006, r = .38, with storage performance better overall when combined with verbal processing than with visuospatial processing. There was no processing type x group interaction, F(1,48) = 0.01, p = .909, r = .01. There was, however, a processing type x storage type interaction, F(1,48) = 47.76, p < .001, r = .71 (Figure 3). Pairwise comparisons showed visuospatial storage was more accurate when paired with verbal processing than with visuospatial processing, F(1,48) = 39.98, p < .001, r = .67. However, verbal storage was more accurate when paired with visuospatial processing than with verbal processing, F(1,48) = 20.35, p < .001, r = .55. Finally, there was no processing type x storage type x group interaction, F(1,48) = .48, p = .492, r = .10.
To further explore the presence or lack of group differences for storage span scores we conducted a series of Welch’s ttests (allowing for unequal variance due to unequal group sizes) to test for differences between and equivalence of group mean scores (Lakens, 2017). To test for group equivalence, we used the two onesided test (TOST) procedure and set equivalence bounds of raw score differences of .05 and .05 (i.e. groups means were treated as equivalent if mathematicians’ scores were less than 5% above or below nonmathematicians’ scores). For verbal processing and verbal storage span scores, Welch’s ttest for group difference was nonsignificant, t(39.38) = 0.58, p = .562, and Welch’s equivalence ttest was also nonsignificant, t(39.38) = 1.24, p = .110. For verbal processing and spatial storage span scores, Welch’s ttest for group difference was nonsignificant, t(33.93) = 0.98, p = .335, and Welch’s equivalence ttest was also nonsignificant, t(33.93) = 0.50, p = .309. For spatial processing and verbal storage span scores, Welch’s ttest for group difference was nonsignificant, t(38.39) = 1.14, p = .262, and Welch’s equivalence ttest was also nonsignificant, t(38.39) = 0.97, p = .169. For spatial processing and spatial storage span scores, Welch’s ttest for group difference was nonsignificant, t(35.52) = 0.46, p = .651, and Welch’s equivalence ttest was also nonsignificant, t(38.39) = 0.97, p = .169. In other words, there is insufficient evidence that the groups either differed or that the groups were equivalent in span scores. Therefore, we can only conclude that the effects were undetermined (Lakens, 2017).
Bayesian analysis was also conducted to examine the presence or lack of group differences for the verbal and visuospatial storage span scores. The analysis was conducted using default prior in JASP to conduct simple Bayesian ttests for group differences in correct scores for the different conditions. There was anecdotal evidence for the null hypothesis that the mathematics and humanities groups were the same in each of the storage conditions (verbal processing, verbal storage BF_{10} = 0.336; verbal processing, visuospatial storage BF_{10} = 0.446; visuospatial processing, verbal storage BF_{10} = 0.539; visuospatial processing, visuospatial storage BF_{10} = 0.35). So, there was no strong evidence that the groups were either different or the same.
Processing Element [TOP]
Mean accuracy and median RT were calculated for each participant in each of the four working memory span conditions. A 2 (group: mathematics, humanities) x 2 (working memory processing type: verbal, visuospatial) x 2 (working memory storage type: verbal, visuospatial) mixed ANOVA was performed for each of accuracy and latencies to examine performance of the two groups on the processing element of each condition. Mean accuracy, mean RT and standard error by group and span type are shown in Table 2.
Table 2
Group  Accuracy (Pc)

Reaction Time (ms)



M  SE  M  SE  
Processing Condition/Storage Condition: Verbal/Verbal  
Mathematics  .97  .01  1254  46 
Humanities  .97  .01  1229  55 
Processing Condition/Storage Condition:Verbal/Visuospatial  
Mathematics  .97  .01  1347  56 
Humanities  .97  .01  1306  56 
Processing Condition/Storage Condition:Visuospatial/Verbal  
Mathematics  .97  .01  1225  45 
Humanities  .97  .01  1354  60 
Processing Condition/Storage Condition: Visuospatial/Visuospatial  
Mathematics  .97  .01  1388  50 
Humanities  .95  .01  1576  103 
Note. Pc = Proportion correct.
Results showed no significant difference in accuracy on the processing tasks between groups or across the different storage conditions (all F < 2.8, ns). There was also no main effect of group on latencies, F(1,48) = 0.79, p = .379, r = .13. There was, however, a main effect of processing type with verbal processing elements being answered faster than visuospatial processing elements, F(1,48) = 13.63, p = .001, r = .47. There was also a main effect of storage type, with the processing elements being answered faster overall when they were interleaved with verbal storage items compared to visuospatial storage items, F(1,48) = 30.28, p < .001, r = .62. There was a significant group x processing type interaction, F(1,48) = 11.99, p = .001, r = .45. Pairwise comparisons showed that, for the mathematics students group, there was no significant difference between latencies for the verbal and visuospatial processing items (p = .866), but that the humanities students were slower to perform visuospatial processing than they were to perform the verbal processing (p < .001). There was no significant group x storage type interaction, F(1,48) = 0.79, p = .379, r = .13, no significant processing type x storage type interaction, F(1,48) = 3.54, p = .066, r = .26 and no significant group x processing type x storage type interaction, F(1,48) = 0.44, p = .511, r = .02.
Regression Analysis to Predict Mathematics Calculation Scores [TOP]
A regression was performed to discover whether visuospatial working memory storage capacity still uniquely and significantly predicted Calculation scores when taking visuospatial processing and general visuospatial skills into account.
As mathematics students were faster than humanities students for the visuospatial processing task, but there was no significant difference between the two groups for accuracy, only processing RT was included in the regression as a measure of visuospatial processing. Because of a strong correlation between accuracy in the two conditions involving visuospatial storage (r_{s} = .66, p < .001) and the two conditions measuring visuospatial processing RTs (r_{s} = .43, p = .002), storage scores and processing RTs were combined across conditions. Calculation Test score was the dependent variable.
Table 3 shows results for the regression model when MRTA scores, for general visuospatial skills, were entered into the model together with visuospatial processing RT at Step 1, followed by visuospatial working memory storage at Step 2. At Step 1, only MRTA scores significantly and uniquely predicted calculation performance. When visuospatial working memory storage was added at Step 2, both MRTA and storage predicted calculation performance and there was significant improvement in the fit of the model.
Comparison of VisuoSpatial Working Memory Results From Experiments 2 and 3 [TOP]
Results from Experiment 3 supported the findings of Experiments 1 and 2 that there is no difference between mathematics and humanities students for verbal working memory storage capacity. However, a different pattern of results emerged for visuospatial working memory storage capacity. In Experiments 1 and 2, when the span tasks included the facematching task as a processing element, which was as neutral as possible with respect to the storage elements, mathematics students were able to store more visuospatial items in working memory. In contrast, in Experiment 3, mathematics students showed no advantage for storing visuospatial information in working memory when storage was combined with either verbal or visuospatial processing. Across the three experiments, it therefore appears that, whilst participants overall found visuospatial storage harder when combined with visuospatial processing and easier when combined with verbal processing, the mathematics students found it easier than the humanities students to store visuospatial information when combined with the neutral as possible facematching processing task. To discover whether these assertions were correct, visuospatial working memory scores from Experiment 2, with neutral as possible processing, were compared to scores for the two visuospatial working memory tasks in Experiment 3.
A 2 (group: mathematics, humanities) x 3 (processing type: neutral, verbal, visuospatial)^{iii} ANOVA was performed on the visuospatial proportion correct scores. Descriptive statistics are shown in Figure 2d.
There was a main effect of group, F(1,145) = 10.08, p = .002, r = .25, with the mathematics students having better visuospatial storage scores overall. The type of processing element significantly affected visuospatial storage ability, as there was also a main effect of processing type, F(2,145) = 11.28, p < .001, r = .27. Pairwise comparisons showed that visuospatial storage scores were greater overall when storage was combined with neutral processing than with visuospatial processing (p < .001) and greater with verbal processing than with visuospatial processing (p < .001). Storage scores were no different between the conditions using neutral and verbal processing (p = 1.00). There was a group x processing type interaction, F(2,145) = 3.34, p = .038, r = .15. Tests of Bonferronicorrected simple main effects demonstrated that for the mathematics students, visuospatial storage scores varied depending on the processing type, F(2,145) = 12.10, p < .001, r = .28. Pairwise comparisons showed that visuospatial storage scores were greater when storage was combined with neutral processing (p < .001), or verbal processing, (p = .011) than with visuospatial processing. Storage scores were no different between conditions using neutral and verbal processing (p = .143). For the humanities students, there was no significant difference in visuospatial storage between any of the three conditions (all ps > .05). The mathematics students were better than the humanities students at storing visuospatial information when storage was combined with the neutral processing task, F(1, 145) = 15.65, p < .001, r = .31. However, there was no significant difference between the two groups for visuospatial storage when it was combined with verbal processing, F(1, 145) = 0.97, p = .328, r = .08 or visuospatial processing, F(1, 145) = .35, p = .557, r = .05.
Discussion [TOP]
Experiment 3 employed working memory span tasks using verbal and visuospatial processing elements to investigate whether the type of processing involved affected the ability of adult mathematics and humanities students to store verbal and visuospatial information whilst using working memory. It also investigated whether there was any difference in storage capacity or processing ability between these two groups. Contrary to predictions, the results showed extremely small and nonsignfiicant differences between mathematics and humanities students for working memory storage capacity for any of the combinations of verbal and visuospatial processing and storage. It should be noted, however, that the tests for equivalence and Bayesian analysis (Section 4.2.2) were inconclusive and we were therefore unable to use them to confirm no group differences. Replication with a larger sample size is therefore necessary to confirm these results. Comparison of results between Experiment 2 and Experiment 3 suggested that mathematics students have superior ability to store visuospatial information in working memory when the processing involved is as neutral as possible, but not when the processing is either verbal or visuospatial. Results of Experiment 3 also showed that mathematics students were faster to perform the visuospatial processing element of the working memory span tasks. There was a moderate difference between groups on the measure of general visuospatial skills, with mathematics students scoring on average 3 points higher than the humanities students. Moreover, both general visuospatial skills and visuospatial storage within working memory were able to uniquely predict mathematics calculation ability.
General Discussion [TOP]
These three experiments have shown that adult mathematics students demonstrate superior visuospatial working memory capacity to humanities students (Experiments 1 and 2), albeit only under certain conditions (Experiment 3). Moreover, this superior visuospatial working memory capacity cannot be explained by superior shortterm memory, endogenous spatial attention or general visuospatial skills. We have also demonstrated for the first time that both visuospatial working memory capacity and general visuospatial skills can significantly and uniquely predict mathematics performance in adults.
The comparison of results across the three working memory processing types indicated that, overall, participants found visuospatial storage more difficult when it was combined with visuospatial processing than with verbal or neutral as possible processing. However, there was a large difference between the groups in storing visuospatial information when it was combined with neutral as possible processing, whereby mathematics students were around 1015% more accurate than the humanities students. The participant profiles of the mathematics and humanities groups used across the experiments were very similar and therefore unlikely to account for the differences in visuospatial working memory performance between experiments. Therefore, the only substantial differences between the methods employed were the types of processing elements included in the working memory span tasks. This explanation is consistent with previous research showing the type of processing element influences the relationship between performance on working memory tasks and higherlevel cognitive tasks (Jarrold et al., 2011; Shah & Miyake, 1996; Vergauwe et al., 2010).
As well as differing according to content domain, it has also been argued that processing tasks differ according to their level of central executive involvement. Miyake et al. (2001) carried out a latent variable analysis and fractionated visuospatial processing tasks into three types: perceptual speed; spatial relations; and spatial visualisation. Perceptual speed involves the efficiency with which an individual can make basic perceptual judgements and involves visual comparisons rather than spatial manipulations. Spatial relations involves transformations, such as the rotation of objects. Finally, spatial visualization requires complex mental manipulation of spatial objects.
The facematching task used in Experiments 1 and 2 was a form of perceptual speed task. It comprised basic visual comparison with little spatial content and therefore had a low level of central executive involvement. In contrast, the paper folding task used in the visuospatial processing condition of Experiment 3 was a spatial visualization task, according to the Miyake et al. (2001) taxonomy, and consequently involved a higher level of central executive resources. In the visuospatial processing condition, with a high central executive load, there was no difference between the mathematics and humanities students. In contrast, with the neutral as possible, facematching task which had low central executive demands, the mathematics students had greater visuospatial storage capacity. Furthermore, the mathematics students showed moderately better visuospatial storage capacity in the neutral condition compared to the visuospatial processing condition, while for the humanities students there was no difference in storage capacity between the two. One possible explanation is that humanities students have a lower visuospatial central executive capacity than the mathematics students. The processing task with high central executive demands used up this capacity in both groups, whereas with the low central executive processing task the mathematics group were able to take advantage of extra resources and consequently could store more items.
The fact that the mathematics students only have superior ability to store visuospatial information when more working memory resources were available in the neutral as possible processing condition is relevant in terms of performing mathematics. If mathematicians are more efficient at remembering and applying calculation strategies (Dowker, Flood, Griffiths, Harriss, & Hook, 1996; Pesenti, 2005), which requires visuospatial working memory, they will have greater resources available to hold, visualize and manipulate numbers during calculation (Geary, 2004; Heathcote, 1994; Logie et al., 1994; Seron, Pesenti, Noël, Deloche, & Cornet, 1992).
The fact that mathematics students had superior visuospatial working memory capacity only when the central executive resources involved in processing were comparatively low might lead to the expectation that they would also have superior visuospatial shortterm memory scores when no processing was present. This did not appear to be the case however. When visuospatial shortterm memory performance was compared in Experiment 2, the effect size was much smaller than the difference in visuospatial working memory capacity, and there was no significant difference between mathematics and humanities students. We see two possible explanations for this. Firstly, whilst the shortterm memory task involved no processing, the working memory task required constant switching between the processing and storage elements of the task. It may be that the mathematics students’ skills lay in combining the processing and storage demands. They may have used central executive resources more efficiently than the nonmathematicians in the neutral as possible processing condition, which resulted in a greater availability of working memory resources to store visuospatial information. The large central executive load in the visuospatial processing condition of Experiment 3 may have caused this advantage in central executive efficiency to disappear. Alternatively, it may in fact be the case that mathematics students also have better visuospatial shortterm memory than humanities students, but that this was not found in Experiment 2 due to a lack of power. The difference between the groups was approaching significance (p = .086) using a nonparametric test. Mathematics students showed moderately superior general visuospatial skills compared to the humanities students. Moreover, general visuospatial skill was a significant independent predictor of mathematics performance. This is in line with previous findings that general visuospatial processing has a role in complex mathematics such as algebra (Landy et al., 2014) and interpreting graphs (Hegarty & Waller, 2005), arithmetical reasoning (Geary et al., 2000) and generally in mathematics (Casey et al., 1995; Casey et al., 1997; Friedman, 1995). The finding that visuospatial working memory storage capacity also significantly and uniquely predicted calculation even after general visuospatial skills were accounted for suggests that the mathematics students’ superior capacity cannot simply be explained by a better general ability to deal with visuospatial information but that the two skills accounts for separate variance in mathematics performance.
Whilst verbal working memory is involved in mathematics (e.g. Bayliss et al., 2003; Frisovan den Bos et al., 2013; Fürst & Hitch, 2000; Imbo & Vandierendonck, 2007; Logie et al., 1994; Östergren & Träff, 2013), we found no difference in verbal working memory capacity between mathematics and humanities students in Experiments 1 and 2, and no evidence for or against a difference in Experiment 3. The majority of evidence for a link between verbal working memory and mathematics comes from research with children; therefore, it may be that the role of verbal working memory in supporting mathematics decreases with age. Alternatively, the studies with adults that do find a relationship with verbal working memory investigate it within the context of arithmetic (Fürst & Hitch, 2000; Imbo & Vandierendonck, 2007; Logie et al., 1994). This suggests verbal working memory may play a role in supporting basic arithmetic but is not as important for the more advanced forms of calculation measured within the current experiments (e.g. matrices, integration and trigonometry). However, the mathematics assessment used throughout this study had a low verbal load. With a more verbal mathematics task, we may have found a different pattern of relationships between mathematics and verbal storage.
In summary, our results show that mathematics students demonstrate enhanced visuospatial working memory capacity under conditions of low central executive load, as well as superior general visuospatial skills. These group differences in visuospatial working memory capacity were not explained by differences in shortterm memory, endogenous attention or general visuospatial skills. There was no difference between mathematics and humanities students for the amount of verbal information that can be stored within working memory. Moreover, both visuospatial working memory capacity and general visuospatial skills predicted mathematics achievement in adults. Taken together, while we are not able to make inferences about the direction of causality, the results point to a strong link between individual differences in visuospatial working memory capacity and mathematics performance in adults. The implications of this are that the more practiced and proficient an individual is at selecting appropriate strategies and following relevant mathematical procedures, the lower the load on the central executive and the more resources the individual will have available for mentally performing calculations and manipulating information. Longitudinal outcomes of gifted adolescents find that those with greater mathematical ability than verbal ability at age 13 are more likely to complete degrees in a STEM subject than a humanities subject (Park, Lubinski, & Benbow, 2007). Taken together with the findings from Dark and Benbow (1990, 1991) this suggests that enhanced working memory skills are present prior to undergraduate study. Further research with both adults and children is still required to determine whether good visuospatial working memory skills support the acquisition of advanced mathematics and/or whether mathematics training enhances working memory skills (cf. the Theory of Formal Discipline; Inglis & Attridge, 2017). Nevertheless, this research indicates that multicomponent models of mathematical processing developed from research with children can also be applied as a framework to study adults and should include working memory, particularly in the visuospatial domain.