Principles underlying the design of

Table 1 Conceptual complexity dimension levels

Level	Format given before choice:			Range restriction? (numbers 1–5 only)	Dot fading present? (duration)	Hazards present?	Addition required?	Subtraction required?	Instructional goal
	Non-symbolic (dot clouds)	Symbolic: Verbal (spoken numbers)	Symbolic: Arabic (digits)
1	Yes	No	No	Yes	No	No	No	No	Attention to and processing of small non-symbolic quantities
2	Yes	No	No	No	No	No	No	No	Attention to and processing of large non-symbolic quantities
3	Yes	Yes	Yes	Yes	No	No	No	No	Link small non-symbolic quantities to symbolic codes
4	Yes	Yes	Yes	No	No	No	No	No	Link large non-symbolic quantities to symbolic codes
5	Yes	Yes	Yes	No	Yes (4 sec)	No	No	No	Increase reliance on symbolic codes
6	Yes	Yes	Yes	No	Yes (1 sec)	No	No	No	Further increase reliance on symbolic codes
7	No	Yes	Yes	No	No	No	No	No	Require complete reliance on symbolic codes
8	No	No	Yes	No	No	No	No	No	Require complete reliance on Arabic code
9	No	No	Yes	No	No	Yes	No	No	Attention towards exact quantity
10	No	No	Yes	Yes	No	Yes	Yes	No	Comprehension and fluency of small addition problems
11	No	No	Yes	No	No	Yes	Yes	No	Comprehension and fluency of larger addition problems
12	No	No	Yes	Yes	No	Yes	No	Yes	Comprehension and fluency of small subtraction problems
13	No	No	Yes	No	No	Yes	No	Yes	Comprehension and fluency of larger subtraction problems
14	No	No	Yes	No	No	Yes	Yes	Yes	Distinguishing between addition and subtraction

Notes.
"Range restriction" means that the range of quantities presented was from 1–5.
"Dot fading" means that the collections of gold pieces were faded from view in the space of either 1 or 4 seconds, gradually helping to introduce a reliance on symbolic codes.
"Hazards" means that there were new anemone hazards placed on the game board, which children had to try and avoid, encouraging a focus on exact quantity
In addition trials, instead of presenting a simple quantity, an addition problem with a sum of up to 9 was presented on one side of the screen.
In subtraction trials, the problems had operands of 9 or below, and thus a result of 8 or below.

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