Cognition 120 (2011) 322–330

Contents lists available at ScienceDirect

Cognition
journal homepage: www.elsevier.com/locate/COGNIT

The double-edged sword of pedagogy: Instruction limits spontaneous
exploration and discovery
Elizabeth Bonawitz a,⇑,1, Patrick Shafto b,⇑,1, Hyowon Gweon c, Noah D. Goodman d,
Elizabeth Spelke e, Laura Schulz caDepartment of Psychology, University of California, Berkeley, CA 94720, USA
Department of Psychological and Brain Sciences, University of Louisville, Louisville, KY 40292, USAc
Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USAd
Department of Psychology, Stanford University, Stanford, CA 94305, USAe
Department of Psychology, Harvard University, Cambridge, MA 02138, USAba r t i c l e

i n f oArticle history:
Available online 8 January 2011
Keywords:
Pedagogy
Bayesian model
Exploratory play
Discovery
Causal learning
Cognitive developmenta b s t r a c t
Motivated by computational analyses, we look at how teaching affects exploration and discovery. In Experiment 1, we investigated children’s exploratory play after an adult pedagogically demonstrated a function of a toy, after an interrupted pedagogicaldemonstration, after a naïve adult demonstrated the function, and at baseline. Preschoolers
in the pedagogical condition focused almost exclusively on the target function; by contrast,children in the other conditions explored broadly. In Experiment 2, we show that children
restrict their exploration both after direct instruction to themselves and after overhearing
direct instruction given to another child; they do not show this constraint after observing
direct instruction given to an adult or after observing a non-pedagogical intentional action.
We discuss these ﬁndings as the result of rational inductive biases. In pedagogical contexts,
a teacher’s failure to provide evidence for additional functions provides evidence for theirabsence; such contexts generalize from child to child (because children are likely to havecomparable states of knowledge) but not from adult to child. Thus, pedagogy promotes
efﬁcient learning but at a cost: children are less likely to perform potentially irrelevant
actions but also less likely to discover novel information.
Ó 2010 Published by Elsevier B.V.

The principal goal of education is to create men who arecapable of doing new things, not simply of repeating what
other generations have done – men who are creative,
inventive and discoverers. Jean Piaget.

⇑ Corresponding authors.
1

E-mail address: p.shafto@louisville.edu (P. Shafto).
The ﬁrst two authors contributed equally to this work.

0010-0277/$ - see front matter Ó 2010 Published by Elsevier B.V.
doi:10.1016/j.cognition.2010.10.001

1. Introduction
Two competing intuitions animate longstanding debates over children’s learning: that children learn primarily
from helpful, informative others (through testimony or‘‘direct instruction’’; Csibra & Gergely, 2009; Gergely,
Király, & Egyed, 2007; Koenig & Harris, 2005; Kushnir,
Wellman, & Gelman, 2008; Tomasello & Barton, 1994;
Vygotsky, 1978), and that, especially in the early years,
children learn chieﬂy through their own active explorationof the environment (‘‘constructivist’’ or ‘‘discovery learning’’; Bonawitz, Lim, & Schulz, 2007; Bonawitz & Schulz,
in preparation; Bruner, Jolly, & Sylva, 1976; Gweon &Schulz, 2008; Piaget, 1929; Schulz & Bonawitz, 2007;
Singer, Golinkoff, & Hirsh-Pasek, 2008). Here we suggest

E. Bonawitz et al. / Cognition 120 (2011) 322–330

that the tension between learning from others and fromself-guided exploration stems in part from a principledtrade-off at the heart of pedagogical learning. Teaching2
produces an inductive bias that constrains children’s
hypothesis space for better and for worse: in promoting rapid and efﬁcient learning of target material, pedagogicalinstruction necessarily limits the range of hypotheses children consider.
Our inquiry is motivated by an ideal learner analysis—
what should a student infer from evidence given by a helpful teacher? Recent research has formalized pedagogicallearning as an inference based on the paired assumptions
that a learner will rationally update her belief in a hypothesis given new data (from a pedagogical demonstration)and that a teacher will choose data (a particular demonstration) likely to increase the learner’s belief in the correct
hypothesis (Shafto & Goodman, 2008; Shafto, Goodman, &Grifﬁths, in preparation). In what follows, we present details of our Bayesian analysis and two experiments motivated from this analysis, exploring the consequences ofpedagogical inference on preschool-aged children’s exploration and discovery.
An ideal learner will update her beliefs rationally given
the demonstration (or data), d, as described by Bayes’
theorem:PL ðhjdÞ / PðdjhÞPL ðhÞ:ð1ÞIn Eq. (1), PL(h) represents the learner’s prior beliefs in ahypothesis h. The term P(d|h), called the likelihood or sampling assumption, captures the learner’s assumption about
the source of the data. If the learner did not believe thedata were chosen by a helpful teacher, then we would
use a default sampling assumption in Eq. (1): PD(d|h). Thisdefault will depend on the situation, and captures the natural source of evidence in the absence of a teacher (e.g. byrandom exploration). However, if the learner assumes thata helpful teacher has chosen the data, we must use a pedagogical sampling assumption:

PL ðhjdÞ / PT ðdjhÞPL ðhÞ;

ð10 Þ

PT ðdjhÞ / PL ðhjdÞ;ð2Þ

Eq. (2) captures the idea that the data are chosen by theteacher in such a way that they will increase the probability that the learner assigns to the correct hypothesis. Notethat the teacher’s choice of data depends in turn on theassumption that the learner will rationally update her beliefs. Eqs. (10 ) and (2), and the default sampling assumption, deﬁne a system of equations that provides a modelof how having a teacher should affect a learner’s inferences. Intuitively, one can imagine beginning with theinferences the learner would draw under the default sampling assumption, then using Eqs. (10 ) and (2) iteratively to‘‘strengthen’’ these inferences into the ideal pedagogicalinferences. (See Shafto & Goodman, 2008; Shafto et al., in
preparation, for further discussion.)
2
Throughout, reference to teachers and teaching refer, not only toclassroom instruction, but to any knowledgeable, helpful communicative
partner providing instruction to a less knowledgeable partner.

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Consider, for example, inferences about novel toy,
which has M potential affordances (a ﬁxed, but arbitrary,large number) of which an unknown number, n, will activate latent functions. We imagine a default sampling process in which m affordances are tested at random(without knowledge of which ones have a function—thisis called a weak sampling assumption, Tenenbaum, 1999).
Under this default, an observation of m tests resulting in
n functions provides strong evidence for these n functions
but provides no evidence for, or against, any functions ofuntested affordances. In particular, the learner gains noinformation beyond her a priori beliefs about the untested
affordances: even though she may believe that functions
are rare (Oaksford & Chater, 1994) and hence additional
functions are unlikely, the evidence does not enhance thisinference compared to baseline.
In a pedagogical context, by Eq. (2), a teacher should
demonstrate all the actual functions: if she demonstrated
fewer, the learner would consider more hypotheses, andhence, each (including the correct one) would receive lower probability. She should demonstrate the functioning
affordances (rather than the non-functions) because these
are a priori rare; hence, observing them raises the probability of the correct hypothesis more than observing nonfunctions. Given this, the learner will infer, by Eq. (10 ), thatthe demonstrated functions are exhaustive—all the functions will be demonstrated by a helpful teacher. (Further
iterations of Eqs. (10 ) and (2) will strengthen this inference,but not change the qualitative conclusion.) Thus, the inference that there are no additional functions to be discovered will be strong in a pedagogical context but weak
(and no stronger than at baseline) in a default context.
What factors affect whether a child should interpret agiven context as pedagogical? The above analysis depends
on the assumption that the data are chosen by a knowledgeable, helpful teacher. If the evidence is sampled randomly (e.g., by a teacher who is ignorant of the true
hypothesis or by the naïve learner herself), the default
sampling assumption should be used, as described above,and the absence of additional functions should not be inferred. Similarly, if the teacher is interrupted in the middleof giving the evidence, it will be ambiguous whether theteacher would have gone onto demonstrate additional
functions; in this case the evidence also does not imply absence of additional functions. Note that we will treat suchcases as ‘‘non-pedagogical’’, even if they involve superﬁcial
cues to pedagogy (i.e., an adult engaging in joint attention
and providing ostensive communicative cues to a child;Csibra & Gergely, 2009). Such cues may be useful precisely
because they tend to predict pedagogical sampling, but if,
in a particular instance, pedagogical sampling has clearly
not occurred, the inferential assumptions of pedagogy
should not hold.
This analysis suggests a trade-off between instructionand exploration. Because pedagogical inferences constrain
the hypotheses children consider, children should be efﬁcient learners in pedagogical contexts, but they may wellassume there is nothing further to learn. (If there were,
the teacher should have provided evidence accordingly.)Thus, when a knowledgeable teacher freely demonstrates
a function of a toy, children should engage in relatively

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limited exploration and discover little else about the toy.
By contrast, in non-pedagogical contexts, children should
not be restricted to any one function, even if demonstrated.
Children should take all the toy’s affordances into account(as they would at baseline) and thus explore broadly. In
Experiment 1, we test these predictions by looking at
whether, relative to children in non-pedagogical contexts,children given pedagogically sampled evidence about a
toy explore the toy more brieﬂy, perform fewer unique actions, and discover fewer non-demonstrated functions.
2. Experiment 1
2.1. Methods
2.1.1. Participants
Eighty-ﬁve preschoolers participated (mean age:
58 months; range: 48–72 months) in an urban science museum. Most children were white and middle-class, but arange of ethnicities resembling the diversity of the population was represented.
2.1.2. Design
Preschoolers participated in one of four conditions: 25
children in a Pedagogical condition and 20 each in one ofthree Non-Pedagogical conditions: Interrupted, Naive, andBaseline. There were no differences in the age of the children across conditions: F(4, 81) = 0.30, p = ns.
2.1.3. Materials
A novel-looking toy was created using colored PVC
pipes attached to a board (see Fig. 1). The toy was approximately 1800  600  1500 . The toy had four different nonobvious causal affordances: it made a squeak sound whena yellow-colored tube was pulled out from inside a larger
purple tube; one end of a blue tube lit up when a small

button hidden inside the other end was pressed; a small
yellow pad attached to the plastic board played musicnotes when different parts of the pad were pressed; there
were two adjoining black tubes with mirrors inside so thata reversed mirror image of the observer’s face was visible.
All other aspects of the toy were inert.

2.1.4. ProcedureChildren were tested individually in a quiet corner ofthe museum. In all conditions, the experimenter brought
the toy out from under the table. In the Pedagogical condition, the experimenter said, ‘‘Look at my toy! This is mytoy. I’m going to show you how my toy works. Watch
this!’’ The experimenter then pulled the yellow tube out
from the purple tube to produce the squeak sound. She
said, ‘‘Wow, see that? This is how my toy works!’’ anddemonstrated the same action again. The Interrupted condition was exactly like the Pedagogical condition, exceptthat the experimenter interrupted herself immediately
after the demonstration saying, ‘‘I just realized, I have tostop because I forgot to write down something over there.
I have to go take care of it right now!’’ In the Naïve condition, the experimenter said, ‘‘I just found this toy! See this
toy?’’ As she brought out the toy from underneath the table, she pulled the yellow tube out from the purple tube
as if she did so by accident. Then she said as if surprised,‘‘Huh! Did you see that? Let me try to do that!’’ and performed the same action to produce the squeak sound. In
the Baseline condition, the experimenter did not initiallydemonstrate the squeaking function of the toy. After she
brought out the toy from underneath the table, she pickedup the toy and said, ‘‘Wow, see this toy? Look at this!’’ She
looked at the toy for about 2 s (to match the other conditions for amount of familiarization time), and then put itback on the table.

Fig. 1. Novel toy stimuli used in Experiments 1 and 2.

E. Bonawitz et al. / Cognition 120 (2011) 322–330

In all conditions, the experimenter then said, ‘‘Wow,
isn’t that cool? I’m going to let you play and see if you
can ﬁgure out how this toy works. Let me know when
you’re done!’’ and left the child to play. If the child said
that she was ﬁnished or stopped interacting with the toy
for more than ﬁve consecutive seconds without indicatingcompletion, the experimenter prompted the child by saying, ‘‘Are you done?’’ She returned to the table and terminated the experiment if the child answered, ‘‘Yes’’.
Otherwise, she let the child continue to play and then returned to the table to terminate the experiment if the childstopped interacting with the toy a second time for morethan 5 s. All sessions were videotaped and coded by a research assistant blind to hypothesis and a second research
assistant blind to hypotheses and condition. Total playtime, the number of unique actions performed, time playing with the squeaker, and the number of target functions(light, music, and mirror) discovered during play werecoded. All but two children (excluded due to technical malfunction) were reliability coded on total playtime, uniqueactions, and number of target functions; 75% of clips werereliability coded for time with squeaker.
2.2. Results and discussion
Because we had a priori hypotheses about the patternsof results, we performed planned linear contrasts throughout. We formalized the prediction that the Pedagogical condition would differ from the Interrupted, Naïve and Baseline
conditions and that the Non-Pedagogical conditions would
not differ from each other by conducting the analyses withthe weights 3, 1, 1, and 1 for the four conditions,
respectively. The analyses will thus be signiﬁcant when
there is a difference between the Pedagogical and NonPedagogical conditions, and no difference among the
Non-Pedagogical conditions.
To look at whether children engaged in less explorationin the Pedagogical condition than in the other three conditions, we coded children’s total time playing, the numberof unique actions children performed, the proportion ofchildren’s play time spent only on the demonstrated function (excluding the Baseline condition where no demonstration was provided), and the total number of targetfunctions discovered in the course of free play. For thenumber of unique actions performed, we coded all the actions children performed during free play, which included
all four possible target actions in addition to any other kindof action the child performed; we enumerated the different
kinds of actions, rather than individual actions per se.
(Thus, seven pulls on the tube were counted as one action,
whereas one pull on the tube and one activation of thelight were counted as two actions.) Reliability on all measures was high. (Total time playing: r2 = .99; Actions taken
on toy: kappa = .77; Time playing with squeaking tube:
r2 = .96; Functions discovered: kappa = .86.)
All the linear contrasts were signiﬁcant. Children in thePedagogical condition played with the toy for signiﬁcantly
less time (M = 119.2 s) than children in the Interrupted(M = 179.6 s), Naïve (M = 132.7 s), or Baseline (M = 205.7)
conditions (F(1, 81) = 4.52, p < 0.05). Children in the Pedagogical condition also performed fewer different kinds of325

actions on the toy (M = 4.00) than children in the Interrupted (M = 5.30), Naïve (M = 5.90) or Baseline (M = 6.15)
conditions, F(1, 81) = 9.39, p < 0.01). This result held evenwhen the playtime was matched across conditions; looking only at the number of actions performed in the ﬁrst
60 s, children in the Pedagogical condition performed fewer
actions (M = 3.16) than children in the Interrupted(M = 3.75), Naïve (M = 4.90), and Baseline (M = 4.15) conditions, F(1, 81) = 7.18, p < 0.05.
What did children do when they played? Although children in the Pedagogical, Interrupted, and Naïve condition
had all seen the experimenter pull the tube to make thesqueak sound, they did not spend equal proportions of
their playtime acting on the squeaker tube across conditions. Children in the Pedagogical condition spent a greater
proportion of time playing with the squeaker (M = 0.68)
than children in the other conditions where the squeaker
was demonstrated: Interrupted (M = .53), Naive (M = .38)
conditions, F(1, 62) = 13.91, p < 0.001.3 Finally, we gavechildren one point for each of the target functions, otherthan the squeaker tube, that they discovered during their
free play. Thus, children could receive a score between 0
and 3. Children in the Pedagogical condition discovered fewer of these target functions (M = 0.72) than children in theInterrupted (M = 1.3), Naïve (M = 1.2), or Baseline (M = 1.15)
conditions, F(1, 81) = 4.58, p < 0.05.
These results suggest that teaching constrains children’s exploration and discovery. Children who were
taught a function of a toy performed fewer kinds of actionsof the toy and discovered fewer of its other functions, thanchildren who did not receive a pedagogical demonstration,even though all children were explicitly encouraged to explore the toy. We predicted such constrained exploration
as the result of a rational inductive inference: if a knowledgeable teacher provides evidence for a function of atoy, absence of evidence for alternative functions provides
strong evidence for their absence.

3. Experiment 2
Our ideal learner analysis suggests that the assumptions of pedagogical sampling apply when the learner believes that the teacher is choosing evidence in order toconvey a particular hypothesis. As discussed, this implies
that learners might treat some contexts as ‘‘non-pedagogical’’ even though an adult engages in direct, ostensive cuing to a child (as in the Naïve and Interrupted conditions ofExperiment 1). Critically, the converse is also true: children
might treat some contexts as ‘‘pedagogical’’ even in the absence of direct, ostensive cueing. According to the model,
the teacher should choose data that are tailored to the individual being taught. Thus, the pedagogical model can apply
both to situations when the teacher is directly teaching thelearner, and to situations when the learner overhears a teacher instructing someone else whose prior beliefs are similar
to the learner’s own. This predicts that learners may engage
in pedagogical inference even when merely observing,
3
Because the Baseline condition was not included in this analysis, thelinear contrast weight were adjusted to 2, 1, 1.

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E. Bonawitz et al. / Cognition 120 (2011) 322–330

rather than participating in, a pedagogical situation. We
call the requirement needed to engage pedagogicalassumptions for overheard teaching the ‘‘similar priors’’
assumption.
Formally, the teacher’s choice of data, PT(d|h), should
depend on the learner’s prior beliefs, PL(h), as describedby Eqs. (10 ) and (2). In the basic pedagogical situation, there
is a teacher and a learner (L1). Now consider a situation inwhich there is a second learner, L2, who has the same priorbeliefs as L1 and vicariously observes the interaction between the teacher and L1. In this case, the data generated
by the teacher are intended to teach L1; however, because
L2 has the same prior beliefs as L1, Eq. (10 ) and (2) are identical to what they would be if the teacher would had intended to teach L2. Consequently, if L2 is observing while
L1 is being taught, and L2 can assume that she and L1 have
similar beliefs, then L2 can treat a pedagogical demonstration to L1 as if it were a demonstration to L2 herself. In
contrast, if the priors for the learners are very different(PL1(h) – PL2(h)), then appropriate demonstrations could
be quite different for the different learners—a teacher
would potentially choose different data to teach the same
hypothesis to the different learners.4 Thus, if L2 is observing
L1 and assumes that L1 has beliefs different from her own,
then she should not assume that the pedagogical demonstration to L1 generalize to herself.
Most previous research (e.g. Gergely, Bekkering, andKiraly (2002), Topal, Gergely, Mikolsi, Erdohegyi, andCsibra (2008); see Csibra and Gergely (2009) for a review)has focused on one-on-one pedagogical situations in which
the teacher engages the learner using direct ostensive cuing (e.g., establishing eye-contact, shifting gaze between
the object and the learner, and using the child’s name)prior to the demonstration. Such work suggests that children are more likely both to learn demonstrated material
and to generalize it to novel contexts in teaching than in
non-teaching situations (e.g. Gergely et al. (2002), Topal
et al. (2008); see Csibra and Gergely (2009) for a review).
This is consistent with Csibra and Gergely’s (2009) proposal that ostensive cuing engages special learning mechanisms (see also Tomasello, Carpenter, Call, Behne, &Moll, 2005). Under these theories, ostensive cues are a critical component of pedagogy; we might therefore expectthat the effects of teaching would only be present whenostensive cues are directed towards the learner herself.
However, our analysis suggests a more nuanced relationship between indirect cues in pedagogy and the resulting inferences of the observing learner. In an indirectpedagogical demonstration, a knowledgeable teacher engages a child (L1) in ostensive cuing and then demonstrates a function of the novel toy with a second learner(L2) observing. The teacher’s choice of demonstrations
depends only on the learner’s (L1’s) beliefs. Thus, theoverheard demonstration supports the same inferences
as a direct pedagogical situation if the observer (L2)believes that the learner’s (L1’s) beliefs are like her own.
4This assumption also holds if L2 believes that L1’s interests weredifferent (e.g. the teacher may not demonstrate all the functions to L1
because she assumed that some of the functions would not be interesting to
L1, but those functions may be interesting to L2).

The observer should not draw inferences consistent withpedagogical sampling if the demonstration is to a learnerwith different beliefs than the observer’s own.
In Experiment 2, we look at whether children’s pedagogical inferences depend primarily on direct ostensive
cueing or whether pedagogical inferences are also engaged when an observing child shares knowledge stateswith the recipient of direct instruction. To investigate
children’s inferences in indirect pedagogical situations,
we contrast exploratory play in four conditions: after adirect pedagogical demonstration (the Direct condition),after an indirect demonstration to a child (the IndirectChild condition), after an indirect demonstration to an
adult (the Indirect Adult condition), and after a nonpedagogical intentional action that the child overhears(the Intentional condition). The Direct condition provides
a replication of the Pedagogical condition in Experiment
1: children should show limited exploration and be lesslikely to discover the other, non-demonstrated propertiesof the toy. The Intentional condition, provides a control forthe intentional manipulation of the toy, but does notprovide pedagogical information for the children (see also
Goodman, Baker, & Tenenbaum, 2009). In this condition,
the experimenter performs the same action as in thepedagogical condition, but makes it clear to the child that
her intention is to satisfy her own preferences not toengage in instruction. We expect that children will
explore readily in this condition, replicating the Baseline
and Accidental conditions of Experiment 1.
Our key questions center on the Indirect Child and Indirect Adult conditions. If pedagogical inferences depend on
direct ostensive cuing, then children in both of the Indirect
conditions should be less susceptible to the pedagogicalcontext, thus exploring the toy more and discovering moreof its properties, than children in the Direct condition. If direct ostensive cues are not necessary, and pedagogicalinferences extend to situations where the observing andobserved learner have similar beliefs, then we expect a different pattern of results. Namely, we predicted that children would treat another child as having beliefs similar
to their own but would not make this assumption about
adult learners. If this is the case, then children should extend the pedagogical inference in the Indirect Child condition but not in the Indirect Adult condition. As a result,
we predict more exploratory play and discovery learning
in Indirect Adult condition than in the Indirect Child
condition.
3.1. Methods
3.1.1. Participants
Sixty-four5 preschoolers (mean age: 61 months, range:
48–72 months; 56% girls) were recruited in a metropolitan
Science Museum. Most children were white and middleclass, but a range of ethnicities resembling the diversity ofthe population was represented.
5
Two children were dropped and replaced. One child was replaced
because of a technical error (camera malfunctioned; play was not coded;
Indirect Adult condition), and the second child fell off her chair during theexperiment and could not continue (Indirect Child condition).

E. Bonawitz et al. / Cognition 120 (2011) 322–330

3.1.2. Design
Preschoolers were randomly assigned to one of four
conditions: Direct, Indirect Child, Indirect Adult, or Intentional condition. There were no differences in the age ofthe children across conditions: F(2, 56) = 0.58, p = ns. An
additional sixteen children (unrelated to the participants
and approximately the same age) were recruited as the primary learners in the Indirect Child condition and sixteen
adults (parents of the children) participated as primarylearners in the Indirect Adult condition.
3.1.3. Materials
The same novel toy from Experiment 1 was used.
3.1.4. ProcedureChildren were tested in a quiet corner in the museum.
The experiment included two phases: observation andplay.
3.1.4.1. Observation phase. In the observation phase, children observed a demonstration of one property of thetoy, which varied by condition. As in Experiment 1, in the
Direct condition, the experimenter said, ‘‘Look at my toy!
This is my toy. I’m going to show you how my toy works.
Watch this!’’ The experimenter then pulled the yellow
tube out from the purple tube to produce the squeaksound. She said, ‘‘Wow, see that? This is how my toy
works!’’ and demonstrated the same action again. In the
Indirect Child, and Indirect Adult conditions, the experimenter ﬁrst said to the child participant ‘‘I have to go overhere for a second, but I’ll be right back.’’ The experimenter
then moved to a table approximately 2 m from the participant and performed the procedure above either to theother child recruited for this purpose (Indirect Child) or tothe observing child’s parent (Indirect Adult). In the Intentional condition, the demonstrator said to the child, ‘‘Lookat my toy. This is my toy. I have to go over here for a second, but I’ll be right back.’’ As with the Indirect conditions,the experimenter moved approximately 2 m from the childparticipant but then said (talking out loud, to herself) ‘‘I
like to make my toy squeak. Wow! I’m going to do thatagain’’ and performed the action twice without any ostensive cuing.
3.1.4.2. Play phase. After the child observed that pulling thetube made the squeaking sound, the experimenter (returning to the table in the Indirect6 and Intentional conditions)said, ‘‘I’m going to go ahead and let you play. Let me know
when you’re done!’’ and left the child to play. Play wasended following the same criteria as Experiment 1.
3.2. Results and discussion
The results were analyzed as in Experiment 1. We formalized the prediction that the Direct and Indirect Child
6
After the demonstration in the Indirect Child Conditions, a research
assistant helping the experimenter gave the child who was recruited as thetarget of instruction another activity to pursue, out of sight of the child who
was the experimental participant. Parents who participated in the Indirect
Adult Conditions stepped out of their child’s line of sight.

327

conditions would differ from the Indirect Adult and Intentional conditions using contrast weights of 1, 1, and 1,
1, respectively. The analyses will be signiﬁcant when
there is a difference between mean of the Direct and Indirect Child and the mean of the Indirect Adult and Intentional
conditions, and no differences between the Direct and Indirect Child conditions, and the Indirect Adult and Intentional
conditions.
As in Experiment 1, we coded children’s total time playing, the number of different kinds of actions the children
performed, their time spent on only the demonstratedfunction (the squeaking tube), and the number of targetfunctions discovered in the course of free play. All children
were reliability coded on action and play measures. Reliability coders were blind to condition and hypotheses.
Reliability on all measures was high. (Actions taken on
toy: kappa = 0.82; Total time playing: r = 0.99; Time playing with squeaking tube: r = 0.96.)
With the exception of overall play time, which did not
differ between conditions (Direct, M = 70 s; Indirect ChildM = 105 s, Indirect Adult M = 84 s, Intentional, M = 125 s;
F(1, 60) = .92, p = ns) all the linear contrasts were signiﬁcant. Children in the Direct (M = 3.13) and Indirect Child(M = 3.94) condition performed fewer different kinds of actions on the toy than children in the Indirect Adult(M = 5.31) and Intentional (M = 5.13) conditions, F(1, 60) =11.50, p < 0.01. The difference between the Direct(M = 2.88) and Indirect Child (M = 2.94) and Indirect Adult(M = 4.94) and Intentional (M = 4.38) conditions persists
considering only actions produced in the ﬁrst 60 s of play,F(1, 60) = 17.57, p < .0001.
What did children do when they played? Although children had all seen the experimenter pull the tube to makethe squeak sound, children in the Direct (M = 52%) and Indirect Child (M = 60%) conditions spent a larger percentage of
their playtime acting on the squeaking tube than children
in the Indirect Adult (M = 37%) and Intentional (M = 36%)
conditions, F(1, 60) = 10.08, p < .01. Looking at individual
children, we gave children one point for each of the nondemonstrated functions that they discovered, thus children could receive a score between 0 and 3. Children’smean score was lower in the Direct (M = .50) and IndirectChild (M = .75) conditions than the Indirect Adult(M = 1.31)
andIntentional(M = 1.00)
conditions,
F(1, 60) = 6.38, p < .05, even when controlling for durationof play by considering only the ﬁrst 60 s (Direct, M = .44;
Indirect Child, M = .44; Indirect Adult, M = 1.19; Intentional,
M = .81; F(1, 60) = 9.88, p < 0.01).
These results replicate and extend the ﬁndings of Experiment 1, showing that preschoolers’ tendency to exploreand discover new properties are limited in pedagogical settings relative to other intentional conditions. Moreover,they show that preschool children rationally extend theirassumptions about pedagogical situations to contexts inwhich they overhear instruction to comparable learners;
they are not dependent on direct ostensive cues. Note that
it is possible that children were less likely to constrain
their exploration in the Indirect Adult than the Indirect Child
condition simply because they paid less attention to theformer than then latter. Certainly children might havefound an unfamiliar child more interesting than the328

E. Bonawitz et al. / Cognition 120 (2011) 322–330

familiar parent. We cannot rule this explanation out
entirely. However, one reason to believe it is not the case,is that the conditions differed only with respect tochildren’s tendency to infer the absence of uninstructed
functions; children were equally likely to learn the demonstrated function in the two conditions. Of course, we do notknow exactly in what respects children believed that theirown knowledge was comparable to another child’s but not
to an adult’s; they might for instance have assumed that
relative to other children, adults are either more or lessknowledgeable about toys. Future research might investigate in more detail what aspects of knowledge go into
how children infer ‘‘similar priors’’ between themselves
and another learner. However, the current results suggestthat even very young children consider the prior knowledge of other learners in identifying contexts that license
the inferences of pedagogical sampling.

4. General discussion
Inspired by the ideas of Piaget and Vygotsky, we set out
to investigate the implications of explicit instruction on
exploratory play. We presented a formal model that captures our intuitions about how sampling assumptions (inpedagogical and non-pedagogical contexts) could inﬂuencea learner’s hypothesis space about possible causal modelsof the world. Our empirical results are consistent with
the qualitative predictions of our model. The results suggest that teaching constrains children’s exploration anddiscovery. Children who were taught a function of a toy
performed fewer kinds of actions on the toy and discovered fewer of its other functions, than children who did
not receive a pedagogical demonstration. We predicted
such constrained exploration as the result of a rational
inductive inference: if a knowledgeable teacher provides
evidence for a function of a toy, absence of evidence foralternative functions provides strong evidence for theirabsence.
The children’s behavior is rational but is it desirable? Ifshowing four and ﬁve-year-olds a function of a toy meansthat they explore less and consequently learn less about it,
do the costs of direct instruction outweigh the beneﬁts?
We believe that there is no fully general answer to thisquestion. The costs and beneﬁts of instruction depend on
how knowledgeable and helpful the teacher is, and on
how likely the learner is to discover either the target information or novel information on her own. The inductive
bias by which teaching constrains the learner’s hypothesis
space cuts both ways.
These trade-offs can be seen in our example. In order toinvestigate the effect of instruction on exploration, wedeliberately designed a toy with more affordances than
we demonstrated. A knowledgeable teacher, with sufﬁcient time and motivation and without other constraints,
would have shown the children all the target functions.
In this case, not only would the children have learned all
four functions, there would also arguably have been little
else for them to discover. Given such a teacher, increasing
the probability that children will learn the target information may be well worth decreasing the (already low)

probability that they will discover novel information. By
contrast, a teacher who knows only one of our toy’s functions or who is constrained in her actions might be able
to demonstrate only a single function (as the experimenter,
deceptively, did here). Such instruction effectively focusedchildren on the target function, but impaired their ability
to discover novel information. Thus, if a teacher is relatively uninformed and/or a domain is largely unexplored,
there may be advantages to seeing what the learner does
spontaneously. Even as simple a recourse as delaying
instruction until the learner has had a chance to investigate on her own could promote innovation and discovery.
Critically however, even a knowledgeable teacher (e.g., one
who knows all four functions of our toy), cannot knowwhat currently unknown information might be discoveredby the variable actions children perform in the absence of
instruction. Because the total amount of information thatmight be learned is neither ﬁxed nor known, the inductive
trade-off introduced by pedagogy is a general one.
Our results also suggest that direct, ostensive cues areneither sufﬁcient nor necessary for children to treat a demonstration as pedagogical. In cases where children were given direct, ostensive cues but there was reason to believethat the adult was not sampling evidence in proportion
to the probability that it would generate the target hypothesis in the learner (e.g., because the teacher was interrupted or naïve), children did not draw the strong
inferences licensed by pedagogical sampling (Experiment1). Conversely, in cases where children lacked direct,
ostensive cueing but a helpful teacher was instructing alearner with knowledge comparable to the child’s own,children did assume pedagogical sampling (Experiment2). Importantly, however, ostensive cues (even when directed to other learners) were not in themselves sufﬁcient forchildren to engage pedagogical sampling assumptions.
Consistent with our analysis, children suspended theseassumptions when the target of the ostensive cueing wasan adult learner whose beliefs were likely to differ fromtheir own.
Our results support the predictions of our Bayesianmodel of pedagogy; however, they are not inconsistent
with the proposals of Csibra, Gergely, and colleagues. We
agree with other researchers (Csibra & Gergely, 2009;
Tomasello et al., 2005) that direct ostensive cues are probabilistically associated with pedagogical contexts, and arevery likely, not only to guide children’s attention to therelevant demonstrations, but also to suggest that thedemonstration is for the purpose of instruction. Indeed,children’s ability to treat the Indirect Child condition as apedagogical condition may have been supported by theostensive cues directed towards the other child. Additionally, note that in our studies, children were presented witha combination of verbal and non-verbal ostensive cues,
whereas other studies (e.g. Gergely et al., 2002; Topal
et al., 2008) have paired neutral language with non-verbal
ostensive cues. Our manipulation was chosen to be an
ecologically valid representation of the kinds of input thatpreschool children receive, however, further researchmight establish whether children would constrain their
exploration if only non-verbal ostensive cues are used toindicate the pedagogical context. Finally, note that Csibra

E. Bonawitz et al. / Cognition 120 (2011) 322–330

and Gergeley’s claims focus on learning mechanisms
present during infancy, and it is entirely possible that by
the time children reach preschool, they have learned thatpedagogical contexts apply beyond situations withostensive cueing.
Our ﬁnding that children distinguish instruction toadults and other children adds to a host of studies suggesting that children are sensitive to the difference between
the mental states of children and adults. Preschool children
understand that adults know different things than they do(Lutz & Keil, 2002), and indeed, children sometimes erroneously attribute omniscience to adults (e.g., Mossler,
Marvin, & Greenberg, 1976; Wimmer, Hogrefe, & Perner,1988). Such results are consistent with our claim thatpreschoolers assume that other children are learners
similar to themselves but do not make this assumption
about adult learners. Our studies are also consistent witha host of studies suggesting that children can learn vicariously, from overheard communication or demonstrations(Correa-Chavez & Rogoff, 2009; Jaswal & Markman, 2003;
see also Akhtar, Jipson, & Callanan, 2001; Jaswal &Markman, 2001; Tomasello & Barton, 1994). However,extending beyond previous work, we show that children
not only learn overheard material, but also draw rational(if fallible) inferences about the absence of informationthat is not instructed.
Although the negative effects of instruction on exploration may seem disheartening, the results suggest a striking
competence in young children: they are able to negotiate
the trade-off between exploration and instruction suchthat they explore more when they can rationally infer that
there is more information to be learned. Moreover, children demonstrate this competence remarkably early. By
preschool, children seem actively to evaluate their teachers
both for the knowledge they have and their ability to demonstrate it. Thus, well before children are immersed in formal education, they are sensitive to some conditions that
promote effective instruction. Furthermore, the ability tolearn selectively from overheard demonstrations is presumably valuable in a world where children are surrounded by siblings and peers who are also subject toadult instruction; by interpreting pedagogical demonstrations to other children as they interpret pedagogical demonstrations to themselves, preschoolers can beneﬁt not
only from information they are taught directly but also
from information provided to others.
Finally, although the current ﬁndings involve young
children in a limited instructional context, the results suggest the possibility of a new perspective on longstanding
debates in the ﬁeld of education. In classroom contexts,
advocates of discovery learning have suggested that direct
instruction is passive and discourages engagement (Dean &Kuhn, 2006; Papert, 1980), whereas advocates of direct
instruction have countered that self-guided exploration is
inefﬁcient and often ineffective (Kirschner, Sweller, &Clark, 2006; Klahr & Nigam, 2004; Mayer, 2004;
Rittle-Johnson, 2006; Vygotsky, 1978). The current results
suggest that instruction leads to inductive biases thatcreate a genuine ‘‘double-edged’’ sword: teaching simultaneously confers advantages for learning instructed
information and disadvantages for learning untaught

329

information. Thus, the decision about how to balance
direct instruction and discovery learning depends largelyon the lesson to be learned. Inspired by Piaget, the challenge for educators may be how to foster learners ‘‘capableof doing new things’’ while simultaneously teaching ‘‘what
other generations have done’’.
Acknowledgments
Thanks to Sydney Katz, Kiersten Pollard, Isabel Chang,
Zhara Ghabyali, Hannah Pelton, Claire Cook, Ali Horowitz,
Juan Francisco Estevez, Emily Mistretta, Stephanie Tong,
Kathie Pham, the Museum of Science, Boston, and participating families. Research supported from the Elizabeth
Munsterberg Koppitz Fellowship from the American Psychological Foundation (EB), the National Science Foundation (LS), the John Templeton Foundation (LS), and theJames S. McDonnell Foundation (LS, EB).
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