BOX 4.2 How Many?

How do 3- to 5-year old children react when they encounter unexpected changes in the number of items? Before the dialog below, children had been playing with five toy mice that were on a plate; the plate and mice were then covered and the experimenter surreptitiously took away two mice before uncovering the plate (Gelman and Gallistel, 1978:172). What follows is one child’s attempts to reconcile the differences in the number of mice:

Child:

Must have disappeared.

Experimenter:

What?

Child:

The other mousses?…

Experimenter:

How many now?

Child:

One, two, three.

Experimenter:

How many at the beginning of the game?

Child:

There was one there, one there, one there, one there, one there.

Experimenter:

How many?

Child:

Five—this one is three now but before it was five.

Experimenter:

What would you need to fix the game?

Child:

I’m not really sure because my brother is real big and he could tell.

Experimenter:

What do you think he would need?

Child:

Well I don’t know…Some things have to come back.

Experimenter:

[Hands the child some objects including four mice].

Child:

[Puts all four mice on the plate]. There. Now there’s one, two, three, four, five, six, seven! No…I’ll take these [points to two] off and we’ll see how many.

Child:

[Removes one and counts]. One, two, three, four, five; no—one, two, three, four. Uh…there were five, right?

Experimenter:

Right.

Child:

I’ll take out this one here [on the table] and then we’ll see how many there is now.

Child:

[Takes one off and counts]. One, two, three, four, five Five! Five.



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