# The Give a number task revisited

The **Give a number task** is used to measure what numbers a preschooler understands. In the task, the child has to give a specific number of objects. Based on the task, it is known that initially children can only give the first few numbers (first only number 1, a few months later 2, then 3, then 4) even if their counting list (known number words) is longer. Later, after an unspecified qualitative change, suddenly preschoolers can give all numbers in their counting list, and they become so called cardinality-principle-knowers.

### 1. Large-number subset-knowers and the titration method

In the current version of the task, (a) the **numbers are asked up to 5** (because it is supposed that if a child knows 5, then she knows all other numbers in her counting list), and (b) with the so called **titration method** if a number is not known, then no larger numbers are asked (because it is supposed that up to the limit of the child’s number knowledge, the numbers are known relatively firmly, and beyond that limit numbers are not known at all).

**We used a modified version of the task** in which (a) 6 items were also asked (i.e., even if children knowing 5 should know 6), and (b) all numbers in this 1-6 range were asked three times, independent of the performance for smaller numbers. With this modified version of the task we found that:

**There are five-knowers**, i.e., children who can give 5, but not 6, which is against the current view suggesting that after learning 4, children become cardinality-principle-knowers, and they can give any numbers that are in their counting list.- Within a child,
**number knowledge decreases gradually as the numbers increase, instead of a sudden performance drop at a single value**, therefore, the titration method together with the usual noise of the measurement may fail to measure the number knowledge reliably. Based on these results we suggest that the Give a number task should be modified. First, numbers should be asked for values larger than 5. Second, instead of the titration method, all numbers should be asked. However, it is still open that after conducting the task, how an index should be created to reflect number knowledge validly.

Read the preprint version of the manuscript.

Find the raw data of this study at osf.io.

Find a presentation about this work.

### 2. The effect of the follow-up questions

At the end of the trial, to avoid performance error, follow-up questions are used, e.g., recount the given set, check if the given set is the same as it was asked for. In the literature, there are various versions of those follow-up questions. To our knowledge, it has not been investigated before whether the different versions have different effect on the children’s performance.

In a simple study, **three versions of the follow-up questions** were compared: (a) no question at all, (b) a question whether the given set includes the appropriate amount, and (c) an instruction to recount. It was found that children show **higher performance with the recount instruction**. Also, the three conditions induce different amount of corrections at the end of the trials.

Read the preprint version of the manuscript.

Find the raw data of this study at osf.io.

### 3. Revising the original validation of the Give a number task

While the validity of the Give a number task is a widely supposed in the literature, in fact, the original validation of the task raises several issues. Find more details about these issues in the General discussion of the manuscript of the first work above. In the present work, we replicate and reinvestigate the original validation results.