Psy 5130 Week 3 Journal & Assignment
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Goddu.pdf
Learning What to Change: Young Children Use “Difference-Making” to Identify Causally Relevant Variables
Mariel K. Goddu and Alison Gopnik University of California, Berkeley
Novel causal systems pose a problem of variable choice: How can a reasoner decide which variable is causally relevant? Which variable in the system should a learner manipulate to try to produce a desired, yet unfamiliar, casual outcome? In much causal reasoning research, participants learn how a particular set of preselected variables produce a particular effect. Here, we investigate 3- to 5-year-olds’ ability to select the relevant variable for intervention in a novel causal system. Results demonstrate that even young children can learn which variable is causally relevant from sparse evidence. In particular, children infer that variables that are “difference-making” in one causal system will also be relevant to other, novel, causal problems. If manipulating a causal variable in a particular way leads to one effect, children assume that other manipulations of that variable will lead to other novel effects.
Keywords: cognitive development, causal reasoning, variable choice
Supplemental materials: http://dx.doi.org/10.1037/dev0000872.supp
Humans frequently navigate scenarios in which they must gen- erate a novel outcome from novel causal variables. Making suc- cessful generalizations about which variables are relevant may be just as important as knowing how those variables lead to particular effects. For example, I may discover that swiping my cell phone left to right with two fingers makes the home screen appear and disappear. When I want to bring about another effect, like opening an app, I might try some other form of swiping, perhaps with one finger or in the other direction, rather than, say, poking the screen or speaking to it. Similarly, when I go to a new hotel and the water is too hot, I will know to manipulate the lever in the shower, rather than twisting the showerhead, even if I do not know which way to move it.
In philosophy of science, the problem of specifying variables for intervention in a novel causal system is known as the “problem of variable choice.” When we already know about the variables that comprise a causal system, then this is not a “problem”: It is relatively straightforward to test (intervene on) prespecified vari- ables or to incorporate them into models for analysis. When we are faced with a novel system, however, we are in a different position: we must actually identify which variables are relevant (Woodward, 2016).
The problem of variable choice is ubiquitous in both the natural and social sciences. Ecologists, economists, meteorologists, and other experts studying complex systems are frequently tasked with constructing and identifying new causal factors that might aid in prediction and explanation, and then testing the effects of inter- ventions on those variables. One idea in the philosophical literature is that causal variables that are “difference-makers” or “control variables” are likely to be causally relevant in general (Campbell, 2007; Woodward, 2003). If manipulating a variable leads to changes in another variable then it is likely to be causally relevant to still other variables and to produce a wider range of effects.
But the problem of variable choice is also a more basic, univer- sal cognitive one: It is a problem we must solve all the time. Each instance in which we must determine how to operate within a novel causal schema to achieve a novel outcome—whether using an unfamiliar ATM machine in a foreign country, navigating the novel set of requirements that will result in registration at a conference we have never attended, or determining which type of stretches we might perform to relieve muscle tension from an unfamiliar activity (e.g., rock climbing)— demands bringing rele- vant prior knowledge to bear on the problem of figuring out how best to intervene on relevant causal variables to accomplish out- comes we have never concretely accomplished before. Our past experiences with causal systems therefore seem to shape not only our hypotheses about variables we have already encountered and
This article was published Online First December 23, 2019. X Mariel K. Goddu and Alison Gopnik, Department of Psychology,
University of California, Berkeley. We gratefully acknowledge the Bezos Family Foundation for funding
this research. Thank you also to Sarah de la Vega, Teresa Garcia, Natalie Mazza, Jack Nelson, Taylor Osman, Yvette Sanchez, Michelle Wong, Jocelyn Woo, and other members of the Gopnik Cognitive Development Lab for providing research support and feedback throughout the research process. Thank you to Lisa Barnum and Luvy Vanegas Grimaud for coordinating data collection at University of California, Berkeley’s Early Childhood Education Program preschools, and to the Bay Area Discovery Museum, Children’s Creativity Museum of San Francisco, and the Law- rence Hall of Science for allowing data collection at their fine facilities. Thank you to Joe Winer, whose real-life childhood pet turtle Shelly provided the inspiration for the protagonists of Experiments 1 and 2. Finally, thank you to the parents who provided permission and to the children who participated. May you continue to be the changers and the difference-makers!
Correspondence concerning this article should be addressed to Mariel K. Goddu, Department of Psychology, University of California, Berkeley, 2121 Berkeley Way West, Berkeley, CA 94720. E-mail: [email protected]
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Developmental Psychology © 2019 American Psychological Association 2020, Vol. 56, No. 2, 275–284 ISSN: 0012-1649 http://dx.doi.org/10.1037/dev0000872
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outcomes we have already produced but also novel hypotheses about novel outcomes. How does this cognitive ability develop?
Investigating the developmental trajectory of the ability to choose relevant causal variables for intervention in novel systems is interesting because it may help shed light on how human children are able to learn so much, so quickly. If anything, young children’s experiences are even more saturated with problems of variable choice than adults’ experiences. With less prior knowl- edge to draw upon, novel instances of water fountains (“What should I press?”), automatic doors (“Where should I stand?”), shoe and clothing fasteners (“What should I put together?”), candy wrappers (“What should I pull on?”), and many more everyday novelties present constant problems for causal intervention. For this reason, understanding how the problem of variable choice is “solved” in cognition is especially germane to developmental psychology.
A large literature on the development of causal reasoning has demonstrated that young children can learn which prespecified variables produce a particular effect (e.g., that particular blocks will make a toy machine activate and play music; see Gopnik, 2012, and Gopnik & Wellman, 2012, for reviews). A variety of additional studies suggest that children can capably observe oth- ers’ actions to achieve a causal outcome, such as turning on a light or determining which sequence of actions are relevant for activat- ing a toy (Buchsbaum, Gopnik, Griffiths, & Shafto, 2011; Gergely, Bekkering, & Király, 2002). However, there are as yet no inves- tigations into the development of children’s ability to learn which variables are relevant for intervention when they are faced with situations in which both the values of the causal variables as well as the values of the desired effect variable are novel. If young children are able to identify relevant, novel values of causal variables to produce novel effects after observing only a small amount of evidence, this would suggest that the ability to acquire abstract causal knowledge is even more powerful and general than previously imagined.
Below, we first review the literature on causal learning in young children. Next, we outline three experiments to test whether chil- dren are able to use evidence about “difference-making” to iden- tify relevant potential causal variables that might lead to novel effects.
Development of Causal Learning
It is well-established that children as young as 16 to 24 months can observe patterns of statistical contingency between causes and effects, learn causal properties of objects, and intervene on causal systems to generate desired effects In these studies, children typ- ically observe evidence that certain causal variables (e.g., blocks placed on a machine, buttons pressed on a toy, or triggers pushed on a remote control) result in the presence or absence of a salient target effect (e.g., a machine playing or not playing music). These studies find that following even just a handful of training trials, children are able to learn which properties of causes will be relevant for reproducing the effect. They may, for example, infer causal rules such as “red blocks make the machine play music” or “square blocks make the machine play music”; furthermore, they may learn to attribute the relative likelihoods of the failure or success of a causal process to different sources, such as a toy’s propensity to malfunction or to deficits in their own competence
(e.g., Cook, Goodman, & Schulz, 2011; Gopnik & Meltzoff, 1997; Gopnik & Sobel, 2000; Gopnik, Sobel, Schulz, & Glymour, 2001; Gweon & Schulz, 2011; Meltzoff, Waismeyer, & Gopnik, 2012; Schulz, Gopnik, & Glymour, 2007; Schulz, Kushnir, & Gopnik, 2007; Sim & Xu, 2017; Sobel & Kirkham, 2006, 2007; Sobel & Sommerville, 2010; for reviews, see Gopnik, 2012; Gopnik & Wellman, 2012). Other research suggests that preschool-aged chil- dren flexibly track and update candidate causal rules when it is relevant to do so, rationally revising their beliefs in sophisticated, context-sensitive ways: For example, they will change their minds about whether a “shape matters” or a “color matters” rule is relevant, depending on both the amount of evidence they have observed in support of a given hypothesis and the order in which they have observed it (Kimura & Gopnik, 2019).
Still other studies have found that even very young (preschool- aged) children are able to form higher-order abstract “overhypoth- eses” about causal variables, including the “forms” of causal variables that will be relevant for producing a particular outcome. This research has been inspired in part by theoretical frameworks in hierarchical Bayesian models, which theorize that learners infer higher-order hypotheses about the type of the most likely causal relations for a given problem. These overhypotheses then serve to both guide and constrain the acquisition of specific, lower-level hypotheses (Goodman, Ullman, & Tenenbaum, 2011; Tenenbaum, Kemp, Griffiths, & Goodman, 2011). For example, 4- to 6-year- old children are able to learn from evidence to infer that conjunc- tive, rather than disjunctive, causation is required to produce an effect, and they can also form abstract generalizations about whether an observed effect can be attributed to properties of an actor or the environment (Lucas, Bridgers, Griffiths, & Gopnik, 2014; Seiver, Gopnik, & Goodman, 2013). Further research has demonstrated that children are able to learn and generalize over- hypotheses concerning abstract relations, such as “a block that is the same shape as the machine will play music” or “two blocks that are the same make the machine play music”—a cognitive skill that cannot be explained by appeal to lower-level perceptual processes (Walker, Bridgers, & Gopnik, 2016; Walker & Gopnik, 2014, 2017).
Still other recent research suggests that young children are also able to learn the abstract forms of effects. Three- and 4-year-olds who observe a sequence of two causal events are able to learn the abstract relation between the beginning and ending states of caus- ally transformed objects to make predictions about the effect that will result from the transformation of a novel object. For example, if preschoolers see an agent transform a small apple into a large apple, and then see the same agent transform a small dog into a large dog, they predict that the agent is more likely to similarly “grow” an unfamiliar novel object (e.g., a die) into a larger form of that object than they are to “stretch” a familiar object (e.g., another apple) in a way that does not reflect the abstract form of the effect they have previously observed (Goddu, Lombrozo, & Gopnik, 2017a, 2017b). In addition, there is one study that sug- gests that children may be able to make inferences about the abstract forms of both causes and effects, simultaneously. In this study, 4- to 6-year-olds attributed a continuously modulating light and tone (the effect) with a continuous cause (turning a dial); similarly, they matched a discretely flashing light and tone to a discrete cause, pressing a button (Magid, Sheskin, & Schulz, 2015).
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There is also a large body of research documenting the emer- gence and gradual changes in children’s “naïve theories” in biol- ogy, psychology, and physics (see Carey, 1985, 2009; Gelman, 2003, or Keil, 1992, for reviews). This research suggests that existing abstract causal knowledge can influence which variables children think will be relevant. For example, children seem to learn that eating something disagreeable—a biological cause—is more likely to cause a stomachache (biological effect), than feeling anxious, a psychological cause (Schulz, Bonawitz, & Griffiths, 2007). They also infer that a human agent is more likely to arrange a group of blocks in an ordered line than is the wind, a nonagent (Newman, Keil, Kuhlmeier, & Wynn, 2010). These overhypoth- eses about the abstract forms of cause and effect then presumably help guide prediction and learning for other similar phenomena governed by similar causal rules. However, there is as yet no empirical research that investigates whether and how children can identify novel relevant causal variables from novel evidence in the first place, and in particular whether they can use “difference- making” as a cue to relevance.
The Current Study
In three experiments, we demonstrate that preschool-aged chil- dren are able to solve variable choice problems. Experiment 1 demonstrates children’s ability to learn from difference-making evidence about the kinds of causes that will result in an effect with two possible (binary) outcomes. Experiment 2 uses the same paradigm with a slightly modified procedure to demonstrate that children will pick out the novel value of a relevant variable even when the variable leads to a new kind of effect, which they have never seen or produced before. Experiment 3 replicates the results of Experiment 2 using new stimuli with still younger children and extends the findings by demonstrating that when children actually must choose a new value of a causal variable to manipulate from several options, they are far more likely to choose the novel value of the variable to produce a novel value of an effect than the familiar value that was previously associated with success.
Experiment 1
In Experiment 1, we presented 3- and 4-year-old children with a novel task in which they observed evidence about causal vari- ables that either made a difference or did not make a difference to a binary outcome (desirable or undesirable). At test, children were faced with the undesirable outcome. They then made a choice about which causal variable they should change to change the outcome.
Method
The methods for all experiments were approved by the Institutional Review Board of the University of California, Berkeley under the protocol titled Causal Learning in Children, #2010 – 01-631.
Participants. Participants were 48 preschoolers: 24 three- year-olds (Mage � 42.4 months, SD � 3.32, range � 36 – 47 months, 11 girls) and 24 four-year-olds (Mage � 54.5 months, SD � 3.13, range � 49 –59 months, 17 girls). The sample size in this experiment, as well as in Experiments 2 and 3, was determined based on previous causal reasoning studies (e.g., Sim & Xu, 2017;
Walker & Gopnik, 2014) that had sample sizes of 24 – 48 children. In addition, the results of a power analysis to detect an effect size of moderate practical significance (d � 0.6) at a power of 0.8 suggested that a sample of 45 participants would be sufficient. Age was treated categorically in Experiment 1 (as well as in Experi- ments 2 and 3) in light of recent work suggesting that children’s performance on causally framed relational transfer tasks may un- dergo shifts during the preschool years (Goddu et al., 2017a, 2017b; Walker et al., 2016). The extent to which the present tasks might be characterized as relational reasoning tasks is explored in the General Discussion.
Two additional children were tested but excluded due to exper- imenter error. Children were recruited from university preschools and local museums in a large metropolitan area, and a range of ethnicities resembling the diversity of the local population was represented.
Materials and procedure. Participants saw a brief Power- Point animated presentation about a turtle character who likes to eat smooth— but not spiky— cactuses. The experimenter said,
In this game, we are going to figure out how to grow some cactuses that Shelly the turtle can eat! Look, Shelly really likes it when the cactuses are nice and smooth, with no spikes on them [the experi- menter played an animation of Shelly taking a bite out of a cactus with no spikes]. But, he really doesn’t like it when the cactuses have spikes on them that hurt his mouth [the experimenter played an image of Shelly looking sad next to a cactus with spikes]. In this game, we are going to try to figure out how to grow the smooth kind of cactus, so Shelly can eat them!
Next, participants were shown an array of six watering cans of different colors and six planting pots of different patterns. These were the two types of causal variables. The experimenter made sure that the participants attended to each array of causal variables:
So in this game, we have a whole bunch of cactus seeds, which we can plant in a pot and water with a watering can. And look: we have a whole bunch of different pots, and a whole bunch of different water- ing cans. Let’s see what happens when we try some out! (See Figure 1 for schematics of the stimulus items; see the online supplementary material for the full PowerPoint stimuli.)
Participants then saw a sequence of three causal events, either suggesting that the kind of watering can made a difference to the outcome, or that the kind of pot made a difference to the outcome (counterbalanced, N � 24 children in each of the two conditions). For example, a participant in the “watering can” condition saw a first event involving a polka-dotted pot and a yellow watering can; this resulted in a smooth cactus. In a script accompanying those animations, the experimenter said, “Look! Let’s find out what happens when we use this pot and this watering can!” A cactus seed appeared on the screen and dropped down into the polka- dotted pot. It was then “watered” by the yellow watering can, which appeared afterward. Then, a smooth cactus appeared to “grow” from the pot, and Shelly appeared next to it and took a bite. The experimenter said, “Cool! We made a smooth cactus! So that’s what happened when we used this pot and this watering can [pointing at the images of the pot and the watering can on the screen in sequence].”
The second sequence followed the same script, but this time showed the result of a striped pot and the same yellow watering
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277PRESCHOOLERS IDENTIFY CAUSALLY RELEVANT VARIABLES
Figure 1. Schematic of the causal narrative procedure in Experiment 1. See the online supplementary material for the full PowerPoint stimuli. See the online article for the color version of this figure.
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278 GODDU AND GOPNIK
can, which again resulted in a smooth cactus. Thus, changing the kind of pot did not produce a difference to the effect. The exper- imenter again said, “Great! We made a smooth cactus! So that’s what happened when we used this pot and this watering can [pointing at the images of the pot and the watering can on the screen in sequence].” On the third sequence, however, the striped pot appeared again, but a new, blue watering can appeared on the screen to water the cactus seed. This time, a spiky cactus resulted. The experimenter said, “Oh no! We made spikes! Shelly is sad.”
Then the experimenter said, “I know. Let’s try a brand new pot and a brand new watering can!” A new pot with a plaid pattern appeared on the screen, and a new purple watering can appeared on the screen to water the cactus seed that was “planted” inside; these were the novel casual variables. Once again, a spiky cactus grew. The experimenter said, “Oh no! We made another spiky cactus!” Then the experimenter asked, “Which thing do you think we should change to make a smooth cactus? Should we change the pot or the watering can [pointing to the pot and the watering can, respectively]? Can you point to the thing we should change?” Participants were given an opportunity to respond verbally or point to the item on the screen that corresponded to their choice. Most participants responded immediately, but for the few who did not the experimenter simply asked again, “Which thing should we change to try to make a smooth cactus for Shelly? Should we change the pot or the watering can?”
Results
The results of Experiment 1 reproduced the results of previous causal reasoning studies, demonstrating that children learned from evidence to infer which variable would be causally relevant for bringing about a binary effect. An analysis of variance (ANOVA) showed that performance did not differ between 3- and 4-year- olds, F(1, 45) � 2.95, p � .09, and participants performed equally well in both the “pot matters” and “watering can matters” condi- tions, F(1, 45) � 0.12, p � .73. Thirty-seven out of 48 participants (77.1%) chose to intervene on the relevant variable at test, which was significantly different from chance, t(47) � 4.42, p � .001. Cohen’s effect size value (d � 0.64) suggested a moderate to high practical significance.
Experiment 2
The results of Experiment 1 suggested that children could suc- ceed in learning which kind of causal variable was “difference- making” to a binary outcome. However, we might interpret these results as simply an extension of earlier research showing that children can learn over-hypotheses about abstract causal features. For example, previous experiments have demonstrated that chil- dren can learn which color or shape of blocks placed on a machine (e.g., a “blicket detector”) will cause it to activate and play music. In these studies, children appear to learn not only low-level hy- potheses about particular blocks (e.g., “this red block makes the machine play music”) or particular features (e.g., “red blocks make the machine play”), but also more abstract overhypotheses that guide their exploration and interventions—for example, “color matters,” “shape matters,” or “sameness matters” (see Kimura & Gopnik, 2019; Lucas et al., 2014; Magid et al., 2015; Sim & Xu, 2017). In the same way, we might interpret these results by saying
that children have learned that watering can colors, in general, rather than pot patterns, in general, make a difference to a pre- specified, binary outcome—that is, whether a cactus is smooth or spiky.
In Experiment 2, we used the same paradigm with minor alter- ations to test whether children would be able to infer that a new value of a causal variable would also be relevant to the production of a new effect. At test, children must decide which of two novel values of familiar causal variables to intervene on to produce a novel effect that they have never before seen.
Method
Participants. Participants were 48 children: 22 four-year-olds (Mage � 53.86, SD � 3.36, range � 48 –59 months, 12 girls) and 26 five-year-olds (Mage � 64.4, SD � 3.15, range � 60 –70 months, 12 girls). Four additional children were tested but ex- cluded due to (a) experimenter error, (b) inattention, and (c) refusal to answer. The recruitment procedures and demographics were the same as those of participants in Experiment 1. These participants were slightly older than those recruited for Experiment 1, which used 3- and 4-year-olds, because the results of piloting showed that 3-year-olds appeared to have difficulty with this version of the task. The implications of this are discussed below in Results, including the motivation for a third experiment with simpler, physical stimuli.
Materials and procedure. The materials and procedures used in Experiment 2 were very similar to those used in Experiment 1, with several key differences. First, during the introduction, chil- dren learned that Shelly prefers to eat cactuses that have specific shapes of fruit at different times, rather than simply smooth over spiky cactuses. The experimenter said, “This is my friend, Shelly the turtle. In this game, we are going to try to feed Shelly the kind of fruits that he likes to eat. Shelly really likes to eat square fruits for dinner, and star fruits for dessert.” Animations showed Shelly approaching and taking a bite out of a square fruited cactus and a star fruited cactus, in sequence. The experimenter pointed out other cactuses with different shapes (triangles, crescents, etc.) and said,
Shelly does not like any of these cactuses. He only likes squares for dinner and stars for dessert. In this game, we are going to figure out how to grow the kind of cactuses that Shelly likes to eat! We have some cactus seeds, pots, and watering cans. Let’s try some out!
Just as in Experiment 1, participants saw an array of six water- ing cans of different colors and six pots of different patterns. The patterns on the pots in this Experiment differed slightly from the pots in Experiment 1 in that the patterns were all continuous (e.g., plaid, stripes, zigzag) to ensure that participants would not make perceptual matches between shapes on the pots with the shapes on the cactuses (e.g., polka dots with circles).
Just as in Experiment 1, participants saw a sequence of three causal events, either suggesting that the kind of watering can made a difference to the outcome, or that the kind of pot made a difference to the outcome (counterbalanced, N � 24 children in each of the two conditions). Instead of two positive outcomes followed by a negative outcome, however, participants in this study saw two negative outcomes followed by a positive outcome: The first two causal events yielded circle cactus fruits instead of
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279PRESCHOOLERS IDENTIFY CAUSALLY RELEVANT VARIABLES
the desired square fruits, and changing the relevant, “difference- making” variable (either watering can or pot, depending on con- dition) on the third observation yielded the desired square fruits (see Figure 2 for schematics of the stimulus items; see the online supplementary material for the actual PowerPoint stimuli). On this trial, the experimenter said, “Great! Look, we made squares! Shelly can eat his dinner!” and participants saw an animation of Shelly eating the square fruits.
For the subsequent test trial, the Experimenter said, “Ok! So we made squares for dinner. Now, let’s try to make stars for dessert! Let’s try a brand new pot and a brand new watering can.” Thus, novel values of the causal variables were candidates for producing a novel value (stars) of the causal effect variable (i.e., shape of cactus fruit). Participants then observed an animated sequence that produced yet another undesirable outcome, triangle shaped fruits.
Then, the experimenter said, “Oh no! We made triangles. Which do you think we should change in order to get stars? Should we change the pot or the watering can?” As in Experiment 1, partic- ipants were given an opportunity to respond verbally or point to the item on the screen that corresponded to their choice.
Notably, there was no normatively “correct” answer to the problem. On the one hand, children have observed evidence that one or the other of the causal variables was relevant for producing squares; thus, they might infer that the watering can or the pot are generally causally relevant for “making a difference” to effects in this system (i.e., producing various shapes of fruit). On the other hand, the test values of each causal variable were entirely unfa- miliar to the children, as is the value of the effect variable (star- shaped fruits) they are motivated to generate by making an inter- vention. Given this lack of familiarity, and given that the value of
Figure 2. Stimuli for Experiment 2. See the online supplementary material for the PowerPoint stimuli. See the online article for the color version of this figure.
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280 GODDU AND GOPNIK
the variable that had previously effected a change is now absent, children might also simply respond at chance. The former pattern of responding would serve as evidence that children were in effect “solving” the problem of variable choice; that is, they were bring- ing their prior knowledge about causally relevant variables to bear on a problem that involved entirely novel values of causal vari- ables as well as a novel effect.
Results
The results of Experiment 2 suggested that children inferred that the novel value of the previously relevant causal variable would be relevant for the production of a novel effect. An ANOVA showed that performance did not differ between 4- and 5-year-olds, F(1, 45) � 0.48, p � .49, and there was no difference between partic- ipants’ judgments in the “pot matters” versus “watering can mat- ters” conditions, F(1, 45) � 0.48, p � .49. Thirty-eight out of 48 participants (79.2%) chose to intervene on the previously relevant variable at test, which was significantly different from chance, t(47) � 4.92, p � .001. Cohen’s effect size value (d � 0.71) suggested a moderate to high practical significance.
The participants’ performance is noteworthy in this experiment because they had received no evidence about either of the two novel values of the causal variables, and they had also not ob- served any evidence related to the production of the desired novel outcome. Thus, participants were faced with a genuine problem of variable choice: They needed to choose which novel value of a variable to produce to bring about an effect that they had never seen. That the majority of participants chose to intervene on the novel previously relevant variable suggests that their learning from the training trials was sensitive to the overall, abstract structure of the causal system—that is, they inferred that a change in the values of the one of the kinds of causal variables would lead to a change in the value of the effect variable.
In Experiment 3, we seek to replicate this effect using a new, physical set of stimuli with younger children.
Experiment 3
The results of Experiment 2 demonstrated that 4- and 5-year-old children learned which causal variable made a difference and generalized that discovery to produce a novel value of an effect in a scenario in which they were also faced with novel values of both causal variables. The additional effects in Experiment 2 as com- pared with Experiment 1 meant that the PowerPoint narrative was longer and more complicated, and this may have made the task too difficult for the 3-year-olds. In Experiment 3, we use novel phys- ical stimuli to replicate the results of Experiment 2. By removing the narrative framing and using real physical objects instead of animations, we aimed to extend the findings in Experiment 2 to younger children. We also added a test question that required children to select the value of a causal variable that they thought would be likely to produce a novel effect from an array of possible options. This question is important for ruling out several alterna- tive interpretations of the children’s success in Experiment 2 (e.g., that children were perseverating on the causal variable that had previously proven successful or that the children were avoiding the causal variable that had previously been causally inert).
Method
Participants. Participants were 40 children: 20 three-year- olds (Mage � 42.2, SD � 3.12, range � 37– 47 months, 11 boys) and 20 four-year-olds (Mage � 54.05, SD � 3.91, range � 48 –59 months, 14 boys). Six additional children were tested but excluded due to experimenter error (n � 3), interference by a parent or sibling (n � 2), and inability to complete task as instructed (n � 1). The recruitment procedures and demographics were the same as those of participants in Experiments 1 and 2.
Materials and procedure. Participants were introduced to a “Shape Machine,” a black box with a small black curtain in front and a platform on top with outlines for placing hotel bells and light switches. The experimenter said,
This is my shape machine! Can I tell you about how it works? When we put different bells and switches on top of the machine, and we ding the bell and switch the switch, then we can make some different shapes. Can I show you some of the shapes that the Shape Machine made?
The experimenter produced a tray containing flat wooden shapes that were painted with silver and glitter. The shapes were the same as the shapes on the cactuses in Experiment 2 (crescents, circles, triangles, squares, and stars). The experimenter put the shapes away and said, “So the Shape Machine makes the shapes, and the shapes come out right here [opening the curtain]. But, there are no shapes there now. That’s because we did not put any bells or switches on top!” The experimenter produced two laminated pages with illustrations of six hotel bells with different patterns and six light switches with different colors. The experimenter gestured at the illustrations of bells and switches and said, “In this game, we are going to try out a whole bunch of different bells, and a whole bunch of different switches, to try to make some different kinds of shapes!” The experimenter then produced a small flashcard with an image of a silver square on it, and said, “First, we are going to make squares.” Next, they produced a flashcard with an image of a silver star and said, “After we figure out how to make squares, then we are going to make stars. Are you ready to get started?”
As in Experiment 2, children observed three sequences of evi- dence during training. Half of children saw a sequence of evidence in which changing the bell on the third trial made a difference, and the other half of children saw a sequence of evidence in which changing the switch made a difference. The evidence in this experiment with physical stimuli was essentially parallel with the evidence that participants saw in Experiment 2: On the first two trials, the machine produced circles, an undesired outcome, yet on the third try (when the difference-making variable was changed), the machine produced squares. On each demonstration, the exper- imenter said, “Let’s try this bell and this switch [placing the bells and switches on top of the machine]. Alright! Let’s see what kind of shape comes out!” The experimenter tapped the bell, which dinged, and switched the light switch, which lit up. Then, the experimenter reached behind the curtain in the front of the ma- chine to “check” to see which shape came out (in reality, the experimenter slid a shape through a hidden opening in the back of the machine). On the first two demonstrations, the experimenter pulled out a silver circle shape and said, “Oh no, we got a circle, not a square! So that’s what happened when we used this bell and this switch [motioning to each of the objects in turn].” As in Experiment 2, they then suggested a new intervention—for exam-
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281PRESCHOOLERS IDENTIFY CAUSALLY RELEVANT VARIABLES
ple, “Ok, well, now let’s try the same bell and a new switch!” and proceeded with the next demonstration.
After the successful trial that produced squares, the experi- menter said, “Great! We made squares! Now it’s time to make a new shape, star. Let’s try a brand new bell and a brand new switch [producing a novel bell and a novel switch].” After dinging the bell and switching the switch, an undesired outcome (triangle shape) was produced. The experimenter said, “Oh no! We got a triangle. Which thing should we change in order to make a star? Should we change the bell or the switch?” The child was then given the opportunity to point to or verbally identify either the bell or the switch. Next, the experimenter removed the bell or switch from the top of the machine and produced a tray containing either three bells or three switches, depending on which variable the child had chosen to change. The tray included one previously unsuccessful bell or switch, one previously successful bell or switch (i.e., the one that had worked to produce “squares”), and one novel bell or switch. Participants then had the opportunity to select which object they wanted to try.
Results
The results of Experiment 3 replicated the results of Experiment 2: Preschoolers’ performance suggested that they again chose to intervene on the variable that had previously been relevant. An ANOVA showed that performance did not differ between 3- and 4-year-olds, F(1, 37) � 0.162, p � .69, and participants succeeded equally well in both the “bell matters” and “switch matters” conditions, F(1, 37) � 0.162, p � .69. Thirty-three out of 40 participants (82.5%) chose to produce a novel value of the previ- ously relevant variable at test, which was significantly different from chance, t(39) � 5.34, p � .001. Cohen’s effect size value (d � 0.83) suggested a high practical significance.
The second measure in this experiment was whether participants would choose to use a switch or bell that had been involved in an unsuccessful attempt to produce the first outcome, a switch or bell that had been involved in a successful attempt to produce the first outcome, or a novel switch or bell. Comparison between rates of choice for the latter two options was of particular interest. If children are operating strictly on their knowledge about concrete particulars (as in a reinforcement learning perspective), they should choose the switch or bell that had been successful previ- ously. However, if they infer that the new situation demands a new value of the relevant variable, then they should favor the novel instance. Of the 33 children who chose to intervene on the relevant variable, 26 of them (79.9%) chose the novel object from the tray, whereas only three children (9%) and four children (12%) chose the previously successful and previously unsuccessful objects, respectively. The proportion of children’s novel object choice was significantly different from chance, t(32) � �5.53, p � .001. This finding suggests that children were not only able to learn which variable was relevant but also that children were inclined to believe that the novel value of the variable would in fact produce a novel outcome. Cohen’s effect size value (d � 1.45) suggested a very high practical significance.
Participants’ responses to this “variable choice” question are significant for several reasons. First, they rule out several defla- tionary explanations regarding why children may have selected the novel value of the previously relevant variable both in the present
experiment as well as in Experiment 2. That so many of the participants seemed to expect that the novel value of the causal variable would map to a novel effect suggests that children who chose the previously successful causal variable were not simply perseverating, nor were they merely avoiding the variable that had previously been causally inert. Instead, the result suggests that children may be forming something like a genuine “naïve theory” about the system, in which they expected a 1:1 mapping between values of causal variables and values of effect variables. In this sense, it seems that children have acquired knowledge about the structure of this novel causal system that is genuinely abstract and theory-like: It represents specific ways in which cause and effect variables are related to one another, even without ever having witnessed these particular values.
General Discussion
In a series of three experiments, we demonstrated that 3- to 5-year-old children are able to rapidly learn which variables are causally relevant. Experiment 1 showed that children could use evidence about “difference-making” to decide which variable to intervene on to produce a desired, binary outcome. Experiment 2 demonstrated that children were also able to do this even when the outcome was one that they had not witnessed and when they did not have any direct evidence for how to produce it. Experiment 3 replicated the results of Experiment 2 and extended the findings to show that children were more likely to pick a novel value of a variable to produce a novel effect, rather than relying on a value that had previously produced a different desirable outcome.
Implications for Theories of Early Causal Reasoning
The present studies demonstrate that children are able to form generalizations about the types of interventions that are likely to be “difference-making” in a novel system of interrelated causal vari- ables. These findings provide a fruitful extension to previous research on children’s causal learning and reasoning about inter- ventions. This earlier research focused on children’s ability to learn which interventions are necessary for producing specific, binary outcomes: for example, the sequence of steps that would make a toy light up, the properties of objects that would cause a machine to activate, or the abstract relations between objects that would cause a toy to play music (Buchsbaum et al., 2011; Cook et al., 2011; Gergely et al., 2002; Gopnik, 2012; Gopnik & Wellman, 2012; Gweon & Schulz, 2011; Meltzoff et al., 2012; Schulz, Gopnik, et al., 2007; Schulz, Kushnir, et al., 2007; Sim & Xu, 2017; Sobel & Kirkham, 2006; Sobel & Sommerville, 2010). Difference-making, or interventionist, accounts of causation from philosophy and computer science are often taken as the foundation for constructivist accounts of children’s causal reasoning (e.g., Pearl, 2009; Woodward, 2003; Xu & Kushnir, 2013). However, the present study is the first to show that children can learn from difference-making evidence to identify causally relevant variables with entirely novel values to produce a novel effect. These findings suggest that a rapidly learned abstract causal structure can be applied to a new set of values: In other words, the higher-order knowledge about causal structure alone seems to serve as the guide for solving the problem of where to intervene.
One limitation of the present studies is that the novel values of the variables were still entirely contained within the same narrative
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282 GODDU AND GOPNIK
structure as the original interventions. Future research might ex- plore whether children might use difference-making to identify causally relevant variables across different narratives or contexts. Given children’s reluctance to transfer causal relations across domains—for example, to infer that psychological causes could produce physical effects (Schulz, Bonawitz, et al., 2007)—it seems that children’s transfer for novel, recently learned causal structures would stretch only so far. Future research might vary either the similarity between the causal structure of the training and test systems or the similarity of the training cause and effect variables to the target cause and effect variables to begin to determine which aspects of a novel causal system correlate most strongly with participants’ willingness to generalize the causal knowledge they have learned.
In this sense, the present study might be construed as a form of analogical reasoning: participants must “transfer” the causal struc- ture that unites a set of known causal variables to a similar, but concretely distinct, set of values. Previous research in the devel- opment of analogical reasoning finds that preschoolers routinely fail to privilege abstract relations over superficial similarities be- tween stimuli used in training and target stimuli at test, unless an experimenter provides explicit scaffolding (e.g., applies novel labels to relations or encourages children to compare exemplars; Christie & Gentner, 2010, 2014). Children’s performance in the present tasks thus corroborates recent research suggesting that causal framing facilitates children’s transfer for abstract rela- tions—for example, the abstract relations that hold between the beginning and ending states of causally transformed objects (Goddu et al., 2017a, 2017b). Furthermore, the results of the present experiments provide an interesting counterpoint to findings from another recent (noncausal) task, in which children who com- pleted “near” (vs. “far”) analogical transfer tasks were less likely to reason relationally in a subsequent paradigm (Walker, Hu- bachek, & Vendetti, 2018). Given that the present stimuli involve what amounts to a “near” transfer of causal structure from values of variables used in training to novel values of those same vari- ables, future research might explore the extent to which children’s performance in variable choice tasks might improve or inhibit their downstream reasoning on other tasks involving relational reason- ing.
Solving the ‘Problem of Variable Choice’ in Cognition
In philosophy of science, the “problem of variable choice” refers to the problem of how best to specify variables for intervention or explanation in a novel causal system (Woodward, 2016). However, this normative problem is also a pragmatic problem in everyday cognition. In cases where a reasoner must identify which variables are relevant for producing a specific outcome without prior expe- rience with the outcome or with the particular causes that may produce it, then they must in effect solve the problem of variable choice. The present study demonstrates that children as young as 3 years old are able to learn from sparse evidence to choose relevant variables for intervention when they are tasked with producing a novel outcome from novel values of variables.
In addition, the present findings suggest that difference-making information by itself is sufficient for learning and exploiting ab- stract causal structure. This accords with an interventionist view of causation, in which causal knowledge is defined in terms of
possible counterfactual interventions rather than in terms of mech- anism or association (Gopnik et al., 2004). Although researchers have suggested that an interventionist framework may be useful for understanding how learners come to devise interventions on sets of variables with prespecified values, the present experiments are the first to demonstrate that difference-making information can be used to construct abstract causal models that may be applied to variables with entirely novel values for both cause and effect (Schulz, Kushnir, et al., 2007). As such, the present findings substantiate philosophical conjectures that “difference-makers” or “control variables” that are useful for predicting or controlling the behavior of one variable are likely to be broadly causally relevant (Campbell, 2007; Woodward, 2003).
Finally, the children’s responses to the additional “variable choice” test question in Experiment 3 provide an interesting and suggestive data point on a hitherto unexplored issue. That more than three-quarters of participants chose the novel value of the previously successful variable to produce a novel effect suggests that they may have expected this novel casual system to obey something like a 1:1 mapping of causal variable values to effect variable values. This finding opens up the possibility that human cognition is equipped even early on in learning with biases to help simplify the problem of choosing which causal interventions to make in unfamiliar situations. Follow up studies might explore the extent to which varying the forms of cause and effect variables might alter children’s intuitions about the mappings (Magid et al., 2015). For example, would children still expect a 1:1 mapping in cases where the causal variables took discrete values, yet the effect variable varied continuously?
Conclusion
The present study demonstrates that young children are able to learn from sparse evidence about “difference-making” to deter- mine where they should intervene on a causal system with unfa- miliar values of causes and effect. These experiments are the first to show that abstract causal knowledge acquired from one set of variables can guide decisions about intervention on a novel set of variables. This research paves the way for future empirical explo- ration of the problem of variable choice—a problem relevant not only to philosophy of science but also to a wide array of everyday problems in causal reasoning.
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Received May 14, 2019 Revision received September 24, 2019
Accepted October 22, 2019 �
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