# 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.

The Give-a-number task is the gold standard to measure preschoolers number knowledge, however, there are several methodological issues that may compromise its reliability and validity.

### 0. Summaries of our works

See a short summary of the methodological issues in the appropriate section of our review on understanding the cardinality principle: Sella, F., Slusser, E., Odic, D., & Krajcsi, A. (2021). The emergence of children’s natural number concepts: Current theoretical challenges. Child Development Perspectives, 15(4), 265–273. https://doi.org/10.1111/cdep.12428.

Find a short presentation about these works.

Watch an MCLS 2020 presentation about the summary of these works.

Find some of our raw data in Numberbank too, where you can compare some results of various datasets that come from different labs/countries/cultures.

Our lab is a member of the ManyNumbers network.

### 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:

1. 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.
2. 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.

Krajcsi, A., & Fintor, E. (2023). A refined description of initial symbolic number acquisition. Cognitive Development, 65, 101288. https://doi.org/10.1016/j.cogdev.2022.101288 Or read the preprint version of the manuscript.

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

### 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.

Krajcsi, A. (2021). Follow-up questions influence the measured number knowledge in the Give-a-number task. Cognitive Development, 57, 100968. https://doi.org/10.1016/j.cogdev.2020.100968 or 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.

### 4. A new validation: Large-number-subset-knowers can compare only the numbers they know

In the literature, 1-, 2-, 3-, and 4-knowers are categorized as subset-knowers and it is assumed that these children have only a limited conceptual understanding of numbers. On the other hand, 5-, 6-, etc. knowers (large-number-subset-knowers or LNS-knowers) are categorized as cardinality-principle-knowers and it is assumed that they understand the fundamental properties of numbers. To verify and validate this categorization, symbolic comparison task performance was measured in those groups separately. It was found that similar to 1-4-knowers, LNS-knowers can compare only the numbers that they know in the GaN task. This shows that LNS-knowers are conceptually subset-knowers because their understanding of numbers is fundamentally limited.

Attila Krajcsi & Bert Reynvoet. Miscategorized subset-knowers: 5- and 6-knowers can compare only the numbers they know. Manuscript is coming soon.

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