Experiment 1

Working Memory Tasks:

     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 ÔyÕ or ÔnÕ 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 (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 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. 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 Ò ? Ó 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 visuo-spatial condition, a black 3 x 3 grid appeared on screen immediately after the Ò ? Ó 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.

Matrix Reasoning Subtest from the Wechsler Abbreviated Scale of Intelligence (WASI; Psychological Corporation, 1999)

Vocabulary Subtest from the Wechsler Abbreviated Scale of Intelligence (WASI; Psychological Corporation, 1999)

Woodcock-Johnson Calculation Test (Woodcock, McGrew & Mather, 2001)

Maths Anxiety Scale Ð UK (Hunt, T. E., Clark-Carter, D., & Sheffield, D. (2011). The development and part validation of a UK scale for mathematics anxiety. Journal of Psychoeducational Assessment, 29(5), 455-466)


Experiment 2

Working memory tasks:
     
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. 

Short-term visuo-spatial memory task: 

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 task:

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 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 ÔxÕ 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 (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.

Matrix Reasoning Subtest from the Wechsler Abbreviated Scale of Intelligence (WASI; Psychological Corporation, 1999)

Woodcock-Johnson Calculation Test (Woodcock, McGrew & Mather, 2001)

Maths Anxiety Scale Ð UK (Hunt, T. E., Clark-Carter, D., & Sheffield, D. (2011). The development and part validation of a UK scale for mathematics anxiety. Journal of Psychoeducational Assessment, 29(5), 455-466)

Experiment 3

Working memory tasks:

     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 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 ÔyÕ key on the laptopÕs keyboard for yes or the ÔnÕ 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 ÔyÕ key for yes or the ÔnÕ key for no.
     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. 

Matrix Reasoning Subtest from the Wechsler Abbreviated Scale of Intelligence (WASI; Psychological Corporation, 1999)

Woodcock-Johnson Calculation Test (Woodcock, McGrew & Mather, 2001)

Maths Anxiety Scale Ð UK (Hunt, T. E., Clark-Carter, D., & Sheffield, D. (2011). The development and part validation of a UK scale for mathematics anxiety. Journal of Psychoeducational Assessment, 29(5), 455-466)

Revised Vandenberg & Kuse Mental Rotations Test: MRT-A (Peters et al., 1995)