Summary

Participants were asked to solve a series of addition problems by either counting, breaking the sum down into smaller parts (decomposition) or retrieving the answer from memory (retrieval) under three different conditions. In the no load condition participants completed the arithmetic problems with no secondary task. In the control load condition participants monitored a sequence of verbally or visually presented information and had to respond to a particular stimulus. In the working memory load condition the participants monitored the same sequence of information but had to respond to a particular pattern in the sequence. This required the participant to continuously update the final few items of the sequence in memory. The participants completed both verbal and visuospatial versions of the control and working memory tasks. 

Equipment and materials

The experimental tasks were created and controlled using E-Prime software and run on a Samsung laptop computer. Responses to the addition problems were made using an external numeric keypad, whilst responses to the secondary working memory tasks were made using the laptopÕs in-built mouse.

Addition task:

Participants were required to answer a series of two-addend addition problems presented horizontally in the centre of the screen. Half of the problems comprised solely single digits and half comprised a double-digit number on the left and single-digit number on the right. The 12-14-year-olds and adults entered the answers themselves using the numerical keypad. The 9-11-year-olds said the answer out loud and the experimenter entered the answers on the keypad. 
Visuospatial secondary task:

This task consisted of two rows of four horizontal boxes, with one row above and one row below the arithmetic problems. Different boxes turned red, randomly and one at a time, for 2 seconds and participants had to respond, using the mouse, when a specified pattern was noted. Three dual task conditions were used: no load, where the boxes were present on screen, but none turned red and participants only had to answer the sums; a control load, where participants had to click the mouse when the box second from left on the top row turned red; and a working memory load, where participants had to respond when the box that turned red was the same as the one two items previously in the sequence. For both the control and working memory loads an event requiring a response occurred at least on every sixth box turning red. If participants missed a response, an auditory ÔbeepÕ was heard, to remind them to pay attention to the secondary task.  

Verbal secondary task:

A string of animal names were presented aurally through headphones in a random order at a rate of one word every 3 seconds. Participants had to respond, using the mouse, when a specified pattern was noted. Three dual task conditions were used: no load, where no animal names were heard and participants only had to answer the sums; a control load where participants had to respond when they heard the word ÔdogÕ; and a working memory load where participants had to respond when the animal name was the same as the one presented previously. For both the control and working memory loads, an event requiring a response occurred at least on every sixth word. If participants missed a response, the boxes surrounding the sums flashed red for 100 milliseconds, to remind them to pay attention to the secondary task.  

Procedure

The participants were tested in a quiet room either at their school or at the university. The verbal and visuospatial versions of the task were split across two sessions for the 9-11-year-olds, with a maximum of three days between sessions. Adults and 12-14-year-olds completed both versions in one session. The order in which the verbal and visuospatial versions were completed was counterbalanced across participants. For each version, the within-participants design required participants to answer 20 addition problems in each possible combination of strategy and dual task load. This resulted in a total of nine combinations (retrieval with no load, control load, working memory load; decomposition with no load, control load, working memory load; counting with no load, control load, working memory load) and therefore 180 problems for each of the verbal and visuospatial versions. 

For both versions participants began with twenty practice problems which could be answered using any strategy. They then practised the control and working memory tasks, which could be repeated if necessary, before moving on to the test trials. At the start of each strategy block (counting, decomposition, retrieval), participants completed eight practice problems before moving on to the three dual task load sub-blocks. The order of strategy blocks was assigned randomly, whilst the order of dual task load sub-blocks (no load, control load, working memory load) was counterbalanced across participants. Nine lists of 20 problems were created with the same mean sum total. The combination of each problem set with the strategy and dual task load conditions was counterbalanced across participants. 

On each trial the arithmetic problems were presented in the centre of the screen between the two rows of boxes used for the visuospatial task. The arithmetic problems remained on screen whilst participants worked out the answer using the required strategy. Reaction time was measured from the time the problem appeared until the enter key was pressed to indicate the problem had been solved. After the answer had been keyed in the enter key was pressed again, which triggered the appearance of the next problem. The control and working memory tasks started when the first problem of each block was presented on the screen and ended when the enter key was pressed to respond to the final problem of the block. The secondary task was paused while the responses to the arithmetic problems were entered but participants were required to remember the previous stimulus across this delay. Participants were told to give equal attention to the addition problems and the secondary task. At the end of each set of 20 problems, participants were asked, on a scale of 1 to 5, how many of the problems they had used the required strategy for, where 1 was Ôhardly anyÕ and 5 was Ôalmost allÕ. The experimenter then entered their response using the numeric keypad.