Quotitive

In the partitive task that we have just described the number of recipients is the divisor and the portion of sweets is the quotient. It is the other way round in another kind of task which is called a quotitive task. Quotitive tasks are portion control tasks. In a quotitive task you decide that each recipient will get, say, 3 sweets and you go on doling out 3-sweet portions until you run out of sweets. So the greater the allotted portion of sweets the smaller will be the number of recipients fortunate enough to receive a portion. So the size of the portion is the divisor, and the number of recipients the quotient. 

The test of this hypothesis, it seemed to us, was to compare partitive with quotitive division again. Quotitive tasks provide the crucial test because here the recipients co-incide with the quotient not with the divisor. This means that the number of the final groups co-incides with the quotient and therefore that children will find the task easier if the initial grouping is by the quotient and not by the divisor. 

In the quotitive task the children were told that each table took a certain number of girls (that number was therefore the divisor) and the question was the number of tables that would be needed to seat all the girls. The equivalent problem for 12 4 in this case would involve twelve... 

The results were as we predicted. When the children were given the partitive task they did much better in the grouping by the divisor than in the grouping by the quotient condition when they were given the quotitive task they did much better in the grouping by the quotient than in the group-... 

Children s scores in the partitive and quotitive tasks with the different ways of grouping the girls. 

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