The knower-level framework, and correspondingly the Give-N task, have been used extensively in the last 30 years of research into children’s number word learning (see Barner, 2017; Carey & Barner, 2019; Sarnecka, 2015; Sella et al., 2021, for reviews). Supported by empirical data drawn primarily from the Give-N task, current theories of early number learning are based on the observations that (1) children learn to recite the count list “one, two, three, four, five…” as early as age 2 but have not yet ascribed numerical meaning to the number words and the counting procedures; (2) between usually 2 and 4 years of age children learn the meanings of the number words up to “three” or “four” sequentially; (3) after learning the meaning of the first number words, children understand the cardinal principle of counting. This stage-like development is correlated with other aspects of numeracy development. For example, children who can only produce some of the first few numbers on the Give-N task were found to lack knowledge of cardinality in a counting puppet task compared to those who can accurately produce larger numbers on the Give-N task (Le Corre et al., 2006). Other studies found a correlation between non-symbolic numerical comparisons and cardinal principle knowledge on the Give-N task (Abreu-Mendoza et al., 2013; Cheung & Le Corre, 2018; Negen & Sarnecka, 2015). Geary et al. (2018) also found that those who learned the cardinal principle of counting early are better at later mathematics (e.g., arithmetic, number line estimation). These findings support the stage-like development of children’s learning of number words and counting that is inherent in the knower-level framework.

The knower-level framework is based on three core assumptions, which are in turn underpinned by children’s performance on the Give-N task. 

These core assumptions are:

In the knower-level framework children who only know the small number words are called ‘subset-knowers’, and those who understand the cardinal principle of counting are called ‘cardinal principle knowers’ (CP-knowers). Differences in performance on the Give-N task between subset-knowers and CP-knowers provides one of the foundations for current theories that propose a developmental discontinuity between knowledge of a subset of the small number words (knowing numbers “one” through “three” or “four”) and knowledge of the cardinal principle of counting (see Barner, 2017; Carey & Barner, 2019; Sarnecka, 2015; Sella et al., 2021, for review). Classifying children as subset- and CP-knowers has facilitated insights into number learning through the investigation of group differences, targeted interventions, and developmental trajectories (e.g., Geary et al., 2018; Huang et al., 2010; O’Rear & McNeil, 2019; Sella & Lucangeli, 2020). However, recent studies have presented nuances of early number learning that pose some challenge to the core assumptions of the knower-level framework.

Subset-knowers may not have all-or-none knowledge of just certain small numbers, but may have partial knowledge of higher numbers. Some studies have argued that, for example, a child might have partial knowledge of the number “two”, if they reliably give 2 objects when asked to give “two”, but also sometimes make overextension errors and give 2 objects when asked for other numbers (Barner & Bachrach, 2010; O’Rear & McNeil, 2019).

The boundary between subset knowledge and cardinal principle knowledge may not be fixed at “three” or “four”. Krajcsi and Fintor (2023) found a group of children who succeed on some large numbers such as “five” but fail to give larger ones such as “six” or “seven” and termed these children large-number subset-knowers (see also Rousselle & Vossius, 2021). To some, these results suggest that what constitutes the subset-knower stages does not necessarily stop at “three” or “four” as previously assumed, which have theoretical implications for what cognitive representations may underlie subset-knowers' knowledge of number words (Carey, 2009; Cheung & Le Corre, 2018; Le Corre & Carey, 2007; Schneider et al., 2022; vanMarle et al., 2018).

Recent studies also show that tasks that are thought to be interchangeable with the Give-N task may, in fact, tap into different aspects of cardinal principle knowledge (e.g., Baroody & Lai, 2022; Baroody et al., 2023; O’Rear et al., 2024; Mou et al., 2021). They show that creating a set that matches a number word (as assessed by the Give-N task) is likely distinct from identifying or labelling the exact number of objects in a given set (as assessed by How Many Task, What’s-on-this-Card Task).

Some of the above-mentioned nuances of early number learning may relate to variations in how the Give-N task is administered and scored, which affect our ability to compare across studies (Krajcsi, 2021; Marchand & Barner, 2021; see also Le Corre et al., 2006). While keeping all other aspects of the Give-N methodology constant, these studies show that (1) administering the trials of the Give-N task as a fixed list or in a titration method leads to similarly reliable knower-level categories (e.g., non-knowers vs. subset-knowers vs. CP-knowers), but individual knower-levels were not always reliable (Marchand & Barner, 2021), (2) asking for numbers larger than “six” leads to differences in knower-level classification for children who may otherwise be equally classified as CP-knowers (Krajcsi & Fintor, 2023), (3) not asking follow-up questions leads to lower knower-level classifications, especially for potential CP-knowers (Krajcsi, 2021; Le Corre et al., 2006) and (4) using different types of objects affects knower-level classifications (Petersen & McNeil, 2013). Overall, even seemingly minor, isolated variations in the administration of the Give-N task affect knower-level classifications.

Furthermore, studies vary in how children’s performance on the Give-N task is scored and classified within the knower-level framework. For example, some studies classify children as CP-knowers if they can give sets correctly up to “six” (e.g., Le Corre et al., 2006), other studies use “four” as the cut-off (e.g., Geary et al., 2017), or apply stricter rules and require children to give sets correctly up to “ten” to be classified as CP-knowers (e.g., Kimura et al., 2013). In addition, children can be classified as an n-knower or an n+1 knower depending on whether one scores overextension errors (e.g., Barner & Bachrach, 2010; O’Rear et al., 2020). When applying this scoring criterion, a child who gives two for numbers other than “two” would be considered a “one-knower”, even if they also correctly gave two when asked for “two”. Children’s knower-level classification can thus vary depending on whether overextension errors are taken into account when coding knower-levels. While some theoretical and modelling work has considered the effect of scoring (Lee & Sarnecka 2011; Sella et al., 2021), empirical investigations into effects of scoring variations for the measurement reliability of the Give-N task are still sparse.

To inform future debates on methodological issues surrounding the Give-N task and theoretical ones about how children learn the meaning of number words and counting, we conducted a systematic review of the Give-N literature. We investigated what aspects of the Give-N task are commonly found across studies and which aspects vary from study to study as an indicator of common and diverging assumptions across researchers. The systematic review minimizes biases by including all relevant studies that meet the search criteria (see details below). We selected variables on the administration and scoring of the Give-N task that are key to the core assumptions of the knower-level framework.

The aims of our review are (1) to provide an overview of the Give-N task literature to date; (2) to examine the scope of methodological similarities and differences in the administration and scoring of the Give-N task, specifically in reference to the core assumptions of the knower-level framework; and (3) to discuss potential theoretical and methodological implications for current research on number word learning that draws heavily on the Give-N task.

We followed the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analysis) guidelines (Page et al., 2021) in developing this systematic review protocol.

The literature search was done in May 2021. The search terms were ((“Give-N task”) OR (“Give-N task”) OR (“give-me-x”) OR (“give-x”) OR (“give-me-n”) OR (“make a set of”) OR (“give-n”) OR (“give-n”) OR (“Give-Number task”) OR (“knower-level”) OR (“knower level”) OR (“cardinality”) OR (“cardinal principle”)) AND ((“preschool”) OR (“children”) OR (“kindergarten”) OR (“nursery”)). We searched PsycINFO, Web of Science, ERIC Electronic databases, and SCOPUS for primary research articles. We also searched for all primary research articles that cited Wynn (1990) or Wynn (1992), given those citations are most commonly used for the Give-N task and the knower-level framework. Grey literature sources such as dissertations, theses and preprints were included. Published conference proceedings were included; oral or poster conference presentations were not included.

All published empirical studies that reported the use of a Give-N task were eligible to be included. A Give-N task was defined as a set production task with manipulable objects in response to verbal requests for multiple numbers across several trials. Articles that reported a Give-N task were not included if participants were non-human animals, adults, or children over the age of 6 years old. Articles were further excluded if they reported secondary data (in this case only the study reporting the primary data was included) or if the full text was not available in English.

After conducting the initial search, we stored the search results with a commercial software for managing systematic reviews, Covidence (n.d., www.covidence.org). After removing duplicates, search results were then screened for eligibility. In a first step, three of the authors screened titles and abstracts and excluded articles that obviously did not meet our eligibility criteria. Each article was assessed independently by two randomly assigned coders. Coders were in moderate agreement about inclusion or exclusion at this stage of the screening process (agreement: 78%, Cohen’s kappa = .58). Disagreement was largely due to one coder making more conservative judgements and being almost twice as likely to exclude an article at this stage. All disagreements between two coders were resolved by the third coder. In a second step, the full text of the remaining articles was assessed for eligibility. Articles were included or excluded based on the consensus of two coders randomly selected from all four authors. Coders were in almost perfect agreement at this stage (agreement: 94%, Cohen’s Kappa = .84). Where coders did not agree, the entire research team discussed whether to include or exclude an article. Each step in the selection process was recorded with a PRISMA flow chart (Page et al., 2021) (Figure 1).

We used Covidence to extract data from all 210 included articles based on a coding scheme that was developed before we started the review process but was further fine-tuned during the planning and training stages. We coded information for three broad categories: setting (e.g., study location, participant information, details of data collection), Give-N administration (e.g., details of materials and procedure used in the Give-N task), and Give-N scoring (e.g., scoring framework and knower-level scoring criteria, number of children assigned to each knower-level and their age distribution). We selected elements on administration and scoring that are key to interpreting the assumptions of the knower-level framework, and these elements may affect knower-level classifications.

To refine the coding scheme and ensure coding consistency, the entire research team jointly coded a small selection of articles. To further ensure the coding scheme is used consistently across coders, 10 randomly selected articles were coded by two coders and the extracted data was compared. Coders agreed on over 90% of the extracted data and disagreements were again resolved by discussion.

The remaining articles were coded by one of the two independent coders, the two first authors. Only articles that posed a challenge to our coding scheme were coded by both coders and discussed with the entire research team. For each article, we coded only the first study that included a Give-N task. Consequently, for articles that used the Give-N task in multiple studies or at multiple timepoints in a longitudinal study we only created one data entry. This decision was made to increase the independence of data entries from each other.

A codebook with detailed explanations of all variables and all extracted data, including data not reported in this review, are publicly available on the OSF (Wege et al., 2022S). Data may be reused and adapted under a CC-BY-NC-SA license.

Our search identified 210 unique articles that described an empirical study using a Give-N task, with about 50% of them published since 2014 (see the Appendix for a visual summary). Taken together these studies report data on the Give-N task from over 15,000 children between mainly 2-5-years of age. Almost 90% of all articles using the Give-N task reported studies conducted in North America and Europe with most studies specifically conducted in the USA, Canada, and the UK. This is in line with the broader field of cognitive development, where most research samples English speaking children based in North America or the United Kingdom (Draper et al., 2023; Nielsen et al., 2017; Singh et al., 2021).

Give-N tasks that meet our definition of a set production task with a verbal request and manipulable objects are referred to by a variety of names (e.g., “give-a-number”, “give-me-x”, “cardinality task”) and reported to measure a variety of constructs with a variety of methodologies. About half of the studies included in our review (n = 109) used the knower-level framework to score and interpret children’s performance on a Give-N task. In the remaining studies (n = 101), the Give-N task is reported to measure cardinality knowledge or number word knowledge, either on its own or in combination with other measures (e.g., scores on a “how many?” task); it is also often reported as one of several measures of general numeracy. The two most prevalent scoring frameworks for the Give-N task beyond the knower-level framework are proportion of correct responses and Grabbers vs. Counters (but note that these scoring frameworks are also used alongside the knower-level framework in some studies). We provide a brief overview of the Give-N methodology of these two scoring frameworks before reporting in-depth analyses of variations in Give-N methodology within the knower-level framework.

We identified 109 articles that report the use of a Give-N task within the knower-level framework, and we refer exclusively to these articles in this section.

One of the most frequently used protocols of the Give-N task is a narrative set-up that asks children to give n as “Can you make four ducks/fish jump in the pond?” and provides 10 to 15 toy ducks/fish and a bowl or a blue piece of paper. Although approximately two-thirds of the studies we reviewed used a narrative set-up, studies vary in details of administration and scoring. In what follows, we review four aspects of the administration of the Give-N task because they bear on the core assumptions of the knower-level framework and might affect knower-level classifications.

Our review found that almost all studies relied on accuracy on giving a number in scoring children’s performance on the task. The Grabbers vs. Counters distinction was not commonly used, and when used, was flexibly defined. Few studies considered children’s overt counting behavior in classifying whether they know the cardinal principle, or whether they use counting to generate a set and to fix a set. This is important, because it is argued that children’s knowledge of counting changes when they become CP-knowers (one of the core assumptions of the knower-level framework) yet it is often not directly assessed. Focusing on accuracy alone may provide an incomplete picture of children’s knowledge of number words and counting (e.g., Barclay et al., 2017; Cheung et al., 2022). Errors on the Give-N Task could reflect performance or distraction errors, or a genuine lack of knowledge of numbers (Jara-Ettinger et al., 2016; Sarnecka & Lee, 2009), which can be difficult to disentangle for larger numbers. In addition, recent studies argue that there may be large-number-subset-knowers (i.e., children who succeed on some large numbers such as “five” but fail on even larger ones) and small-number-subset-knowers (i.e., Wynn’s n-knowers), but children may fail to give n correctly for different reasons (see Barclay et al., 2017; Fuson, 1988). Information on how children generate a set of objects on the Give-N task remains a gap that may help resolve the current debate on the nature of subset-knowers’ knowledge of numbers (Krajcsi & Fintor, 2023).

Second, we found that certain aspects of the Give-N task were under-reported but were nevertheless important for knower-level classifications. Specifically, follow-up questions were reported less than half of the time. Not asking follow-up questions can underestimate children’s accuracy on giving a number, because children who may otherwise be CP-knowers are not provided with an opportunity to fix an incorrect response (Krajcsi, 2021; Le Corre et al., 2006).

Third, we found that studies differ on what counts as evidence that a child knows the meaning of a certain number word. Most studies that adopted the knower-level framework used a “two out of three” rule, classifying children as knowing n if they give n correctly two out of three times, and not giving n + 1 two out of three times. But only half of the studies scored overextension errors and categorized children as not knowing n if they gave n for other numbers. Without this criterion, children with the same performance on the Give-N task could thus be coded as n-knowers in one study but n + 1 knowers in another study. In addition, it is often not clear how the scoring of overextension errors is applied. For example, do “other numbers” include all numbers in the study or only numbers larger than n? How does the number of total trials affect the application of this rule?

Fourth, we found that the boundary for what counts as a cardinal principle knower is not always clear. Some studies classified children as CP-knowers if they can give up to “five”, and some require children to be correct on multiple numbers up to “six”, or also numbers larger than “six”. Children’s success at giving larger numbers has been taken as evidence that learning the cardinal principle involves acquiring a conceptual insight into how counting maps number words to set sizes (Le Corre & Carey, 2007). But our data show that what counts as a “large” number is not always the same across studies, which has implications for the subset- vs. CP-knower distinction.

After 30 years of the Give-N task, a challenge for future research into children’s early number learning will be to disentangle how the knower-level framework has been shaped by the methodology of the Give-N task and vice versa. Throughout the paper, we note how intertwined core assumptions of the knower-level framework are with methodological decisions of the Give-N task. We see several issues with this.

First, the core assumptions of the knower-level framework should stand the test from diverging methods. On this front, however, existing studies that compare the Give-N task with another task that assesses number word knowledge such as the Whats-on-this card task or the Point-to-X task show that one- and two-knowers, along with CP-knowers may be more reliable than other knower-levels (Le Corre et al., 2006; Le Corre et al., 2016; Marchand & Barner, 2021). More work is needed to validate the number word learning trajectory, beyond using the Give-N task itself, and beyond the use of primarily cross-sectional designs. Future studies can address the following questions: are the small numbers always learned one at a time and in sequence, or could a child learn more than one number word at a time (e.g., Palmer & Baroody, 2011)? Can we reliably differentiate subset-knowers from CP-knowers based on accuracy on the Give-N task alone? And is there a fixed boundary (e.g., “four”) that differentiates between the two groups of children? Converging evidence from diverging methods will help advance research on early number learning.

Second, a focus on accuracy on the Give-N task as the measurement of number word and counting knowledge may limit our current conceptualization of cardinal principle knowledge (e.g., Baroody et al., 2023; Gelman, 1993; Gelman & Gallistel, 1986). In particular, the operationalization of cardinal principle knowledge taps into whether children can produce a set of 5, 6, 7, or 8 objects upon request. Accuracy on giving sets correctly may reflect children’s understanding about when to stop counting (e.g., you ask for N, it means once I count to N, I can stop; see also Baroody & Lai, 2022; Baroody et al., 2023). But, do CP-knowers understand the meaning of number as an exact representation of number – two sets that are in one-to-one correspondence have the same cardinality (Frege, 1960; Izard et al., 2008; Sarnecka & Wright, 2013; Wiese, 2003)? And do they understand the relationship between the last word of the count and the counting procedures? Existing studies suggest that CP-knowers know two sets that have the same number can be placed in one-to-one correspondence, but they have limited knowledge about when two sets do not have the same number (Le et al., 2024; Soto-Alba & Le Corre, 2019). CP-knowers also seem to accept that the last word of a count denotes the numerosity even in the face of violations of counting procedures (e.g., they accepted a set has 16 fish if a puppet double-counted each of the eight fish; Cheung et al., 2020). Analyzing children’s accuracy on giving sets of 5 to 8 correctly may thus provide an incomplete picture of cardinal principle knowledge. Future studies should explore other aspects of learning the cardinal principle knowledge and how they vary across tasks.

Third, equally important as replicable empirical data is theory development (see van Rooij & Baggio, 2021, for a recent discussion on this issue). Explaining why and how children learn small numbers differently from large ones and what it means to have cardinal principle knowledge can guide empirical investigation of number learning (e.g., Barner, 2017; Baroody et al., 2023; Carey, 2009; Carey & Barner, 2019; Mix et al., 2002; Simon et al., 2023). The Give-N task may be a highly optimized methodology to pinpoint children’s number word and counting knowledge, but validating the knower-level framework requires us to go beyond binning children into knower-levels based on the titrated Give-N task. Theorising and directly testing the cognitive processing that underlies the various patterns of performance we ascribe to subset-knowers and CP- knowers will allow us to make great strides in understanding the learning of number words and counting.

Our review suggests that clarifying methodological practices and detailed reporting would be beneficial for research on children’s early number learning. In the following section we discuss avenues to improve on methodological practices in the Give-N literature. We developed a short checklist to aid researchers in the comprehensive selecting and reporting of their Give-N methodology (see Figure 3 for the checklist). The checklist draws on the coding scheme we used in this review and our observations about aspects of the task that commonly were not reported. We hope this checklist may (1) facilitate future studies that aim to explore the impact of different methodological practices, (2) provide an overview of design considerations for the Give-N task, and (3) be used as a guideline for researchers to use as a starting point when reporting their study.

To aid researchers in designing a Give-N task for their study, we have the following recommendations. If the goal is to classify children into knower-levels, the titration method is more efficient (see also Marchand & Barner, 2021, for discussion). If, however, the goal is to examine the relationship between cardinal number knowledge and other aspects of numerical understanding such as estimation, comparison, or ordering, then the fixed trial list allows for a more balanced analysis as it provides the same amount of data on a set of numbers. We recommend using a simple narrative set-up and 3D stimuli that are easily graspable but do not roll around. Following studies by Krajcsi and Fintor (2023), if the goal of the study includes identifying CP-knowers, children should be allowed to fix their responses so as not to underestimate their performance. As suggested by a reviewer, the initial confirmation question (“Is that N?”) to ensure that a child is done placing objects on the plate can be simplified to “Are you done?” as the original request might be perceived as a challenge to children’s initial response. In short, methodological decisions reflect researchers’ assumptions and goals of the research and should be accompanied by justification or explanation.

Although the current paper focuses on the Give-N task as a standard assessment of number word knowledge and counting, expanding on and adapting the Give-N methodology has proven a versatile research tool. The Give-N task has been expanded with clever variations to measure other aspects of numerical knowledge. For instance, Give-N using number words with different types of nouns or noun phrases (“one person, two animals, and three pieces of furniture"; Sorariutta et al., 2017), ordinal number (“give me the third toy”; Colomé & Noël, 2012; Meyer et al., 2018), the base-10 number system (“give me twenty-three” with tens and units; Guerrero et al., 2020), and quantifiers (“give me some toys”; Barner, Chow, & Yang, 2009). Researchers have also adapted the task to suit their research purpose (e.g., Baroody et al., 2023; Huang et al., 2010). We expect to see more variations and adaptations beyond its original purpose and design features, including in educational settings for pedagogical purposes (McDonald et al., 2021).

Finally, large scale research collaboration promises to be key in evaluating Give-N methodology and theories of early number learning. Different protocols for the Give-N task may be collected, peer-reviewed and disseminated via open methods databases (Krajcsi & Reynvoet, 2019, http://numericalcognitionmethods.org; UCSD Language & Development Lab, 2022, https://Give-N.ucsd.edu) and large representative datasets with consistent Give-N methodology can be generated in Many-Labs collaborations (such as the Many-Numbers research consortium, www.manynumbers.org/home).

Since Wynn’s seminal work 30 years ago, the Give-N task has been instrumental for our understanding of how children learn number words and counting. Current theoretical challenges, such as investigating the mechanisms of number word learning or what it truly means to grasp the cardinal principle of counting, will require further interrogation into what the Give-N task does (and does not) measure. Our review contributes to these efforts by providing an overview of past research, highlighting how the core assumptions of the knower-level framework have become intertwined with Give-N task methodology, and discussing Give-N methodology in relation to gaps in our current understanding of early number learning. We have shared the data from this review and developed a checklist of suggestions for detailed reporting that we hope can lay the groundwork for future studies. More reflection on the use of the Give-N task and large-scale collaboration on testing theories related to the knower-level framework can lead to greater strides in understanding how children learn number words.