Escape From Metaignorance: How Children Develop an Understanding of Their Own Lack of Knowledge
This study is part of two research projects financed by the European and Austrian Science Funds (ESF/FWF Project I93-G15 “Metacognition of Perspective Differences” and FWF Project V00-122 “How Can We Change the Way We Think?”). We express our gratitude to management, staff, and children of the following kindergartens and after-school care centers for their friendly cooperation: Kindergarten Leonfeldnerstraße, Kindergarten Sattledt, Kindergarten Dornacherstraße, Kindergarten Johann-Wilhelm-Klein-Straße, Kindergarten Minnesängerplatz, Kindergarten Commendastraße, Hort Weißkirchen (after-school care center), Hort Linz-Solarcity (after-school care center), and Hort Haid (after-school care center).
Abstract
Previous research yielded conflicting results about when children can accurately assess their epistemic states in different hiding tasks. In Experiment 1, ninety-two 3- to 7-year-olds were either shown which object was hidden inside a box, were totally ignorant about what it could be, or were presented with two objects one of which was being put inside (partial exposure). Even 3-year-olds could assess their epistemic states in the total ignorance and the complete knowledge task. However, only children older than 5 could assess their ignorance in the partial exposure task. In Experiment 2 with one hundred and one 3- to 7-year-olds, similar results were found for children under 5 years even when more objects were shown in partial exposure tasks. Implications for children’s developing theory of knowledge are discussed.
Children’s understanding of their own knowledge or ignorance is of considerable importance in a multitude of different areas of cognitive development. For instance, children’s assessments of their own present knowledge or ignorance states are fundamental for the their reading and listening comprehension skills (e.g., Baker & Brown, 1984; Markman, 1977; Myers & Paris, 1978), their communication skills (e.g., Flavell, Speer, Green, August, & Whitehurst, 1981), their ability to efficiently allocate study time and thus their memory performance (e.g., Dufresne & Kobasigawa, 1989; Lockl & Schneider, 2004), their conceptual perspective-taking skills (e.g., Flavell, 1992), their understanding of ambiguity and inference (e.g., Beck & Robinson, 2001; Sodian & Wimmer, 1987), and they make a critical contribution to children’s successful learning (Paris & Winograd, 1990). That is to say, better achieving children often have a better understanding of what they know and do not know, they better know what they can and cannot do, and they know what they have to do to gain the knowledge they need (Fisher, 1998). Children’s ability to assess and to report their own epistemic states therewith serves as a fundamental basis on which competent performance in a number of different domains builds up.
It is obvious that the ability to report and assess their own epistemic states requires from children both sufficient linguistic capacities and the ability to metacognitively monitor their own concurrent mental states. However, it is less evident that children can only report epistemic states accurately if they can form them correctly, that is, if they understand that the most important determinant of knowledge is a sufficient access to an informational source. By investigating children’s performance in assessing their own epistemic states through a set of different epistemic tasks, light could be shed both onto when children get access to their own concurrent epistemic states and onto whether (or not) metacognitive monitoring skills develop in children at the same time as does children’s capacity to conceptualize their own and other people’s knowledge correctly. This could not only help to understand the development of children’s epistemic thinking better, but could also yield relevant aspects for the ongoing debate in the theory of mind literature regarding whether children understand and predict the minds of others by means of using their own mental states for mentally simulating those of others (simulation view; e.g., Harris, 1992) or whether children rely on laws, heuristics, or nomological rules (theory-theory view; e.g., Gopnik & Wellman, 1992; Perner, 1991) for that purpose.
Regarding children’s understanding of another person’s epistemic thinking, a large amount of research has been conducted. Some of these studies suggested that children under 4 years do not understand that seeing is associated with knowing in others (and not seeing with not knowing; e.g., Gopnik & Graf, 1988; Wimmer, Hogrefe, & Perner, 1988). Other studies, however, challenged this view by showing that even 3-year-olds understand that a person, who has looked into a box, knows what is inside, whereas a person who has not looked does not know (Pratt & Bryant, 1990) and that 2-year-olds can show some sensitivity to their mother’s knowledge state based on her previous visual experience (O’Neill, 1996). See also Sodian, Thoermer, and Dietrich (2006) or Poulin-Dubois, Sodian, Metz, Tilden, and Schoeppner (2007) for evidence that even 3-year-old children (and younger children) can differentiate between an ignorant and a knowledgeable person based on what that person has or has not seen.
Without doubt, these studies provide compelling evidence that children associate seeing with knowing in others from an early age onward and can be quite good in accurately assessing the epistemic states of other persons based on their previous informational access. However, notwithstanding this fact, children’s early competence has been found to improve over the preschool period; only by school-age children seem to sufficiently consider the informativeness of another person’s informational access when assessing his or her epistemic state (e.g., Taylor, 1988).
Fewer studies investigated children’s understanding of their own epistemic states or their own competence in acknowledging the seeing and knowing association. Typically, the methodical approach of these studies was to ask children metacognitive questions about their own epistemic states after a hiding event had taken place. Although this approach has yielded a consensus that children aged at least around 3 years understand that they know what is “hidden” inside a container, if they have previously looked inside (e.g., Pratt & Bryant, 1990; Tardif, Wellman, Fung, Liu, & Fang, 2005), it has yielded a conflicting pattern of results in respect to the age at which children can acknowledge their own ignorance. For instance, in a study by Wimmer et al. (1988, Experiment 1) 3- to 5-year-old children were shown various boxes. Two children were always sitting opposite to each other on a table on which various boxes with an unknown content were placed. The experimenter then either showed (visual access) or told (without visual access) one of the children the content of the box, whereas the other child remained totally ignorant. Children then had to assess their own epistemic state and the epistemic state of the other child. Although only 50% of the 3-year-olds were able to correctly assess their own epistemic state, 94% of the 4-year-olds and 100% of the 5-year-olds could make correct assessments. Children from 4 years on therefore seemed to have few problems acknowledging their own ignorance when they were totally ignorant and claimed to “know” when they had seen what was in the box; see also Pratt and Bryant (1990) for results that even 3-year-olds can acknowledge their own ignorance with a high accuracy in a very similar total ignorance task (no presentation of any possible contents ahead of hiding).
However, children might experience more problems in assessing their own epistemic states in a partial exposure task, in which children possess knowledge of a range of objects but then cannot see which object is being put inside a box. This was found to be the case in a control condition by Sodian and Wimmer (1987, Experiment 1). In this experiment, 4- and 6-year-olds were shown a container with two kinds of differently colored balls in it. Then one of the balls was covertly transferred to a bag by the experimenter. Children were only told that one of the two balls had been transferred to the bag and were then asked: “Do you know what color the ball in the bag is?” About 35% of the 4-year-olds and even 13% of the 6-year-olds wrongly claimed “to know.” In Experiment 2, even 50% of the 4-year-olds overestimated their knowledge of which ball had been transferred. This result stands in contrast to both the results of Pratt and Bryant (1990) and Wimmer et al. (1988). Thus, the pattern of results suggests that the structural difference between the studies, namely whether children were exposed to a set of possible contents ahead of hiding as in Sodian and Wimmer’s study (partial exposure task) or not (total ignorance task) as in the two other studies, is important. However, other studies do not quite fit this explanation because in these studies even 3-year-olds could accurately assess their own ignorance in a partial exposure paradigm (Pillow, 1989; Ruffman & Olson, 1989).
Interestingly, there are theoretically postulated cognitive mechanisms that could account for a difference in children’s capacity to assess their own ignorance in total ignorance tasks compared to partial exposure tasks. For example, Wimmer et al. (1988) suggested that if children are asked knowledge questions like, “Do you know what is in the box?” they simply think of an answer and check whether this answer “feels correct.” If it does, they equate this answer with knowledge; otherwise, they deny it. Although Wimmer et al. suspected that children by 4 years would already understand that their knowledge has causal origins (and thus stems from an informative access given at the right time), the results by Sodian and Wimmer (1987) suggest that children until the age of 6 years do not possess this understanding, but instead just check for the ability to come up with an answer that “feels correct” when assessing their own epistemic states. As coming up with such an answer is presumably easier in the partial exposure task (in which a set of objects is shown to the children ahead of hiding), than in the total ignorance task (in which nothing is shown to the children), this might explain children’s differential performance on these two tasks.
One can refine this assumption by asking about the basis of preschool children’s feeling of correctness. One possibility is that preschool children only check whether they can easily respond to the question, “Do you know what is in here?” That is, if they can easily think of some plausible object name, then they feel competent and answer, “Yes, I know.” This is to be called the competence account.
Another possibility is that preschool children, in addition, check the risk of their answer, that is, to what degree their answer could be wrong given the set of possible alternative answers. That would mean that if the possible set only consists of two objects (which could be hidden in a container) they are more likely to say, “yes, I know,” than if the set is larger, and practically infinite in the total ignorance condition. This is to be called the risk account.
An inhibition deficit, too, might account for the fact that children assess their own ignorance more accurately in the total ignorance than the partial exposure task. That is, children could have difficulty inhibiting a response when at least one suitable response comes to mind, which is more likely in the partial exposure than in the total ignorance task. However, whether such an inhibition deficit can account for Sodian and Wimmer’s (1987), partial exposure task remains unclear because it is not clear whether Sodian and Wimmer only counted children who answered the test question (“Do you know what color the ball in the bag is?”) with “yes” in their “yes category” (wrong answer to partial exposure) or whether they also counted children who gave an affirmative answer by only naming a ball’s color in this category. Clearly, an inhibition deficit could only account for responses of the latter type.
In Experiment 1, we accordingly set out to investigate whether children would generally show differences in their ability to acknowledge their own ignorance in a total ignorance task setting versus a partial exposure task setting. We also wanted to check whether any differences detected are best explained by children’s reliance on some feeling of being able to produce an answer that feels right when assessing epistemic states (Wimmer et al., 1988) or a higher inclination for guessing, or a basic inhibition deficit. To differentiate between these explanations, we included a “know–guess” control question.
Experiment 1
Given that our classification of epistemic task settings into total ignorance and partial exposure task settings made sense of some of the inconsistencies in the literature, but not all (Pillow, 1989; Ruffman & Olson, 1989), we decided to systematically investigate whether the structural difference would really make the suspected difference. We therefore used a set of previously used verbal epistemic task settings, which differed in the informational input children received about possible contents of a closed box and compared them in a single study for the first time. To this end, a partial exposure task was used in which children were exposed to a set of two objects, one of which was subsequently covertly hidden in a box. To make the knowledge test question comparable to the one used in Sodian and Wimmer’s (1987) study (“Do you know what color the ball in the bag is?”), children in our task were also asked a test question which provided a cue for the hidden object (“Do you know now which toy is inside or do you not know?”). We also used a total ignorance task, in which no possible contents were presented ahead of hiding. To make the test question as similar as possible to the one used in the partial exposure task, children were also asked a test question providing a cue (“Do you know now which toy is inside or do you not know?”). Last but not least, a basic epistemic task was used, which consisted of two subtasks. The first subtask was a varied total ignorance task, which was similar to the total ignorance task except that we used a test question (“Do you know what is inside the box or do you not know?”), which did not provide a cue. This subtask was included to check whether a difference in responding between the two total ignorance tasks was to be found, as this could indicate that children have more difficulties inhibiting a relevant response in one of the two total ignorance tasks (e.g., after having been provided with a cue) or that they find it easier to come up with a plausible response (e.g., after having been provided with a cue; competence account) or consider the risk of their responses to be different (risk account). The second subtask of the basic epistemic task was a complete knowledge task (presentation of one specific content) in which we wanted to see whether children can acknowledge their knowledge when provided with full visual access.
Previously reviewed empirical studies demonstrated that children tend to overestimate their own knowledge in situations, in which they have been exposed to a set of relevant objects ahead of hiding (e.g., Sodian & Wimmer, 1987). We therefore expected children to have more difficulties in acknowledging their own ignorance in a partial exposure task than in the total ignorance tasks. Between the two total ignorance tasks, no difference in children’s rate of acknowledging their own ignorance was expected, as we assumed that children could neither consider the risk of responding to be sufficiently different between the two tasks (as both tasks allow for almost an infinite number of alternative responses) nor find it significantly easier to produce a plausible response in either of the two tasks or would have more difficulties with inhibition.
As prior studies have indicated (e.g., Pratt & Bryant, 1990; Tardif et al., 2005) that young children typically have no problems in acknowledging their own knowledge when they are allowed to look at the specific content of a box, we expected children to have no difficulties in the complete knowledge subtask.
Method
Participants. A total of 92 children, 52 boys and 40 girls, participated. They came from three different nurseries and one after-school care club in Upper-Austria with a mixed working and middle-class background. Their ethnical background was mainly Austrian. All children were deemed competent by their teachers for the tasks. There were sixteen 2- to 3-year-olds ranging in ages from 2 years 11 months (2;11) to 3 years 11 months (3;11) (M = 3;5); sixteen 4-year-olds (range = 4;0 to 4;11), mean age of 4;6; twenty 5-year-olds (range = 5;0 to 5;11), mean age of 5;5; twenty-one 6-year-olds (range = 6;0 to 6;11), mean age of 6;6; and nineteen 7-year-olds (range = 7;0 to 7;11 years), mean age of 7;6.
Materials A black partition wall (45 × 4.5 × 32 cm) was used to screen the hiding process from the view of the children. A black, opaque shoe box (28 × 20 × 11.5 cm) with a lid served as hiding place for the toys. Eight different toys were used (e.g., pig, monkey, ball, train, etc.). If children were not familiar with one of the toys, one of three other toys (cat, car, and puppet) was used (only three children needed a replacement of the original toys).
Design and procedure. Each child was tested individually in a quiet, separate room in the nursery or in the after-school care club. Each child was seated at a table opposite to the experimenter. Three different tasks were used: a total ignorance task, a partial exposure task, and a basic epistemic task, consisting of two subtasks, namely, a varied total ignorance subtask followed by a complete knowledge subtask. Children’s responses in each of the specific tasks were manually recorded on paper during the experiment. Each child received all three tasks twice. The two test runs were separated by a short pause. The sequence of the tasks was counterbalanced between participants using a Latin Square.
In the total ignorance task (no presentation of possible contents), children were first shown an empty box. Then they were told that a game would be played in which a toy (never presented) would be hidden behind a screen in the box. After the toy had been hidden, the experimenter said: “Ok, I have now hidden a toy in the box. Do you know now which toy is inside or do you not know?” Depending on the child’s answer different sequences of control questions followed. If the child incorrectly made a knowledge statement, the experimenter asked: (a) “Ok, then, tell me what toy is inside?” (b) “Do you really know that or are you just guessing?” and (c) “How do you know that there is an X (name of toy) inside?” If the child correctly denied knowledge on the test question, only one control question was asked: “Why don’t you know which toy is inside?”
The partial exposure task (presentation of possible contents) differed from the total ignorance task in only one aspect: Children in this task were shown a set of two toys before the hiding process started and were asked to name them. Then, as in the total ignorance task, children were told that a hiding game would be played. Before one of the toys was hidden, children were allowed to have a brief second glance (1–2 s) at the objects. This was done to give those children the chance to catch up, who had not paid much attention to the toys beforehand without knowing what the game was about. After hiding, children were asked the test question: “Ok, I have now hidden one of the two toys in the box. Do you know now which toy is inside or do you not know?” Depending on the child’s response, one of the two sequences of control questions (as described in the total ignorance task) followed.
The basic epistemic task consisted of two subtasks. The first subtask was a varied total ignorance task in which we checked whether children would acknowledge their own ignorance more than in the total ignorance task if we used a test question, which did not provide a cue for the hidden object. The second subtask was a complete knowledge task (presentation of one specific content) in which we wanted to see whether children can acknowledge their knowledge when provided with full visual access.
The varied total ignorance task started with the experimenter showing the child a closed box and then he asked: “Do you know what is inside the box or do you not know?” If children gave an affirmative answer the experimenter asked what was inside the box and whether the child was guessing. Subsequently the experimenter added (in case that the child reaffirmed his knowledge): “No there is no X inside, but I will show you now, what is really inside the box.” If children denied knowledge on the initial question (as was most often the case), the experimenter said: “Ok, I will show you what is inside the box.” Herewith, the complete knowledge subtask started and all the children were allowed to see the content of the box and were prompted to name the critical object. After the child’s response, the experimenter closed the lid again. After a brief delay (5 s) the knowledge question followed, “Do you know now which toy is inside or do you not know?” Depending on the child’s answer, one of the two sequences of control questions (as described in the total ignorance task) was asked.
Results
On each total ignorance, varied total ignorance, and partial exposure trial, children received a score of 1 if they spontaneously admitted ignorance in response to the test question (e.g., “Do you know now which toy is inside or do you not know?”). Children also received a score of 1, if they erroneously named an object on the initial test question, but then corrected their statement on the subsequent know–guess control question (“Do you really know that or are you just guessing?”) by admitting to guess. Children received a score of 0 if they indicated their knowledge in one way or the other in these two tasks, that is, by either responding with “I know,”“Yes,” or by immediately naming an object in response to the test question (without correcting it subsequently). On the complete knowledge trials, children received a score of 1 if they were able to correctly assess and report their own knowledge based on visual input and a 0 if they could not do that. Table 1 displays the number of children scored with 0, 1, and 2 (two runs) on the test questions in the different epistemic conditions. Four goodness-of-fit tests (chi-square) yielded that children did not respond randomly on the test questions in the different epistemic conditions (all ps < .001.).
| Score | Total ignorance | Total ignorance varied | Partial exposure | Complete knowledge |
|---|---|---|---|---|
| 0 | 3 | 5 | 33 | — |
| 1 | 10 | 10 | 12 | 5 |
| 2 | 79 | 77 | 47 | 87 |
- Note. Maximum score = 2 (two runs).
As can also be seen in Table 1, children’s performance on the different epistemic tasks varied markedly. Only scores on the two total ignorance tasks were similar. A series of Wilcoxon tests revealed no significant differences between the two tasks in terms of overall performance or between age groups in the two conditions (all ps > .05). The two total ignorance tasks were also strongly correlated, even when age was controlled for, r(89) = .62, p < .001. On these grounds, the varied total ignorance was excluded from further analyses.
Children (N = 92) performed significantly worse in the partial exposure task (M = 57.61% correct, SD = .92) than in the total ignorance task (M = 91.30% correct, SD = .46) and in the complete knowledge task (M = 97.3% correct, SD = .23), Wilcoxon tests: all ps < .001. In addition, there were significant age-related changes on these tasks (see Table 2).
| Condition | 2- to 3-year-olds n = 16 |
4-year-olds n = 16 |
5-year-olds n = 20 |
6-year-olds n = 21 |
7-year-olds n = 19 |
|---|---|---|---|---|---|
| Total ignorance | 96.9 (.25) | 84.4 (.60) | 80 (.68) | 95.3 (.30) | 100 (.00) |
| Partial exposure | 21.9 (.63) | 31.3 (.89) | 35 (.92) | 92.9 (.48) | 94.8 (.32) |
| Complete knowledge | 87.5 (.45) | 96.9 (.25) | 100 (.00) | 100 (.00) | 100 (.00) |
Children had no profound difficulties on the total ignorance test question (“Do you know now which toy is inside or do you not know?”) at any age. Even the 2- to 3-year-olds (M = 96.9% correct, SD = .25) and the 4-year-olds (M = 84.38% correct, SD = .60) performed very well. Although performance did not increase monotonically with age as assessed using Jonckheere–Terpstra test (p > .17), there was evidence for a significant performance difference between the age groups, Kruskal–Wallis H test: χ2(4, N = 92) = 10.21, p < .05. Post hoc Mann–Whitney U tests revealed a significant difference (p = .023) between the 4-year-olds (M = 84.38% correct, SD = .60) and the 7-year-olds (M = 100% correct) and a significant difference (p = .011) between the 5-year-olds (M = 80% correct, SD = .68) and the 7-year-olds (M = 100% correct). All other differences were nonsignificant (all ps > .06).
All children who either correctly claimed ignorance on the test question or (n = 4) who admitted that they had just guessed on the know–guess control question, received the ignorance justification question (“Why don’t you know which toy is inside?”). Children’s justifications were scored as correct, when they referred to the lack of informational access (e.g., “You did not show me the toy!” or “The lid has remained closed the whole time!”). All other answers were scored as incorrect (e.g., “My mother has not told me that” or “I do not know that”). Whereas in particular children under 6 years of age had profound difficulties in justifying their own ignorance (M = 21% correct, SD = .67), the 6- and 7-year-olds (M = 81.3% correct, SD = .73) were significantly better, Mann–Whitney test: U(50, 40) = 303, p < .001.
The second epistemic task setting, in which children had to acknowledge their own ignorance was the partial exposure task. Performance on the test question increased monotonically with age as assessed using Jonckheere–Terpstra test (p < .001), and performance differed between the age groups, Kruskal–Wallis H test: χ2(4, N = 92) = 44.64, p < .001. Particularly, children under 6 years of age often wrongly indicated knowledge in the partial exposure condition (M = 29.81% correct, SD = .82). Only 6- and 7-year-old children (M = 93.75% correct, SD = .40) were able to adequately assess their own epistemic state in a partial exposure setting. Post hoc Mann–Whitney U tests revealed that the 2- to 3-, 4-, and 5-year-olds did not differ significantly from each other (all ps > .50), but all three younger age groups differed significantly from the 6- and 7-year-olds (all ps < .001).
Only 5 (11%) of 45 children under 6 years, who claimed knowledge on the initial test question and who were consequently asked the know–guess control question, revised their incorrect initial answer by admitting that they were “just guessing” (in at least one of the runs). The majority of children under 6 years still insisted on “knowing.” In contrast, twenty-one (91.3%) of twenty-three 6- and 7-year-olds correctly admitted to having “guessed” (in at least one of the runs).
If children had (incorrectly) claimed knowledge on the initial test question and then insisted on “knowing” on the know–guess control question, children were asked the knowledge justification question (“How do you know that there is an X inside?”). Consistent with the fact that correct answers were not possible, only a small minority (n = 13) of children tried to justify their knowledge by either referring to a nonexistent source (e.g., “My mother has told me”) or by referring to their perceptual access at the beginning of the task (e.g., “Because I saw the X beforehand”) in at least one of the runs. All the other children either reiterated that they “knew” or simply remained silent, when asked the question.
Children who correctly stated that they were ignorant (or that they had just guessed) were asked the ignorance justification question (“Why don’t you know which toy is inside?”). Only 18 children under 6 years were given this question, and only 6 of them (33.3%) justified their ignorance, in at least one of the runs, in terms of not having had visual access. In contrast, 31 of 37 children (83.8%) over 6 years, who were given this question, were able to justify their ignorance, in at least one of the runs.
Consistent with prior research (e.g., Tardif et al., 2005), in the complete knowledge subtask, all age groups had no major problems in correctly assessing and reporting their knowledge (M = 97.3% correct, SD = .23). Nevertheless, there was a significant monotonic age trend in performance as assessed using Jonckheere–Terpstra test (p = .002) and also significant group differences, Kruskal–Wallis H test: χ2(4, N = 92) = 15.22, p = .004, which consisted of the youngest age group differing significantly from the 5-, 6-, and 7-year-olds (all ps < .05). After correctly claiming knowledge in the complete knowledge task, only three children did not substantiate this statement in the know–guess control question (but only in one of the two runs).
Regarding children’s justifications of knowledge (“Why do you know that there is an X inside?”), children under 5 years of age (M = 23.4%, SD = .76) had striking difficulties, whereas the 5- to 7-year-olds (M = 85%, SD = .59) were significantly more proficient in justifying their knowledge, Mann–Whitney test: U(32, 60) = 274, p < .001.
Finally, it was examined whether individual children tended to respond exclusively with either “yes” (yes bias) or “no” (no bias) on all the knowledge test questions (“Do you know now which toy is inside or do you not know?”) of the total ignorance, the partial exposure, and the complete knowledge task (in both runs). No child showed a no bias, and only three children showed a yes bias.
Discussion
We found no difference between the total ignorance task, which provided a cue to the hidden object in the test question, and the varied total ignorance task, which did not entail a cue. Thus, most 3-year-old children correctly admitted their ignorance in both total ignorance tasks. Children additionally had no problem in correctly assessing and reporting their own knowledge in the complete knowledge task. However, only 6-year-olds and older children were able to reliably assess their ignorance in the partial exposure task, in which one of two initially displayed objects had been hidden.
In sum, consistent with our predictions, we found the expected difference in children’s performance between the partial exposure task and the total ignorance tasks; children generally performed worse in the former task than in the latter, in spite of the fact that we employed a know–guess control question. This suggests that a simple inhibition deficit cannot account for the poor performance in the partial exposure task, as otherwise children could have used the know–guess control question to revise their initial answer after accidentally naming a toy on the test question (“Do you know now which toy is inside or do you not know?”) due to difficulties with inhibition.
Furthermore, it seems unlikely that children were relying on a simple guessing strategy during the partial exposure task because children did not admit to “guess” on the know–guess control question. It might, however, be objected that preschool children simply do not understand the terms know and guess and therefore could not make use of our know–guess control question. This objection seems unlikely because there is evidence that even 3-year-olds use the words know and guess in their spontaneous speech and partially even for real mental referencing in the appropriate context (e.g., Bartsch & Wellman, 1995; Shatz, Wellman, & Silber, 1983). Interestingly, children of this age also start to differentiate between linguistic expressions that vary in their degree of certainty (e.g., “may” and “is,” or “might be” and “has to be”) and show differential behaviors in dependence on which of the two terms is used in an instruction (e.g., Byrnes & Duff, 1989; Hirst & Weil, 1982). Along the same lines, 4-year-olds were found to understand the two terms know and guess as an indication of different degrees of certainty, that is, they associate know with a high confidence in the correctness of a statement and the term guess with a low confidence (Moore, Bryant, & Furrow, 1989).
In the relevant age range, children thus have a basic understanding of the two terms. This was also substantiated by the fact that there was no evidence that children responded randomly on our know–guess control question, but instead, an overwhelming majority of children until school age systematically claimed to “know” (reflecting certainty) after having produced a response in the partial exposure task. Children could, however, have still guessed and then claimed to “know” on the know–guess control question because of being generally motivated to present themselves as knowledgeable as possible. However, this claim does not likely hold either, because contrary to such a tendency, the vast majority of children under 6 years refrained from coming up with responses in the total ignorance tasks.
Taken together, a vast majority of preschool children in this experiment was found to be unable to justify their own epistemic state by referring to its informational source and was also found to not check for a sufficient informational access when assessing their own epistemic state.
These results are consistent with the risk account because if children just check for the risk of their answer, that is, claim to “know” when the set of possible alternative answers is small and acknowledge their ignorance when the set size of possible alternative answers is large, then children should refrain from claiming to “know” in the total ignorance tasks (as there was an almost infinite number of possible alternative responses), but should claim to “know” both in the complete knowledge task (as this task did not entail any alternative response) and the partial exposure task (as this task only contained one alternative response, and thus the risk of answering incorrectly was reasonably low).
The results of this experiment are, however, also in line with the competence account because if children just check for a feeling of competence, that is, claim to know when they are able to easily come up with a response and acknowledge their own ignorance when this is not the case, then children should refrain from claiming to “know” in the total ignorance tasks (as nothing relevant was shown to the children during hiding that should have undermined their ability to easily come up with a response), but should claim to “know” both in the complete knowledge task (in which children had seen a relevant object) and the partial exposure task (in which children had seen a set of relevant objects ahead of hiding, and thus could have found it easy to come up with a plausible response).
Interestingly the fact, that children claimed to “know” in the complete knowledge and partial exposure tasks but not in the total ignorance tasks, although a cue about the hidden object was given in the total ignorance task, could then (when the competence account’s validity is supposed) indicate that it is not children’s ability to work out a plausible answer on their own (e.g., by means of a cue), which is the main cause of children’s feeling of competence, but the ease with which information comes to children’s minds.
Noteworthy, the ease with which information comes to mind (e.g., Koriat, 1993; Mazzoni & Nelson, 1995) and the ease with which information is accessible or the efforts experienced in reaching a decision (e.g., Kelley & Lindsay, 1993; Nelson & Narens, 1990) have also been found to influence (and strengthen) adults’ subjective confidence in the correctness of retrieved information in memory tasks.
To summarize, first, Experiment 1 yielded evidence that discrepancies in results between previous studies can be put down to a structural difference in the experimental design of these studies (namely, if a task can be classified as a partial exposure or a total ignorance task). Second, children until 6 years seem to rely on an immature cognitive heuristic when assessing their own epistemic states, apparently because they have an immature conceptualization of what constitutes their own knowledge (i.e., children do not check the causal origins of their knowledge).
Experiment 2
To differentiate between the two cognitive heuristics derived from the Wimmer et al. (1988) account, we decided to compare four partial exposure task settings which comprised varying set sizes of objects shown to the children prior to a hiding event. These tasks either caused a 50% risk of coming up with the wrong answer (Set Size 2 task), a 66.7% risk (Set Size 3 task), an 80% risk (Set Size 5 task), or a 90% risk (Set Size 10 task).
If children indeed only consider low-risk responses as incidences of knowledge, their performance should now differ between tasks because each of the tasks results in a different risk or a different degree to which their answer could be wrong given the set of possible alternative responses. However, if children base their epistemic state assessment only on a feeling of competence, no differential performance pattern should be obtained between these partial exposure tasks because children then do not consider the set of alternative responses, but just consider the ease with which they can produce a plausible response as their main indicator of knowledge. As producing a plausible response is equally easy in all four partial exposure tasks, children should have an equal tendency to overestimate their knowledge.
Method
Participants. A total of 101 children, 58 boys and 43 girls, from three different nurseries and two after-school care clubs in Upper-Austria, participated. The children had a mixed working- and middle-class background and their ethnical background was mainly Austrian. All children were deemed competent by their teachers for the tasks. There were thirteen 3-year-olds (range = 3;3 to 3;11), mean age of 3;7; seventeen 4-year-olds (range = 4;2 to 4;11 years), mean age of 4;6; thirty-four 5-year-olds (range = 5;0 to 5;11), mean age of 5;6; eighteen 6-year-olds (range = 6;0 to 6;11), mean age of 6;5 years; and nineteen 7-year-olds (range = 7;0 to 7;11), mean age of 7;6.
Materials. In the partial exposure tasks, the same materials were used as in Experiment 1, with the exception that we used a slightly larger set of toys. In total, 20 toys (e.g., pig, tiger, monkey, rabbit, etc.) were used for the partial exposure tasks. Specific subsets of toys were always linked with specific tasks. Four toys (cat, aircraft, truck, and lion) were kept in reserve in case that a child was not familiar with one of the toys in the partial exposure tasks. But, again, this was rarely the case. Only six children needed a replacement of the original toys.
Design and procedure. Each child was tested individually in a separate, quiet room in the nursery or in the after-school care club. Each child was seated opposite to the experimenter’s seat at a table. Four different partial exposure tasks were used. Children’s responses were again manually recorded on paper during the experiment. Each child received all tasks in one session. The sequence of the tasks was counterbalanced between participants using a Latin Square.
The partial exposure tasks differed from the tasks in Experiment 1 only in the quantity of objects that were shown to the child prior to hiding. Children, thus, either saw 2 objects ahead of hiding (Set Size 2 task), 3 objects (Set Size 3 task), 5 objects (Set Size 5 task), or 10 objects (Set Size 10 task). Children had to name all the toys correctly before the hiding games started.
Results
For the partial exposure tasks, scoring was the same as in Experiment 1.
Figure 1 shows children’s performance on the different partial exposure tasks. Children’s performance did not differ significantly for different set sizes, Friedman test: χ2(3, N = 101) = 3.41, p > .33. Also, when we compared performance on the four tasks within each age group, there were no significant differences, all Friedman tests p > .19. Also performance did not monotonically improve with increasing set size within any of the age groups as assessed by Page’s L test (all ps > .05). Jonckheere–Terpstra tests, however, showed that performance on the test question of all four partial exposure tasks did monotonically improve with age (all ps < .001).
Mean percentage of correct performance in children’s ability to assess own ignorance states in different age groups. Note. Children had to assess their ignorance states in four partial exposure tasks, where a set of 2 toys (Set Size 2), 3 toys (Set Size 3), 5 toys (Set Size 5), or 10 toys (Set Size 10) was shown to them prior to hiding.
A minority of the children under 6 years, who claimed knowledge on the initial test questions, correctly revised their initial claim of knowledge on the know–guess control question by answering, “I am just guessing.” However, the majority of children under 6 years still insisted “to know” across the tasks (M = 26% correct). Six- and seven-year-olds more often correctly admitted to “guess” on the control question across the tasks (M = 62.5% correct).
As in Experiment 1, on the second control question of the partial exposure tasks (“Why do you know that there is an X [name of toy] inside?”), only a few children (n = 19) tried to justify their incorrect knowledge claim by either referring to a nonexistent source or by referring to their perceptual access at the beginning of the task (e.g., “My mother told me”; “I saw that it was a tiger”), at least in one of the tasks, which was consistent with the fact that correct justifications were not possible.
Children, who had correctly stated that they were ignorant on the test question or later admitted to “guess” on the know–guess control question, were asked the ignorance justification question (“Why don’t you know which toy is inside?”). Only about one third of the children under 6 years were able to justify their ignorance states in terms of denied visual access across the different partial exposure task settings (M = 36.7% correct). The 6- and 7-year-olds (M = 77.8% correct) were significantly better at justifying their ignorance than the under 6-year-olds, Mann–Whitney test: U(49, 36) = 449, p < .001.
Discussion
To answer the question whether the obtained dissociation between the partial exposure task and the total ignorance task in Experiment 1 was due to young children’s reliance on a “feeling of competence” or a consideration of their response’s relative risk, we compared four different partial exposure task settings, which comprised different set sizes of objects shown to the children prior to a hiding event. Interestingly, children’s performance did not differ on these four partial exposure tasks. This indicates that children are prone to faulty performance in partial exposure tasks not because they consider the degree to which their answer could be wrong, given the set of possible alternative responses, but because children deem the ability to easily come up with a plausible response, a strong indicator of knowledge.
General Discussion
Prior studies have yielded discrepant conclusions regarding when children can correctly answer metacognitive questions about their own epistemic states (e.g., Pratt & Bryant, 1990; Sodian & Wimmer, 1987). In Experiment 1, we found evidence that much of this disagreement can be put down to a structural difference between studies, namely, whether tasks can be classified as “total ignorance” or “partial exposure.” In Experiment 2, we found further evidence that children’s poor performance in partial exposure tasks is brought about by young children’s reliance on an immature cognitive heuristic, which causes a misleading “feeling of competence” in them. In keeping with this, children did not consider the overall quantity of alternative responses in our partial exposure tasks and were thus neglecting the risk of their response.
We acknowledge that children might, nevertheless, have experienced differential feelings of uncertainty, which varied with the chance structure of the partial exposure tasks but which went undetected because we used a too insensitive measure (i.e., the verbal test and control question could have made it hard for children to express their feelings accurately). Although this speculation is not implausible, there is evidence that children do not express accurate feelings of uncertainty in a task that can be considered a partial exposure task, even when they are given the chance to respond on a nonverbal certainty rating scale. For example, 5-year-old children in a study by Pillow (2002) rated a statement about the color of a hidden ball as overly certain, although they had only seen a pair of two differently colored balls ahead of hiding, but then they had not seen which ball had been hidden in which location (77% certainty in guess task of Experiment 1; 82% certainty in informed guess task of Experiment 2). In contrast with these ratings, children, however, showed remarkably accurate assessments of own certainty or uncertainty in tasks in which they had to rate how certain or uncertain they were about the names of familiar objects (90% in Experiment 1; 93% in Experiment 2) or about the names of unfamiliar objects (16% in Experiment 1; 19% in Experiment 2). Children’s overratings of their own certainty in the partial exposure tasks of this study, therefore, clearly provided a stark contrast with children’s accurate certainty assessments in the control tasks. However, in light of our competence account, one can make sense of this finding because children should have experienced a feeling of competence in the partial exposure tasks, and such a feeling can equally be understood as a feeling of being overly certain about a response’s correctness. Children’s certainty ratings, however, do not reconcile with the notion that children accurately experienced the risk associated with a specific response (in terms of accurate feelings of uncertainty) as certainty ratings should have been more moderate then.
Support for the notion that children fail in partial exposure tasks, due to a reliance on an immature cognitive heuristic and not due to our verbal procedure or a guessing strategy, also comes from recent pilot studies (N = 57) by Rohwer, Kloo, and Perner (raw data), in which nonverbal response options were used. In these studies, children from 3 to 8 years of ages saw, for instance, two kinds of animals (i.e., a cat and a dog), one of which was then covertly transferred to an opaque building (i.e., an animal house). Children then had to decide whether they wanted to feed the unknown animal in the house with either a bone (which could only be eaten by the dog) or a fish (which could only be eaten by the cat), or whether they wanted to place both kinds of plastic foods to the house to ensure that the specific animal in the house would not get hungry. Children who opted for both kinds of foods and thus acknowledged their ignorance or uncertainty behaviorally won a star, whereas children who overestimated their knowledge lost one (direct reinforcement strategy). However, until school age, children still overestimated their own knowledge even when they were made subject to losses. See also Robinson, Rowley, Beck, Carroll, and Apperly’s (2006, Experiment 1) epistemic uncertainty task (which can also be considered as a nonverbal partial exposure task) for comparable results.
Given that there is sufficient evidence to back up the claim that our findings are not an artifact of our verbal methodology, it is now appropriate to examine how our claim that children do not adequately reflect on their informational sources when assessing epistemic states, but instead rely on a subordinate indicator of knowledge, can explain findings in the self-assessment literature. As discussed, it can account both for the results in the partial exposure task and the total ignorance task. We can also account for why the majority of 4- (86%) and 5-year-olds (57%) in a study by Taylor, Esbensen, and Bennet (1994, Experiment 1), who had been taught novel facts (e.g., that tigers’ stripes provide camouflage) about animals in different stories, insisted to have known these facts for a long time, although the learning event in fact had taken place only a few minutes ago. In keeping with our account, this is the case because children rely on a feeling of competence (also provided by full informational access) and are thus made oblivious to transitions in their factual knowledge states. That children have problems justifying their own epistemic states by referring to its informational source is further supported both by previous literature (e.g., Gopnik & Graf, 1988) and our own current findings that a substantial amount of children until school age were not able to justify their epistemic states. Furthermore, we can account for findings in the ambiguous referencing literature, namely, that children produce responses, which indicate knowledge, instead of relying on response options, which would show that they acknowledge their ignorance (e.g., Beck & Robinson, 2001, Experiment 3; Somerville, Hadkinson, & Greenberg, 1979), and also that children regard an ambiguous instruction as sufficient (e.g., Ironsmith & Whitehurst, 1978; Robinson & Robinson, 1982; Singer & Flavell, 1981). This is the case because our account predicts that children should consider instructions which allow them to easily think of a plausible response as sufficient and should produce responses in such tasks, because of having a feeling of competence.
However, it is also worthwhile to examine how our findings fit into the more general frame of the “self” versus “other” knowledge assessment literature, as this might yield relevant implications for the ongoing debate in the “theory of mind” literature regarding whether children understand and predict the minds of others by means of using their own mental states for mentally simulating those of others (simulation view) or whether children rely on laws, heuristics, or nomological rules for that purpose (theory-theory view).
To sum up, it can be said that children by the age of 3 years can assess their own—and another person’s—epistemic states remarkably well in tasks in which either no informational access (total ignorance tasks) or full informational access is given to the person whose epistemic state is assessed (complete knowledge tasks; e.g., Pratt & Bryant, 1990). Interestingly, such a parallel between children’s self-assessments and other assessments cannot be found in partial exposure task settings (either in terms of general accuracy or in terms of certainty ratings). Children in our partial exposure tasks constantly overestimated their own knowledge until they reached school age. In contrast, children in a study by Sodian and Wimmer (1987) made very accurate assessments of a puppet’s ignorance when both the puppet and the child had seen a transparent container with two differently colored balls at the beginning but then had not seen the transport of one of the balls to a bag (same perspective condition). Twenty-five percent of 4-year-olds and no single 5- or 6-year-olds answered the test question, for example, “Does John (puppet’s name) know which color the ball in the bag is?” affirmatively. Similarly, in a study by Ruffman (1996, Experiment 1), children from 4 to 5 years of ages (and older) were found to reach ceiling performance when assessing the ignorance state of a puppet in a partial exposure task (two color task), in which two differently colored sweets were shown to a child and a puppet ahead of hiding, one of which was subsequently covertly hidden in a container (from the puppet’s perspective). Along the same lines, whereas Pillow (2002) found that children overrated the certainty of their own statement in partial exposure tasks (see above), Pillow, Hill, Boyce, and Stein (2000, Experiment 1) found that children did not overrate the certainty of another person’s statement in such tasks (e.g., 4-year-olds: 28% certainty; 5-year-olds: 49% certainty). See also Experiment 3 in Pillow et al. for comparable results.
This pattern of results can hardly be reconciled with a simple simulation view, as otherwise strong parallels in children’s self and other assessments should have been observed, not only between total ignorance and complete knowledge tasks but also between children’s self and other assessments in partial exposure tasks (as children should decide on what another person will think by simulating their own thoughts in the same situation).
Given that a simple simulation view consequently has difficulties accounting for the dissociation between self and other assessments in partial exposure tasks, it is interesting that a theory-theory account (e.g., Gopnik & Wellman, 1992; Perner, 1991) can account for the results, when a different evidential basis is assumed for self (feeling of competence) than for other (informational access). Children could then acknowledge their own ignorance in total ignorance tasks (as they do not have a feeling of competence in these tasks) and can also acknowledge the ignorance of another person in these tasks (as the other person does not have direct access to information). Children can further acknowledge their own knowledge in complete knowledge tasks (as they have a strong feeling of competence in these tasks by being exposed to one specific object) and can also acknowledge the knowledge of another person in these tasks (as the other person has direct access to information). Children, however, fail to acknowledge their own ignorance in partial exposure tasks (as they rely on a misleading feeling of competence, which is induced by the fact that they have been exposed to a set of relevant objects ahead of hiding), whereas they can correctly acknowledge another person’s ignorance in these tasks (as children acknowledge that the other person did not have direct access to information at a crucial point in time).
Interestingly, studies that revolved around children’s understanding of inference as a source of knowledge also yielded results that support the view that children rely on a seeing–knowing rule when assessing another person’s epistemic states and on a feeling of competence when assessing their own epistemic states. For instance, Sodian and Wimmer (1987) showed 4- to 6-year-olds and another person a container with blue balls. Then either the child or the other person (depending on the trial) was allowed to see which one of the balls was being transferred from the container to an opaque bag. The individual, who had not been allowed to watch the transfer from the container to the bag, however, received premise information (i.e., was told that the object, which had been put into the bag, had been taken from the first container). Importantly, children younger than 6 years did not understand inference as a source of knowledge when assessing the other person’s epistemic state, and attributed ignorance to the other person when the other person had not seen what had actually been put into the bag (children apparently just checked for the other person’s direct access to information), whereas children who themselves had not seen the ball’s transfer, but who had received premise information, said that they would know the ball’s color in the bag (children apparently relied on a feeling of competence). See also Pillow (1999) and Ruffman (1996) for further evidence that children until the age of 6 years do not understand inference as a source of knowledge when assessing another person’s epistemic state but just check whether the other person had direct access to critical information.
The dissociation between self and other assessments in the partial exposure task and inference tasks can therefore be brought in line with our competence account, but it has to be emphasized that it is also incompatible with a copy theoretical position (e.g., Carpendale & Chandler, 1996; Chandler & Boyes, 1982), according to which children are understood as passive receptacles of incoming information, for whom seeing something is necessarily equated with knowing. Given this, a copy theorist would have to predict that children must show the same tendency to overestimate their own and another person’s knowledge in partial exposure tasks and inference tasks because both the child and the other person should have the same imprints of knowledge on their mind (both have seen something ahead of hiding).
In sum, our account can be used to explain results in a wide variety of contexts, but it cannot account for the self-assessment findings in the partial exposure tasks used by Ruffman and Olson (1989) or by Pillow (1989). We, however, assume that the difference in results obtained between these studies and our study is rooted in the fact that in the two other studies children did not retain the items equally well in their memory as was the case in our task. Thus, while both the connection between the possible contents and the subsequent hiding was made very clear to children in our partial exposure task (i.e., children had to name the possible contents ahead of hiding on their own and were allowed to have a brief second glance at the objects, which were relevant for hiding after they had been informed that the game was about hiding), this was not done in Ruffman and Olson’s (1989) and Pillow’s (1989) study and might have thus made their partial exposure tasks more like total ignorance tasks for the children.
To summarize, in two experiments we obtained evidence from the partial exposure tasks that children can only assess their own epistemic states reliably when they reach school age. The fact that preschool children’s persistent problems are limited to partial exposure tasks suggests a very specific deficit of metacognition of knowledge, in particular, an inability to accurately judge their own state of ignorance. Before school age, children are still ignorant about their state of ignorance; that is, they are meta-ignorant. Only by about 5–6 years of age do they amend this deficit and, thus, are able to escape their meta-ignorance.
Preschool children’s meta-ignorance should, however, not be understood as a complete failure to reflect on or monitor their own abilities. Their earlier competence in the total ignorance and complete knowledge tasks shows, they must be able to reflect on their ability to produce something like a “relevant guess,” which gives them the feeling of being able to respond competently. They mistake this feeling as knowledge, as we have argued to explain their wrong affirmative answers in the partial exposure tasks.
Older children and adults, too, often rely on their feeling of being able to produce a correct answer for judging their own knowledge. For instance, in the tip-of-the-tongue phenomenon we can be certain that we know the answer to a question, for example, “What is the capital of New York?” even if we cannot actually retrieve the answer. This feeling of knowing is deemed to be due to how easy our retrieval attempts feel (e.g., Koriat, 1993). However, there is an important difference to what the younger children seem to be doing in the partial exposure task. Even if the first answer that rushes to our mind is “New York City,” we do not announce it and claim that we know that it is New York City and firmly deny having guessed. For it is not any plausible answer that comes to mind that we admit as knowledge. We must be able to find a suitable propositional fact like, “Albany is the capital of New York,” in our knowledge base before we can admit to having found the correct answer. In the case of the partial exposure task, there is no such relevant fact, for example, “The toy car is in the box,” in the child’s knowledge base. The children do not check whether they have a definitive fact available for answering the question, they seem content with just any plausible answer they can easily muster. Their spontaneous guess seems to turn subjectively into knowledge. Mistaking their relevant guesses for actual knowledge constitutes a deep limitation in being able to accurately gauge their own ignorance.
We have therewith advanced the literature by putting some of the heterogeneity between previous studies down to methodical differences in experimental paradigms and also by supporting the notion that children have an immature conceptualization of knowledge. However, at the same time we do not advocate the notion that children’s errors in many epistemic task assessment task settings can be attributed to an inhibition deficit or the fact that the mind is a passive recorder of information. We instead support the notion that the mind is actively forming epistemic states and actively interpreting incoming information, in light of its immature cognitive heuristics, which lead preschool children to a striking neglect of the informational basis of their own knowledge.
