brightness comparison condition, trials began with the occluder presented for 500 ms. An oval image then appeared to the left and the right of the occluder and ...
S1 Appendix: Further Methodological Details Training task gameplay Training tasks were presented as a game in which either a good cartoon character surreptitiously added more items to a set (or made a line segment taller, or made an object lighter,) or a bad cartoon character surreptitiously stole items from the set (or made the line segment shorter, or made the object darker) while the set of items, line segment, or object was hidden behind an occluder, resulting in a final set (or line or object) that was more or less numerous (or tall or bright) than the expected outcome. The game was devised in an effort to maintain children’s attention throughout the training task. Familiar male and female cartoon characters were assigned based on the sex of the child. Training task stimuli timing details For the approximate numerical addition training condition and the line length addition condition, trials began with the occluder presented for 500 ms. An image (dot array or line) appeared on left, was static for 1000 ms, and then moved behind occluder over the next 500 ms. After a pause of 500 ms, a second image appeared to the right of the occluder (dot array or line), was static for 1000 ms, and then moved behind the occluder over the next 500 ms. The occluder remained on the screen for 1250 ms and then disappeared to reveal an outcome (dot array or line). The outcome remained on the screen for up to 5000 ms, during which the participant was instructed to make a more or less judgment on the relevant magnitude dimension. For the brightness comparison condition, trials began with the occluder presented for 500 ms. An oval image then appeared to the left and the right of the occluder and was static for 1000 ms. Over the next 800 ms, the left side of the oval disappeared behind the occluder, leaving only the right side of the oval visible and static for another 600 ms. The right side of the oval then moved behind the occluder over the next 800 ms. After a pause 500 ms, the occluder disappeared to reveal a circle of a different brightness than the original oval. Participants were instructed to make a more or less judgment on the brightness of the circle relative to the brightness of the original oval.
Problem details for approximate numerical addition training task Addend 1 (dots)
Addend 2 (dots)
Actual Sum (dots)
Foil (dots)
Correct Response
Ratio
13 26 21 15 40 22 18 13 30 19 16 12 24 16 13 9 19 13 9 8 40 28 27 21 35 23 23 17 30 20 20 15 25 16 17 11 20 13 13 10
43 30 11 17 9 27 10 15 12 23 8 12 11 19 7 11 9 15 7 8 16 28 13 19 14 26 12 18 12 22 10 15 10 19 8 14 8 15 7 10
56 56 32 32 49 49 28 28 42 42 24 24 35 35 20 20 28 28 16 16 56 56 40 40 49 49 35 35 42 42 30 30 35 35 25 25 28 28 20 20
32 32 56 56 28 28 49 49 24 24 42 42 20 20 35 35 16 16 28 28 40 40 56 56 35 35 49 49 30 30 42 42 25 25 35 35 20 20 28 28
Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More
0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71
Problem details for line length addition training task Addend 1 (pixels)
Addend 2 (pixels)
Actual Sum (pixels)
Foil (pixels)
Correct Response
Ratio
84 85 41 60 68 75 35 60 61 70 32 47 33 55 30 35 40 55 20 26 84 85 59 71 68 82 40 55 57 73 30 50 47 68 35 45 42 50 28 30
84 83 55 36 79 72 49 24 65 56 40 25 72 50 30 25 44 29 28 22 84 83 61 49 79 65 65 50 69 53 60 40 58 37 40 30 42 34 32 30
168 168 96 96 147 147 84 84 126 126 72 72 105 105 60 60 84 84 48 48 168 168 120 120 147 147 105 105 126 126 90 90 105 105 75 75 84 84 60 60
96 96 168 168 84 84 147 147 72 72 126 126 60 60 105 105 48 48 84 84 120 120 168 168 105 105 147 147 90 90 126 126 75 75 105 105 60 60 84 84
Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More Less Less More More
0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.57 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71 0.71
Problem details for brightness comparison training task Objects with eight levels of brightness were generated by holding hue and saturation constant and changing the brightness settings from 30 to 100 in Adobe Photoshop (objects with brightness values of 30, 40, 50, 60, 70, 80, 90, and 100, with saturation set as 30 across all objects, see A. in figure below). In easy brightness comparison condition, comparisons between the initial object brightness and the outcome object were 30 units apart (60 vs. 90; 60 vs. 30; 70 vs. 40; 70 vs. 100). Difficult brightness comparisons involved comparisons only 20 units apart (50 vs. 30; 50 vs. 70; 60 vs. 40; 60 vs. 80; 70 vs. 50; 70 vs. 90). See B. in figure below for schematic of comparisons.
A.
B.
Problem details for symbolic addition test Addend 1
Addend 2
Answer
Problem Set
12 14 9 11 8 7 6 13 7 9 16 17 15 15 8 12 9 13 9 15 18 19 15 17 19 16 17 15 16 14 20 17 18 19 17 37 46 58 25 64
3 2 3 4 6 4 5 3 7 6 3 3 5 3 8 8 7 6 8 6 4 6 9 5 9 14 13 12 8 14 14 14 16 18 17 28 38 23 13 36
15 16 12 15 14 11 11 16 14 15 19 20 20 18 16 20 16 19 17 21 22 25 24 22 28 30 30 27 24 28 34 31 34 37 34 65 84 81 38 100
1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4
Sample problem for number line placement task
