from two to three or four) or type (three digit vs two digit) of addends
N] particle indifference principle has been applied, resulting in the equivalence of all the addends
under the summatory symbol.
It seems indeed, that the process used by subjects in our study was a retrieval process insofar as the best predictive variable was the product of the two addends
Separating the last addend
of the first sum in the right-hand side of (15), replacing in this sum index j by j- 1, and taking into account that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we obtain
The instructional value of the game used in this study was clearly illustrated by the child who initially quantified each addend
separately, but then jumped to a short-cut sum strategy during the course of only one playing of the game.
where q is a proportionality factor not dependent on j; it has been defined according to the second equation to eliminate the second constant addend
of eq (7,6).
It could be that children with weaker working memory are unable to store representations of the addends
mentally while they carry out the calculations and so retain finger counting strategies for longer than those children who are able to represent the numbers mentally in working memory.
As the student types the first addend
, boxes on the number line automatically turn blue to represent the quantity; as the student types the second addend
, boxes on the number line automatically shade yellow to signify that quantity.
The first addend
characterizes the component of economy-wide productivity growth which depends on the 'productivity effect', the second one the component related to the 'reallocation effect'.
For example, when considering the number sentence 8 + 4 = _ + 5 some students notice that both expressions include addition and that one of the addends
, 4, on the left side is one less than the addend
, 5, on the other side.
At this stage, in problems of change, they are capable of estimating the direction of the change (increase or decrease) and of relating it to the operations of addition and subtraction, so that, for example, they solve problems of change with the unknown in the second addend
by counting from the lowest quantity to the highest.
1-[sigma])] instead of the second addend
inside the braces.