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Previous research has demonstrated that working memory performance is linked to mathematics achievement. Most previous studies have involved children and arithmetic rather than more advanced forms of mathematics. This study compared the performance of groups of adult mathematics and humanities students. Experiment 1 employed verbal and visuo-spatial working memory span tasks using a novel face-matching processing element. Results showed that mathematics students had greater working memory capacity in the visuo-spatial domain only. Experiment 2 replicated this and demonstrated that neither visuo-spatial short-term memory nor endogenous spatial attention explained the visuo-spatial working memory differences. Experiment 3 used working memory span tasks with more traditional verbal or visuo-spatial processing elements to explore the effect of processing type. In this study mathematics students showed superior visuo-spatial working memory capacity only when the processing involved had a comparatively low level of central executive involvement. Both visuo-spatial working memory capacity and general visuo-spatial skills predicted mathematics achievement.

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 (

A key domain-general skill linked to individual differences in mathematics is working memory, the ability to temporarily store and manipulate information in mind (

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 (

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 visuo-spatial (visuo-spatial sketchpad) storage components and an executive component (central executive) that coordinates them (

In contrast, other studies find a stronger relationship between visuo-spatial working memory capacity and mathematics (e.g.

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.

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 visuo-spatial working memory (e.g.

Experiment 1 investigated differences between the working memory storage capacity for number, word and visuo-spatial stimuli of adult mathematics and humanities students. Individuals with good visuo-spatial working memory have been shown to have higher levels of mathematics achievement (

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 to-be-remembered storage items, such as numbers, words or the orientation of arrows (

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 (

A Viglen Pentium D computer, running Windows XP and PsychoPy2 version 1.73.06 (

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 face-matching task (

The storage element of each span task consisted of numerical, word or visuo-spatial 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). Visuo-spatial 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

Experiment 1. Examples of trial sequences (2 Span) in the a) numerical, b) word and c) visuo-spatial conditions.

The Matrix Reasoning and Vocabulary subtests from the Wechsler Abbreviated Scale of Intelligence (WASI;

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 face-matching task. All three span tasks commenced with a practice of one 2-span set and one 3-span 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.

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 visuo-spatial 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 Greenhouse-Geisser estimates of spherity where necessary and Bonferroni corrections for multiple comparisons were used. For all analyses other than ANCOVA or correlations involving non-normal distributions,

An independent

Proportion correct scores were first calculated for each participant for the number of storage items recalled in their correct serial position (

There was a significant group x working memory storage type interaction, _{s}_{s}

There was a significant correlation between Woodcock-Johnson Calculation scores and visuo-spatial span performance, _{s}_{s}_{s}

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

Bayesian analysis was also conducted to examine the presence or lack of group differences for number, word and visuo-spatial storage span scores. The analysis was conducted using default prior in JASP to conduct simple Bayesian _{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 visuo-spatial condition (BF_{10} = 46.724).

Mean accuracy and median RT on the face-matching 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, visuo-spatial, word) mixed ANOVAs (see

Group | Experiment 1 |
Experiment 2 |
||||||
---|---|---|---|---|---|---|---|---|

Accuracy (Pc) |
Reaction Time (ms) |
Accuracy (Pc) |
Reaction Time (ms) |
|||||

Storage Condition: Number | ||||||||

Mathematics | .94 | .01 | 1264 | 63 | .95 | .01 | 1304 | 56 |

Humanities | .95 | .01 | 1326 | 72 | .94 | .01 | 1252 | 59 |

Storage Condition: Visuo-spatial | ||||||||

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 |

For accuracy, there was no main effect of group,

Face-matching latencies showed no main effect of group,

We found that mathematics students have superior working memory capacity within the visuo-spatial, but not the verbal domain. There was a large difference between groups for the visuo-spatial storage condition, where mathematics students were around 10% more accurate than the humanities students. This was underlined by the strong correlation between visuo-spatial span and Woodcock-Johnson Calculation scores, which revealed visuo-spatial 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 (

There were no group differences on the processing element of the task. In both groups, there was a medium-sized effect of storage condition on the face-matching task where accuracy was slightly worse in the word condition than in the number and visuo-spatial 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 (

In Experiment 2 we investigated potential mechanisms to account for our finding that mathematics students had a greater working memory capacity for visuo-spatial information than humanities students. We explored whether differences in visuo-spatial short-term memory (with no processing) or controlled spatial attention could account for this effect. Research has found that the short-term storage of information is required when solving mathematical problems (

An alternative explanation for mathematics students’ superior visuo-spatial 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.

Experiment 2 again compared the working memory storage capacity of undergraduate mathematicians and undergraduate humanities students for verbal and visuo-spatial 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 visuo-spatial condition. The visuo-spatial condition in Experiment 2 was identical to that used in Experiment 1 to see whether the result that mathematicians have superior visuo-spatial 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 visuo-spatial short-term memory capacity would correlate with calculation skill (

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 (

Equipment was identical to that used in Experiment 1.

The working memory tasks in Experiment 2 were identical to those used in the number and visuo-spatial 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 visuo-spatial condition.

This task consisted of a series of sequentially presented visuo-spatial storage elements. The format and timings of the task were identical to those of the working memory tasks, except that it consisted solely of to-be-remembered storage items, with no processing element.

Endogenous spatial attention was measured via a basic Posner task (

The on-screen 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 stimulus-onset asynchronies (SOA) of 200, 400 or 800ms (

WASI Matrix Reasoning and Woodcock-Johnson Calculation Test were administered as in Experiment 1.

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 short-term memory task, followed by the attention task. For the short-term memory task, after reading initial instructions, participants completed a practice of one 2-span set and one 3-span 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 self-rate 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.

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.

An independent

An independent

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:

A 2 (group: mathematics, humanities) x 2 (working memory storage type: number, visuo-spatial) mixed ANOVA was then performed on the proportion correct scores using span lengths 3 to 7 for both conditions. Descriptive statistics are shown in _{s}

There was a significant correlation between participants’ visuo-spatial span performance and their Woodcock-Johnson Calculation scores _{s}_{s}

To further explore the presence or lack of group differences for spatial and number storage span scores we conducted a series of Student’s

Bayesian analysis was also conducted to examine the presence or lack of group differences for number and visuo-spatial storage span scores. The analysis was conducted using default prior in JASP to conduct simple Bayesian _{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).

Mean accuracy and median RT on the face-matching 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, visuo-spatial) mixed ANOVAs (see

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 (

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:

An ANCOVA was run to investigate whether mathematics students had greater visuo-spatial working memory storage capacity when controlling for short-term memory performance and endogenous spatial attention. Results showed the covariate visuo-spatial short-term memory was significantly related to visuo-spatial working memory

In a new sample of participants we replicated our finding of greater visuo-spatial working memory storage capacity in mathematics student

As predicted, results of the ANCOVA showed that, when controlling for visuo-spatial short-term memory scores and endogenous spatial attention, there was still a large difference between mathematics students and humanities students in the ability to store visuo-spatial information in working memory. This therefore suggests it is the ability to hold visuo-spatial 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 short-term memory skills of complex cognitive processes (

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 visuo-spatial 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 visuo-spatial items that can be stored and the relationship between working memory capacity and more complex cognition (

Experiment 2 ruled out the possibility that short-term memory and endogenous spatial attention were driving group differences in visuo-spatial working memory. A further possibility is that the visuo-spatial working memory difference stems from differences in general ability for dealing with visuo-spatial information.

To determine whether mathematics students possess greater visuo-spatial skills, participants’ performance was compared on the

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 visuo-spatial 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 visuo-spatial processing & verbal storage condition. It was also expected that mathematics students would perform better than humanities students for general visuo-spatial skills as measured by scores for the MRT-A, and faster and more accurately for the visuo-spatial processing elements of the span tasks (e.g.

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 (

An Acer Aspire 5736Z laptop computer, running Windows 7 and PsychoPy2 version 1.77.01 (

There were four span tasks. Each had a different combination of interweaved processing and storage elements: verbal processing & verbal storage; verbal processing & visuo-spatial storage; visuo-spatial processing & verbal storage; and visuo-spatial processing & visuo-spatial storage. Timings used were identical to those used in the working memory span tasks of Experiments 1 and 2.

The visuo-spatial processing task was adapted from one used by

The verbal processing task was a word rhyming judgement task (e.g.

Two blocks of unique visuo-spatial 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 visuo-spatial 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.

The Woodcock-Johnson Calculation Test and WASI Matrix Reasoning were again administered. Participants also completed the Revised Vandenberg & Kuse Mental Rotations Test: MRT-A (

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 2-span set and one 3-span 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 MRT-A tests, the order of which was counterbalanced across participants. Finally, participants completed the Calculation Test.

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.

An independent

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, visuo-spatial) x 2 (working memory storage type: verbal, visuo-spatial) mixed ANOVA was performed on the proportion correct scores. Descriptive statistics are shown in

Storage accuracy for each processing condition in Experiment 3. Error bars represent the standard error.

To further explore the presence or lack of group differences for storage span scores we conducted a series of Welch’s

Bayesian analysis was also conducted to examine the presence or lack of group differences for the verbal and visuo-spatial storage span scores. The analysis was conducted using default prior in JASP to conduct simple Bayesian _{10} = 0.336; verbal processing, visuo-spatial storage BF_{10} = 0.446; visuo-spatial processing, verbal storage BF_{10} = 0.539; visuo-spatial processing, visuo-spatial storage BF_{10} = 0.35). So, there was no strong evidence that the groups were either different or the same.

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, visuo-spatial) x 2 (working memory storage type: verbal, visuo-spatial) 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

Group | Accuracy (Pc) |
Reaction Time (ms) |
||
---|---|---|---|---|

Processing Condition/Storage Condition: Verbal/Verbal | ||||

Mathematics | .97 | .01 | 1254 | 46 |

Humanities | .97 | .01 | 1229 | 55 |

Processing Condition/Storage Condition:Verbal/Visuo-spatial | ||||

Mathematics | .97 | .01 | 1347 | 56 |

Humanities | .97 | .01 | 1306 | 56 |

Processing Condition/Storage Condition:Visuo-spatial/Verbal | ||||

Mathematics | .97 | .01 | 1225 | 45 |

Humanities | .97 | .01 | 1354 | 60 |

Processing Condition/Storage Condition: Visuo-spatial/Visuo-spatial | ||||

Mathematics | .97 | .01 | 1388 | 50 |

Humanities | .95 | .01 | 1576 | 103 |

Results showed no significant difference in accuracy on the processing tasks between groups or across the different storage conditions (all

A regression was performed to discover whether visuo-spatial working memory storage capacity still uniquely and significantly predicted Calculation scores when taking visuo-spatial processing and general visuo-spatial skills into account.

As mathematics students were faster than humanities students for the visuo-spatial 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 visuo-spatial processing. Because of a strong correlation between accuracy in the two conditions involving visuo-spatial storage (_{s}_{s}

Predictor | β |
---|---|

Step 1 | |

Constant | |

MRT-A | .41** |

Combined visuo-spatial processing RT | -.17 |

Step 2 | |

Constant | |

MRT-A | .33* |

Combined visuo-spatial processing RT | -.15 |

Combined visuo-spatial WM storage | .27* |

^{2} = .24 for Step 1 (^{2} = .06 for Step 2 (

*

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 visuo-spatial working memory storage capacity. In Experiments 1 and 2, when the span tasks included the face-matching task as a processing element, which was as neutral as possible with respect to the storage elements, mathematics students were able to store more visuo-spatial items in working memory. In contrast, in Experiment 3, mathematics students showed no advantage for storing visuo-spatial information in working memory when storage was combined with either verbal or visuo-spatial processing. Across the three experiments, it therefore appears that, whilst participants overall found visuo-spatial storage harder when combined with visuo-spatial processing and easier when combined with verbal processing, the mathematics students found it easier than the humanities students to store visuo-spatial information when combined with the neutral as possible face-matching processing task. To discover whether these assertions were correct, visuo-spatial working memory scores from Experiment 2, with neutral as possible processing, were compared to scores for the two visuo-spatial working memory tasks in Experiment 3.

A 2 (group: mathematics, humanities) x 3 (processing type: neutral, verbal, visuo-spatial)^{iii} ANOVA was performed on the visuo-spatial proportion correct scores. Descriptive statistics are shown in

There was a main effect of group,

Experiment 3 employed working memory span tasks using verbal and visuo-spatial processing elements to investigate whether the type of processing involved affected the ability of adult mathematics and humanities students to store verbal and visuo-spatial 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 non-signfiicant differences between mathematics and humanities students for working memory storage capacity for any of the combinations of verbal and visuo-spatial 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 visuo-spatial information in working memory when the processing involved is as neutral as possible, but not when the processing is either verbal or visuo-spatial. Results of Experiment 3 also showed that mathematics students were faster to perform the visuo-spatial processing element of the working memory span tasks. There was a moderate difference between groups on the measure of general visuo-spatial skills, with mathematics students scoring on average 3 points higher than the humanities students. Moreover, both general visuo-spatial skills and visuo-spatial storage within working memory were able to uniquely predict mathematics calculation ability.

These three experiments have shown that adult mathematics students demonstrate superior visuo-spatial working memory capacity to humanities students (Experiments 1 and 2), albeit only under certain conditions (Experiment 3). Moreover, this superior visuo-spatial working memory capacity cannot be explained by superior short-term memory, endogenous spatial attention or general visuo-spatial skills. We have also demonstrated for the first time that both visuo-spatial working memory capacity and general visuo-spatial 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 visuo-spatial storage more difficult when it was combined with visuo-spatial processing than with verbal or neutral as possible processing. However, there was a large difference between the groups in storing visuo-spatial information when it was combined with neutral as possible processing, whereby mathematics students were around 10-15% 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 visuo-spatial 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 higher-level cognitive tasks (

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.

The face-matching 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 visuo-spatial processing condition of Experiment 3 was a spatial visualization task, according to the

The fact that the mathematics students only have superior ability to store visuo-spatial 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 (

The fact that mathematics students had superior visuo-spatial 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 visuo-spatial short-term memory scores when no processing was present. This did not appear to be the case however. When visuo-spatial short-term memory performance was compared in Experiment 2, the effect size was much smaller than the difference in visuo-spatial working memory capacity, and there was no significant difference between mathematics and humanities students. We see two possible explanations for this. Firstly, whilst the short-term 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 non-mathematicians in the neutral as possible processing condition, which resulted in a greater availability of working memory resources to store visuo-spatial information. The large central executive load in the visuo-spatial 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 visuo-spatial short-term 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 (

Whilst verbal working memory is involved in mathematics (e.g.

In summary, our results show that mathematics students demonstrate enhanced visuo-spatial working memory capacity under conditions of low central executive load, as well as superior general visuo-spatial skills. These group differences in visuo-spatial working memory capacity were not explained by differences in short-term memory, endogenous attention or general visuo-spatial 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 visuo-spatial working memory capacity and general visuo-spatial 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 visuo-spatial 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 (

The authors have declared that no competing interests exist.

The authors have no support to report.