Arithmetic tasks

Number recognition task:

A series of digits were presented on the screen and children were asked to name the digit aloud as soon as they recognized it. There were two practice trials, and six experimental trials with numbers ranging from 4 to 26, which were presented in a random order. Accuracy scores were recorded. 

Counting task: 

Children were asked to complete five counting sequences. They were asked to count up to 10, on from 28, on from 45, backwards from 12, and backwards from 33. With the exception of the first trial children were stopped after they had given seven numbers, which ensured that they had crossed a decade boundary in each case.  Accuracy scores were recorded.

Abstract arithmetic/Strategy task: 

Children were shown a series of addition and subtraction abstract problems printed onto cards and were asked to solve them using any strategy of their choice. There were four practice trials and eight experimental trials. All problems involved single digit addends. The items were presented in one of two orders, counterbalanced across participants. Number lines marked from 1 Š 10 and 1 Š 20 and a set of counters were provided for children to use if they wished. After solving each problem children were asked what strategy they had used to solve the sum. A sheet with pictures representing different strategies (retrieval, mental counting, finger counting and decomposition) was shown to the children and used by the experimenter to help elicit childrenÕs strategy reports. Observations of childrenÕs actions were also recorded. All trials were audio-recorded. Accuracy scores, and the proportion of strategy use (retrieval, counting) were recorded. 

Conceptual understanding: 

To assess conceptual understanding children played a game involving a puppet. Children watched the puppet solve an arithmetic problem using counters and were shown the example problem (including the answer) written in a booklet (e.g. 3 + 6 = 9). They were then shown four probe problems which were presented without answers and for each probe problem children were asked whether the puppet could use the example (completed) problem to solve each probe problem, or if he would need to use the counters to solve it. Of the four probe problems, three were related to the example problem and one was unrelated (e.g. 6 + 9 = ). One of the related problems was identical (e.g. 3 + 6 = ), one was related by commutativity (e.g. 6 + 3 = ) and one was related by inversion (e.g. 9 Š 3 = ). The children were first asked to decide whether or not the example problem could help the puppet solve each probe problem, and asked to explain why. There were 24 experimental trials in total (six example problems each with 4 probe problems) and before these children completed two practice example problems, each with one identical, one unrelated and one related (addend + 1 rule) probe problem. Feedback was provided during the practice trials to help children understand the task. All trials were audio recorded. Accuracy measures were calculated for how many relationships were correctly identified, and for how many accurate explanations children provided.   

Dot comparison task:

On each trial the participants were shown two sets of white dots on a black screen and were instructed to identify which set had the highest number of dots. The dots were created using an adapted version of the matlab script provided by Gebius and Reynvoet (2011). Participants were required to ignore the size of the dots and the array on the screen and to respond based on the number of dots only. The number of dots in each array ranged from 5 to 28 and the ratio between the number of dots ranged from 0.5 to 0.8. Participants completed 6 practice trials and 80 experimental trials in random order. They were given breaks during the task as needed. 

Executive function tasks.

Verbal short-term memory:

Verbal short-term memory was assessed via a word span task. Participants heard a list of single syllable words and were asked to recall them in order. There were three lists at each span length, beginning with lists of two words, and the participants continued to the next list length if they responded correctly to at least one of the trials at each list length. 

Verbal working memory:

Verbal working memory was assessed via a sentence span task. Participants heard a sentence with the final word missing and had to provide the appropriate word. After a set of sentences they were asked to recall the final word of each sentence in the set, in the correct order. Participants first completed an initial practice item with two sentences, and therefore two words to remember. They then continued to the test trials where they received three trials at each span test length. Provided they recalled at least one trial correctly, the sequence length was increased by a single item and three further trials were administered.

Verbal processing:

ParticipantsÕ performance on the processing task was assessed separately in two blocks (one before the sentence span task and one after) of 20 trials each. In these blocks they only had to provide the final word of the sentence, without the need to recall the words. Response times were measured.

Visuospatial short-term memory:

In the visuospatial short-term memory task participants saw a 3 x 3 grid on the screen. They watched as a frog jumped around the grid and after he had finished the sequence they had to point to the squares he jumped on in the correct order, which was recorded by the participant using the mouse. There were three trials at each sequence length, beginning with sequences of two jumps, and participants continued to the next sequence length if they responded correctly to at least one of the sequences at each length.	

Visuospatial working memory:

Visuospatial working memory was assessed via a complex span task. Participants saw a series of 3 x 3 grids each containing three symbols and they had to point to the symbol that differed from the other two. After a set of grids children were asked to recall the position of the odd-one-out on each grid, in the correct order. There were three sets at each span length, beginning with sets of two grids, and children continued to the next span length if they responded correctly to at least one of the sets at each span length. 

Visuospatial processing:

ParticipantsÕ performance on the processing task was also assessed separately in two blocks (one before the complex span task and one after) of 20 trials each. In these blocks participants only had to identify the location of the odd-one-out, without the need to recall the position. Response times were measured.

Animal Stroop/Inhibition task: 

Children saw a series of trials in which two animal pictures were presented on the screen. On each trial one picture was drawn from a set of large animals (e.g. bear, gorilla, giraffe) and one was drawn from a set of small animals (e.g. ant, rabbit, mouse). ChildrenÕs task was to identify which animal was the larger in real life. On each trial one animal image was presented with an area on screen four times larger than the other image. On congruent trials the animal that was larger in real life was also the larger image on the screen, and on incongruent trials the animal that was smaller in real life was the larger image on the screen. On each trial, the images were presented on screen and children responded as quickly as possible by pressing one of two keys that corresponded to the side of the screen with the larger animal. Prior to completing the task children were shown each of the animals and asked whether the animal was large or small in real life, to ensure they had the necessary knowledge to perform the task. All children completed this without problem.

Children completed four blocks of 24 trials. In each block 75% of the trials were congruent and 25% were incongruent. Median response times for the correctly solved congruent and incongruent trials were calculated, omitting the first trial of each block. 

Cognitive flexibility card sort task: 

To assess cognitive flexibility children completed a version of the Flexible Item Selection Task (Jacques & Zelazo, 2001). On each trial children were shown three images that varied according to color, size or shape, for example one set included a large red dolphin, a large blue dolphin and a small blue dolphin. Children were asked to identify two cards that matched on one dimension (e.g. the two large dolphins) and to explain why, and then to identify two cards that matched on a different dimension (e.g. the two blue dolphins) and explain why. There were 12 experimental trials preceded by 2 practice trials. Prior to the practice trials the experimenter demonstrated how different dimensions could be used to match cards.  

For each trial children received one score according to whether their first pairing was correct, and a second score according to whether their second pairing was correct. To be correct children had to select a meaningful pairing and to provide an accurate explanation why. The proportion of correct first pairings identified was used as the measure of performance. 

Visual search task: 

 In this task children saw a screen full of simple drawings of small animals (elephants, donkeys and bears). In the first trial all the animals faced right and children were asked to point to the elephants. In the second trial half of the animals faced left and half faced right; children were asked to point to all of the elephants that faced left. In the final trial again half of the animals looked left and half right, this time children were asked to point to all of the bears that looked right. When children pointed to an animal the experimenter clicked on the animal with the mouse and the image of that animal shrunk in size. During each trial the experimenter did not remind children which target they were looking for, or encourage them to look for any more. When children had stopped identifying any further targets themselves, the experimenter asked them if they thought they had found them all and if they replied yes moved onto the next trial. There was no time limit. The number of targets correctly identified, the number of distractors selected, the time between item selection and the distance between item selections were all recorded. 

Maths Anxiety: 


Maths anxiety in Year 1 was measured with the Child Maths Anxiety Questionnaire, or CMAQ (Ramirez, Gunderson, Levine & Beilock, 2013).

Behavior Rating Inventory of Executive Function (BRIEF):

Teachers completed the teacher report form of the BRIEF individually for each child.