preschool children can learn to transfer: learning to learn and learning from example

COGNITIVE PSYCHOLOGY 20,493-523 (1988)

Preschool Children Can Learn to Transfer: Learning to Learn and Learning from Example

ANN L. BROWN

University of Illinois at Urbana-Champaign

AND

MARY Jo KANE

Bowling Green State University

In a series of seven experiments we examined preschool children’s ability to learn and transfer across problems that shared a common underlying structure but differed in surface manifestations. The problems involved novel uses of familiar tools or simple biological themes such as mimicry as a method of defense. In the fust three studies, we examined children’s ability to learn to transfer after being exposed to a variety of transfer situations. Three-year-olds benefit from conditions that encourage them to reflect upon relational similarity; four-year-olds show a learning to learn effect without prompts to look for similarity. Both ages rapidly form a mind set to look for analogous solutions across problems. In Stud- ies 4 to 7, we looked at preschoolers’ learning from examples. When required to explain why an example is an illustration of a general theme, transfer to other instances of that theme is rapid, often occurring on the basis of only one example. Explanations and elaborations provided by the children, either spontaneously or in response to prompts, are much more effective at promoting transfer than those provided by an experimenter. The data are discussed in terms of explanation- or analysis-based models of both machine and human learning. o tw~l ~~adetic

Ress, Inc.

The major question addressed in this series of studies is whether preschool children can learn a principle on the basis of one or few examples. In both the cognitive science and artificial intelligence literatures, there is considerable interest in explanation-based learning (DeJong & Mooney, 1986; Lewis, 1986; Mitchell, Keller, & Kedar-Cabelli, 1986) where leaming takes place on the basis of a single or few training examples. The

The research presented in this paper was supported by NICHHD Grants HD 06864 and HD 05951. The authors thank Joseph Campione, John Flavell, Dedre Gentner, Usha Gos- wami, and Robert Reeve for thoughtful discussions on the progress of this research. We thank Susan Hills for making the three-dimensional scenarios or stage sets for the tool use problems, Anne Slattery for finding and drawing the examples of animal defense mechanisms and natural pest control, and Rita Gaskill for her patient text editing of the many versions of this manuscript. Reprints may be obtained by writing to Dr. Ann L. Brown at her current address at the School of Education, University of California, Berkeley, CA 94720.

493 OOlO-O285/88 $7.50 Cqqmigbi 0 19&l by Academic Press, Inc. All rights of reproduction in my fom reserved.

494 BROWN AND KANE

artificial intelligence systems analyze training examples by constructing an explanation of how they satisfy the conditions of the concept under study. Such systems contrast with similarity-based methods that seek regularities over a large number of examples. Psychologists interested in human learning have also been concerned with learning from exemplar information (Medin & Schaffer, 1978). In this series of studies we examined whether young children can abstract a general rule from examples and, if so, whether their learning is influenced by their ability to explain why the concept is an instance of the rule. In addition, we asked whether young children, exposed to a variety of transfer experiences where they must extract and apply rules over examples, would form a mind set to look for analogies. In other words, can children learn to transfer?

The question of transfer is a time-honored one in psychology; indeed, it is a topic that provokes extreme opinions, some claiming that it is a rare commodity (Thorndike, 1913), others that it is ubiquitous in human leaming (Ferguson, 1956; Hebb, 1949). Many contemporary arguments concerning transfer can be traced back to their roots at the turn of the cen- tury. Particularly pertinent to this research is the theoretical battle that took place between Thomdike and Judd.

Thorndike, attacking the prescientific notion of formal discipline (that learning Latin trains the mind), claimed that transfer occurs if and only if “identical elements” are shared between tasks (Thorndike, 1913; Thorndike & Woodworth, 1901). Although exactly what constituted “identical elements” was in considerable dispute (Allport, 1937; Orata, 1945; Sandiford, 1928), it was taken to mean identical at the level of surface features. The theory was translated to mean that if two situations share an underlying deep structure but differ in their surface manifestations, transfer cannot be expected, whereas if there are surface elements (e.g., physical or perceptual similarity) in common, transfer will be a “necessary result.”

This position was widely upheld and is cited in textbooks as a truism today, despite the fact that Thomdike himself was an unreliable source for a definition of just what constitutes an element. In the spirit of the learning theories of his day, Thomdike posited a neurologically inspired stimulus-response explanation of identical elements that, indeed, the two situations would stimulate “common cell action in the brain.” Unfortu- nately for the theory, he went on to include as basic elements a variety of “identities beyond our cognizance,” such as “getting to the heart of the problem, ” “respect for the scientific method,” and “the disposition to neglect irrelevant things.” Granting the status of basic elements to these general tendencies certainly weakened the identification between identical elements and “common cell action in the brain.”

Notwithstanding the vagueness of the original description, identical

LEARNING TO LEARN 495

elements became a core explanatory concept in the psychology of leaming. A spate of studies to test the theory followed, many of which selected “absurdly inconsequential tasks for training” (Allport, 1937, p. 37) such as crossing out p’s, then q’s in texts. In general little evidence for transfer was found unless the tasks were extraordinarily alike, with Thomdike even claiming that learning a + b would not transfer to x + y (Thorndike & Woodworth, 1901). Criticism of the theory was mounted on two fronts, first against the pseudo-neurological basis (Lashley, 1929) and second by psychologists who were able to make a coherent case for transfer under reasonable situations (Orata, 1928).

The counterclaim in support of transfer was that one cannot expect transfer if there is nothing to transfer. However, in situations where leaming can be organized around a guiding principle, transfer is determined by the extent that the subject is privy to that principle, through either dis- covery or instruction. A classic study of principled transfer was conducted by Scholchow and Judd (1898, reported in Judd, 1908). Twelve- year-old boys were asked to throw darts at an underwater target, a skill that requires considering the deflection that the light suffers through refraction. Half the subjects were instructed in the principle of refraction, the remainder were not. Both groups did equally well at first; all needed time to practice the skill. But when the amount of water was reduced, thereby altering the degree of deflection of the light, the boys without the principle became confused; practice with one setting did not transfer to the other. In contrast, the boys with the principle adapted readily. The same pattern recurred when the target was changed again, with the principle group adjusting more rapidly, and the no principle group less rapidly, over time. Judd argued that, “Theory is no substitute for direct experience; it is rather the frame in which experiences may be properly held apart and at the same time held together” (Judd, 1908, p. 38). Other experiments reporting essentially the same results surfaced at this time (Ruediger, 1919; Ruger, 1910). Transfer is not automatic but depends upon insight into general principles.

Unfortunately, Judd’s position lost favor, and it became generally as- sumed that transfer is a rarity, and when it occurs, it is most often cued by some surface features of the stimulus environment. The popularity of this position was not weakened even when Thomdike eventually capitu- lated (Thomdike, 1926), a change of heart that had little apparent effect on the continuing popularity of the original identical elements theory (Orata, 1945).

Recent laboratory studies of analogical learning in children reinforce the view that transfer is a hard-won commodity. It is claimed that children resist transferring what they know and that even when they do transfer, they rely on shared surface features of the task environments, not deeper

496 BROWN AND KANE

relational properties (Gentner dz Toupin, 1986; Holyoak, Junn, & Bill- man, 1984) Children are called “perceptually bound,” meaning that they are unduly infhrenced by the appearance of things. If this were true, children could be described as extreme Thomdikians. But is it true? On the one hand, children can make inductive projections on the basis of deep underlying structure such as natural kind membership, even when it conflicts with surface similarity (Gelman & Markman, 1986, 1988). But on the other hand, there is considerable evidence that children tend to re- spond on the basis of perceptual similarity on a variety of tasks such as classification, free association, free recall, and word definitions (Mans- field, 1977) as well as analogy, metaphor, and transfer tasks (Brown & Campione, 1978, 1984; Gentner & Toupin, 1986; Vosniadou, 1987). In fact, no one denies that physical similarity or perceptual attributes are important in mediating transfer for adults as well as children (Anderson, 1987; Campione & Brown, 1974; Gentner & Toupin, 1986; Pirolli & Anderson, 1985; Reed, Dempster, 8z Etlinger, 1985); the issue is whether they are all-important for young children, i.e., whether children cannot transfer on any other basis.

If this were true, it would support a strong development stage hypothesis, namely that it is not until a certain age that children can show relational transfer in the absence of perceptual support. An alternative explanation is that young children have a developmental preference for relying on perceptually salient features if given a choice. A third hypothesis is that children often lack the requisite knowledge to transfer on any basis other than perceptual similarity. In the absence of pertinent knowledge, it is difficult to imagine any basis for operating other than appearance, whether one is an adult or a child. Reliance on surface similarity is indeed a typical finding with novice learners. For example, Chi, Felto- vich, and Glaser (1981) found that novice physicists sorted physics problems in terms of surface similarity, such as key words in the problem or, at best, in terms of the objects (“rotational things”) mentioned. By contrast, surface features did not infhtence experts, who classified according to the major physics principles governing solutions; indeed, the deep structure relations guiding their classifications could be detected only by other expert physicists.

The key question then is, are young children extreme Thomdikians, or can they mediate transfer on principled as well as perceptual bases, as Judd would have argued? Few studies of laboratory transfer in young children exist and most of those include children below 5 years of age only as experimental foils: subjects who fail to learn and transfer because the tasks are calibrated to be of suitable difficulty for the older children in the study. The younger children thus provide a baseline against which the greater proficiency of older children can be measured (Brown &


DeLoache, 1978). However, there have been a few reports of successful laboratory transfer in children below 5 or 6, but these studies all provided some degree of surface similarity to act as a crutch to learning and transfer. This similarity was either in the solution tools (Holyoak et al., 1984) or the actions (Crisafi & Brown, 1986), or in both the tools and actions used to reach a goal (Brown, Kane, & Echols, 1986). In addition, studies that have shown successful transfer in very young children have involved the simple expedient of telling the child that the tasks are the same (Crisafi, 1986; Crisafi 8z Brown, 1986). So to date, the data base supporting laboratory transfer in young children can indeed be interpreted as showing reliance on perceptual similarity. In this series of studies, we examined analogical transfer in preschool children under conditions where they are not told that the tasks are the same and where the surface similarity of the problems was minimized.

The choice of tasks through which to look at transfer presents some problems. First, the difficulty level of the tasks must be carefully calibrated so that we avoid the experimental foil problem mentioned earlier. We took care of this by pilot testing until we found a set of problems that approximately lO-20% of subjects solved spontaneously. This is the proportion of adults who routinely transfer on laboratory problems without aid (Gick & Holyoak, 1980, 1983), and we used this proportion as a calibration metric.

Second, in order to continue in the tradition of this field, we needed tasks that children could understand although they did not already have the requisite knowledge; in other words, there must be something to learn and transfer. Children were asked to learn and transfer in two domains. The first two studies used a variety of simple but novel tool-use problems. These were similar in spirit to those used in the 192Os-1940s to study problem solving in human adults (Maier, 1929) and apes (Kohler, 1925). We know that even infants have considerable knowledge about tools as “means for bringing” (Piaget, 1952, p. 204) inanimate objects into reach (Brown, 1986; Leslie, 1984), so the causal mechanisms in question are familiar to young children. In the first two experiments, children were required to note novel uses of familiar tools. The last five studies required children to learn about simple biological themes, such as mimicry as a method of defense. The mechanisms we used, although actually occurring in nature, are not grounded in the child’s prior experience and therefore could be more difficult to learn and apply. Indeed, the rules required a fairly high level of abstraction. For example, the specific fact that the crested rat disguises itself as a skunk to avoid attack should not be transferred at that level to other animals, none of which can look like skunks. But the abstract rule, “mimic something more dangerous,” can be transferred to the hawkmoth caterpillar that can mimic a poisonous snake.

498 BROWN AND KANE

These animal defense mechanisms were also ideal for our purposes, as they can be embedded in simple narratives about animals from which the child must extract both the general theme “look dangerous” and why the animal in question is an exemplar of that theme. Of issue here is whether children can learn and transfer abstract rules on the basis of one or two examples when the actual mechanisms are different (look like a skunk, look like a snake) and the animals are also distinct (rat, caterpillar). Thus, neither the objects (protagonists) in the examples were similar (Gentner & Lander, 1985; Ross, 1988), nor were the actual means of defense (look like a snake); only the regularities, or systematicity (Gentner, 1983), at the level of abstract mechanism (mimicry) could be abstracted and transferred.

LEARNING TO LEARN

Study 1

In the first three studies we examined whether preschool children could form a positive learning set (Hat-low, 1959) to solve problems by analogy, given repeated experience. The basic paradigm was as follows. Children are given a series of problem pairs and required to use the information in the first problem of a pair to solve the second. Over a series of such tasks, would the child pick up the abstract rule, “transfer prior solutions,” even when that solution is novel across pairs? Such a positive learning set would rely on an abstract set to transfer, i.e., the expectation to solve problems by analogy. In other words, required to solve a series of iso- morphic problem pairs, will the child develop a mind set to look for analogies?

Methods Subjects. Sixty-eight 3-year-olds (mean-3 years 3 months), 29 4-year-olds (mean-l

years 6 months), and 34 Syear-olds (mean-5 years 4 months) took part in this study. There were approximately equal numbers of boys and girls at each age. The children were recruited from day-care centers in such a way that approximately equal numbers of children from each center were represented at each age.

Materials. A variety of problem pairs were constructed. Each pair required the child fust to invent (with assistance) and then to transfer a novel solution using a particular tool.

After considerable pilot work, we devised the set of three story pairs illustrated in Table 1, These problem sets were selected because (a) the children had the prerequisite knowledge concerning the simple act of physical causality involved; (b) the tasks demanded a different action for their solution: swinging, stacking, pulling, etc.; (c) the constituent pairs were physically different from one another; and (d) they generated similar levels of accuracy as shown in Table 2, with Syearolds successful and 3-year-olds unsuccessful in their spontaneous attempts to solve the transfer problems.

Each problem contained the critical piece of information (the basis of the analogy) plus other irrelevant details. For each scenario there was a three-dimensional set with the appropriate actors and props, so that the child could enact the solution. For example, for the


TABLE 1 Tool Use Problem Pairs Used in Studies 1 and 2

A2

B,

B2

c,

c*

Problem set 1: Stacking

John, the garage mechanic, has a problem. He needs to take all of the tires that have been delivered to his garage and put them up on a shelf. But the shelf is too high and he doesn’t have a ladder so he can’t reach the shelf by himself. How can he solve his problem?

Solution: Stack two tires and stand on top of them. Bill, the farmer, has a problem. He needs to put his bales of hay on top of his tractor so he can take them to the market. But Bill isn’t tall enough to reach the top of the tractor by himself. How can he solve his problem?

Solution: Stack two bales of hay and stand on top of them.

Problem set 2: Pulling

Mrs. Smith is a lady who grows flowers. One day she is digging in her garden, removing weeds (with a spade), when she hears a little boy crying. She looks up and sees that the little boy has fallen down a big hole at the bottom of her garden. She can’t reach him because the ground around the hole will give away. How can Mrs. Smith help?

Solution: Mrs. Smith sticks out her spade, the boy grabs it, and he is pulled up. Linda, the girl guide, has a problem. She is fishing (with a pole) when suddenly she sees that a boat with a little girl in it has broken away from the dock and is floating downstream. She has to get the little girl and the boat back to shore. How can Linda solve her problem?

Solution: Linda holds out her fishing pole and has the little girl grab it, and she pulls the boat to shore.

Problem set 3: Swinging

Carolyn, the nurse, has a problem. Earlier in the day when the water wasn’t deep she walked across the stream to go visit a sick lady in the house on the other side. But while she was there, the weather got very bad, there was a big flood and now the water is too deep and fast for her to walk, jump or swim across. She needs to get back to the other side before dark. How can she solve her problem?

Solution: Grab onto a willow tree branch on the bank and swing across to the other side.

Mr. Brown, the telephone repairman, has a problem. He is up on a roof to connect the telephone wires to the two telephone poles. He has all of his tools up there. Suddenly, he notices that the house is on fire. He needs to get to the roof on the other house to save himself. How can he solve his problem?

Solution: Grab onto the telephone wires and swing across.

stacking problems, one scenario consisted of a garage with appropriate cars and petrol pumps, plus a toy figure of a repair man and a stack of miniature tires to be stacked on shelves. The farmer scenario consisted of a farm scene with barns and animals, plus a toy farmer, a flatbed tractor, and miniature bales of hay. Two tires (bales) stacked on top of each other would indeed allow the toy character to reach the shelf (tractor). We should point out that the second problem in the swinging pair was changed halfway through the study to a problem demanding that a toy use washing lines to swing across a garden wall. This change took place when we realized that children might learn something dangerous about live wires

500 BROWN AND KANE

TABLE 2 Proportion Unassisted Transfer on the Three Problem Sets

Age Stacking

10 years .93 5 years Ali 3 years 36

Pulling Swinging

.88 .86

.64 .64 a3 .lO

from the existing telephone wire problem. This change made no difference in the proportion of correct solutions.

Procedure. The children were tested individually. Each child received the problem pairs shown in Table 1. The problems were presented in random order but blocked by pairs (e.g., C,C, A,A, B2B1). If the child could not solve a problem, the experimenter demonstrated the solution and then required the child to imitate the solution before passing on to the next problem.

The 3-year-olds were assigned to one of five conditions. There were three conditions that we thought would promote reflection on the underlying deep structural similarity of the problems: Hint, Discussion, and Instruction. In the Hint condition the children were explicitly told after the Brst member of a pair that “the next problem is just the same” and that “now you know how to stack, pull, swing, etc., the next problem will be easy.” Telling children that problems are the same, without specifying how, is one of the methods that has promoted successful transfer in young children (CrisatI, 1986; Crisafi & Brown, 1986). Therefore, this obvious mention of the common action and of problem similarity should promote transfer if anything would; thus, the hint condition was regarded as a yardstick against which the other manipulations could be measured.

In the Discussion condition the child was asked to say how the problems in a pair were alike after solving the second member of each pair. The third reflection condition was the least constrained; the child was required to teach the two solutions of the pairs to a Kermit the Frog puppet. It was left up to the child whether she would mention problem similarity at the level of common action.

The remaining two conditions consisted of a No Reflection group who merely received the six problems with no discussion and a control group who were presented with only one problem set after performing two irrelevant problems that did not require transfer (block design and seriation tasks, etc.).

The 4- and S-year-old children were assigned to only three groups. Discussion, No Re- flection, and Control, where they were treated identically to the comparable three-year-olds.

Results

Inspection of the 3-year-olds’ data revealed no significant differences between the three Reflection conditions: Hint, Discuss, or Instruct; henceforth the data were collapsed into three conditions, Reflection, No Reflection, and Control, comparable to the 4- and Syear-old sample. Note that the Discussion and Instruct conditions, where the child was not required to mention problem similarity, were as efficient at promoting transfer as the blatant Hint condition where the child was explicitly told about the common actions.

The critical learning to learn data are the proportion correct transfer on


the third problem set. These data are presented in Fig. 1. The difference between the Reflection and No Reflection groups is significant for the 3-year-olds, x2(1, N = 60) = 9.88, p < .Ol but there is no significant difference between the No Reflection and Control conditions. This means that the 3-year-olds show a reliable learning to learn effect only if they are encouraged to reflect on their solutions, either through discussions, instructing Kermit, or explicit prompts to problem similarity.

However, children as young as 4 years of age show the learning to learn effect even without the benefit of explicit discussion; the difference between the Reflection and No Reflection conditions is not significant, but the difference between the No Reflection and Control is reliable, x2(1, N = 24) = 5.45, p < .02. As expected, the Syear-olds show a near ceiling effect (see Table 2), although the difference between the two learning to learn groups and the control is still reliable, x2(1, N = 34) = 4.51, p < .05, despite the high level performance shown by the control children.

Another difference between 3- and 4-year-olds is illustrated in Fig. 2. These data are from the children in the Reflection groups only. Whereas there is no significant difference on the first or last pair, the difference between 3- and 4-year-olds is reliable on the second pair, x2( 1, N = 45) = 7.92, p < .Ol. It took only one experience of analogical transfer for the 4-year-olds to catch on with these simple problems, whereas the majority of 3-year-olds needed two prior experiences.

RW+E Refktion- m Control gpg

t loo-

co Qo- 3 d 80- 0 if 70-

f 60-

B 50- L 2 40- E 5 30 -

f 20-

[ lo-

O- Four Year Olds Five Year Olda

FIG. 1. The proportion of subjects in Study 1 achieving solution on the third problem as a function of Age and Reflection Condition.

502

loo-

Qo-

so-

t

!I 70. -

30 5 i 40- 50-

30-

20-

BROWN AND KANE

~3YEARlxD3

YEAR aDs

82 C2

TRANSFER TASKS

FIG. 2. Differences between subjects in the Reflection Condition of Study 1 as a function of Age and Problem Order.

Examples of the type of discussion generated by 3- to Syear-olds are given in Table 3. Even 3-year-olds hone in on the common action pattern within the pairs and can discuss problem similarity with some help from the experimenter; 84% of 3-year-olds in the Discuss group were judged to have mentioned within pair similarity at some level, and 79% of those teaching Kermit did so too. Note however, that in the Kermit condition they were not required to do so. Interestingly enough, the 4- and 5- year-olds in both the Reflection and No Reflection groups mentioned problem similarity (.86 and .79 respectively), even though they were under no constraint to do so.

Discussion

Four- and five-year-olds can form a mind set to look for analogies without instructions to concentrate on problem similarity. By the second related pair, the majority show transfer and by the third pair, 90% can transfer a novel solution to a matching pair. They rapidly catch on to the fact that the name of this game is to use the demonstrated solution to the first member of a pair to solve the problem posed in the second. The learning to learn effect is rapid and the children understand the rules of the game (Flavell, 1977). With these very simple problems, when the analogy is blatant, where the children understand that the goal is to look for a common action pattern, transfer of analogous solutions is rapid,


TABLE 3 Learning to Learn: Tool Use-Examples of Justifications in Discussion Groups

Sl:

s2: E: s2:

E: s2:

E: s3: E: s3: E: s3:

E: s4: E: s4:

E: s5: E: ss: E: ss:

Subject 1. Five years old These stories are all the same things. The farmer, he had to stack the hay things . . . now the garage man is going to have to stack the tires. Both games have to stack things up, and then he can reach.

Subject 2. Four years old I know how to do it by myself. . . we just pile up wheels like before. Ummm. In that story the man had a problem . . . he piled up wheels. This man needs wheels too. What do you mean? No wheels! (surprised-tries to get down and retrieve tires from previous task, now hidden under the table. Told she must use only those things now on the table, she continues) . . . oh, . . . so we can use these grass things. Both stories have things to make piles. Isn’t that lucky?

Subject 3. Four years old How did you know how to solve the problem that way? Well, the reason you stack the hay is because we already seen it from before. Before? Yep . . . in that other game about the tires. What do you mean? Could you tell me a little more? The tire man had to stack the tires . . . the farmer man had to stack the hay . . . they the same, aren’t they?

Subject 4. Three years old So tell me . . . how did you know how to solve the problem that way? Because you showed me with the other one. What do you mean, the other one? Well, in the other game, from before . . . the hay was to reach. So in this game we st . . . put on top . . . st-st (E: “stack?“). Yes, stack the tires so we could reach again.

Subject 5. Three years old You said my games are the same. How are they the same? They both have to put things on top. Could you tell me a little more? In the farmer game we put these green things (yellow bales of hay) on top. Umm. In the game we pile up wheels like before. Both games are for you to pile up things to reach.

even though there is no similarity across problem pairs at the level of either surface features or action patterns.

Three-year-olds are also able to learn to look for analogous solutions; however, they need the additional help of being encouraged to reflect on the problem similarity and they need two prior experiences before they transfer. The two reflection procedures that encourage but do not force

504 BROWN AND KANE

the children to make comparisons among analogous pairs work just as well as quite simply telling them that a pair of problems are identical at the level of action (“stacking, swinging, etc. ,” i.e., giving them the answer). Holyoak (1985) argues that experiencing two stories with the same underlying structure leads to greater analogical transfer only when subjects have to compare the stories. Similarly, Dellarosa (1985) has argued that answering questions that force a comparison between problems leads to better learning. Apparently, children as young as 3 can benefit from instruction to discuss problem similarity. But note that no mention was ever made of transfer UC~OSS pairs. Children were required to form a mind set to look for analogies on their own.

Unlike previous studies of children’s analogical transfer, the learning to learn manipulations expose children to a variety of underlying commonalities thereby inducing them to look for deeper structural similarity although they cannot know in advance what it will be. This is distinctly different from prior studies where the hints or clues served to teach children one particular structure that is common to all problems (Brown et al., 1986; Brown, Kane, & Long, in press; Holyoak et al., 1984). The learning to learn procedure enhances a set to transfer, whereas previous studies encouraged learning of a single rule.

Study 2

One could argue that the experimental setup in Study 1 was ideal for bypassing the access problem and forcing the child to “notice” common solutions. After the first member of each pair was demonstrated and imitated, the analogous member was always presented immediately. Maybe preschool children’s precocity would break down if they had to select pertinent knowledge from a range of prior experiences.

In reality, transfer involves retrieval of a previously learned solution even when other experiences have intervened; the learner must access the prior appropriate experience and not inappropriate knowledge. In Study 2, we examined whether young children can select from a stream of previously learned solutions the one appropriate to the transfer problem at hand. Thus, we tested the limits of the young child’s ability to apply knowledge flexibly by embedding learning and transfer problems in a series such that related pairs were not adjacent.

The question is whether children can remember a set of previously learned tool use solutions and apply them appropriately to a series of subsequent problems; can they match tool use solutions to appropriate occasions of use? Having learned swing, stack, or pull, can the child apply that knowledge flexibly to three subsequent novel tasks requiring stack, swing, and pull? It is both a more stringent test of the child’s ability to notice problem isomorphs and a more representative test of “real-life”


transfer to ask children to hold what they have learned in memory and apply it to an appropriate situation but not to an inappropriate one, in other words, to discriminate as well as to generalize.

Method Subjecrs. Twenty-eight 3-year-olds (mean-3 years 9 months) and 25 Syear-olds (mean-

5 years 6 months) took part in this study. They were selected from two day-care centers attended by a high proportion of university faculty children. There were approximately equal numbers of boys and girls in each group.

Materials. These were the same as Study 1. Procedure. The procedure was identical to Study 1 with the exception that the children

received all the fist members of pairs before the second members of pairs. The order of presentation was randomized with the restriction that no two members of a pair were adjacent (e.g., B, A, C, A2 C, B,). The children were assigned to Reflection and No Reflection conditions. This time the Reflection condition was the least constraining, i.e., the one where the chid is asked to instruct Kermit in how to play the game after each problem. No mention is made ofproblem similarity. The children must discover this for themselves.

Results

The data are presented in Table 4. The children could not solve the first members of the pairs. The critical transfer data consist of performance on the second problem of each pair; if the child could access the appropriate previously learned solution, the second problems can be solved by analogy to one of the first three.

Both 3- and 5-year-olds show a learning to learn effect, in both the Reflection and the No Reflection groups. Indeed, by the third problem set there are no significant effects of Age or Reflection. The apparently lower level of performance of the 3-year-olds in the No Reflection group is not reliable. All children show significantly greater transfer on the third than the first problem pair.

Significant difference between Ages and Conditions were found only for the second transfer problem (B2), where there was a marginally significant effect for the Reflection, No Reflection comparison, x2(1, N =

TABLE 4 Proportion of Correct Responses on Transfer Problems of Study 2

Transfer

Task

Reflection Age 3 Age 5

No reflection Age 3 Age 5

A2 B2 c2

.21 .42 .75

.28 .81 .86

.23 .29 .54

.42 .62 .75

506 BROWN AND KANE

53) = 3.40, p < .lO. And the Age comparison is reliable, x*(1, N = 53 ) = 5.79, p < .02. The older children and those instructing Kermit catch on in one trial. This age effect is directly analogous to Study 1. The majority of 5-year-olds (75%) mentioned problem similarity on the second problem. And 68% of 3-year-olds mentioned problem similarity on the third problem, e.g., “Oh, here’s another pulling problem” or “I could pile up the tires like the farmer piled the hay.”

We saw no evidence that forcing the child to select a relevant analogous experience from a stream of such experiences made the access problem harder. Taken together, the results of Studies 1 and 2 suggest that children as young as three years of age can form a mind set to look for analogies, becoming quite facile at the process. They can also learn that the rule of the game is to use prior demonstrated solutions to solve the novel problems. They can search their memory of a series of prior problems to find an appropriate match.

Study 3

Study 3 is directly analogous to Study 1 with the exception of a change in materials. Here we introduced a series of problems about animal defense mechanisms. Although perhaps more interesting to the children, these defense mechanisms were novel to a young child who does not have the requisite background knowledge to grant coherence to the examples. One could argue that the tool use problem of Studies 1 and 2 were trivially easy for 3-year-olds who have considerable experience using tools as “means for bringing” (Piaget, 1952) inanimate objects into reach (Brown, 1987; Leslie, 1984). All that was needed was for them to note novel instances of familiar forms of physical causality. The animal defense mechanism used in the remaining studies, may prove more difficult for children to solve as they are not grounded in the child’s prior experience. Children of this age do not know about mimicry. They must learn the themes. And the theme to be transferred is quite abstract, “look more dangerous when under attack.”

Again, as in Study 1, the children were set to learn six problems, three sets of pairs. The first solution of a pair was demonstrated by the experimenter; the child then was required to apply it to the second member of a pair. Again, we asked whether the child would acquire a positive learning set to seek out analogies?

Method Subjects. Sixty 3-year-olds (mean age-3 years 7 months) took part in this study, 24

assigned to the Reflection group, 23 to the No Reflection group, and 10 to a Control condition. Three children were dropped from the study for failure to cooperate. They were selected from day-care centers that serve the community at large. There were approximately


equal numbers of boys and girls in each group. The mean age was comparable across groups (3 years 6 months to 3 years 8 months).

Materials. The materials consisted of six story problems and an accompanying set of pictures. The problems all concerned animal defense mechanisms and contained irrelevant information (having to do with habitat, physical appearance, food gathering habits, etc.) as well as the critical defense mechanism. There were three sets of pairs, shown in Table 5. Two animals, the hawkmoth caterpillar and the crested rat, mimic more dangerous animals to defend themselves. The hawkmoth caterpillar can turn over and reveal markings on its underside that resemble a poisonous snake, and the crested rut can part its fur to reveal skunk-like markings. Two other animals, the arctic fox and the chameleon, change color as their method of defense, one by season and one on a momentary basis. The remaining two animals, the walking stick insect and the pipe fish, change shape as a means of camouflage. The mechanisms connecting the pairs are similar at a fairly high level of abstraction (change appearance for defense); the physical manifestation of the underlying mechanism is not at all similar. For each story there were three pictures, one showing an irrelevant piece of information (e.g., the animal feeding, shedding, etc.), one showing one state of the animal, and the other the changed state (e.g., caterpillar/snake).

Procedure. The procedure was essentially similar to Study 1. The children were given all six problems with the order of problems in pairs randomized. The children were assigned to Reflection, No Reflection, and Control conditions. In the Reflection condition, the children were asked to teach Kermit about the animal’s defense mechanism. In the No Reflection

TABLE 5

Biological themes story pairs used in Study 3 Problem set 1

Defense mechanism = mimicry-look like a more dangerous animal A, Hawkmoth caterpillar

Mimics a poisonous snake A, Crested rat

Mimics a skunk Problem set 2

Defense mechanism = camouflage-change color B, Arctic fox

Seasonal color change B, Chameleon

Fluctuating color change Problem set 3

Defense mechanism = camouflage-change shape C, Walking stick insect

Changes shape to look like a twig or a leaf C, Pipe fish

Changes shape to look like a reed Biological theme sets used in studies 4-7

Mimicry: Hawkmoth caterpillar (snake) Crested rat (skunk) Capricorn beetle (wasp)

Natural Pest control: Ladybug (eats aphids on farmers’ crops) Purple martin (eats gardener’s mosquitos) Manatee (eats water weeds)

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condition the six problems were presented without comment. The Control group performed two unrelated tasks before tackling one of the problem pairs.

As in the preceding study, the child listened to the stories which contained a series of facts about the animal in question including the strange markings, the color and shape change, etc. That these qualities could be useful for defense was never explicitly mentioned. After each story, the child was asked three questions inciuding the critical defense question. “How could the hawkmoth caterpillar stop the big bird that wants to eat him?“-answer, “look like a snake.”

Results

The data for the critical third transfer problem are presented in Fig. 3, along with the comparable data from the 3-year-olds’ solving tool use problems in Study 1. The overall effect of condition is reliable, x2(2, iV = 57) = 14.49, p < .OOl. The difference between the Reflection and No Reflection groups is not significant, but that between the No Reflection and Control groups is, x2(1, N = 33) = 8.51, p < .Ol. With these materials, 3-year-olds form a mind set to look for analogies without the assistance ofteaching Kermit. Indeed 3% of the children in the No Reflection condition mention problem similarity for at least one of the pairs. And for the children engaged in instruction 83% chose to describe the problem similarity to Kermit.

Inspection of Fig. 3 suggests that the biological themes material was no more difficult than tool use solutions; indeed, these stories might be easier for young children to learn, at least in one respect. In the condition where the children are not prompted to talk about problem similarity, they do much better on the biological themes than on the tool use problems.

100

5 80 UJ E 2 80 a 2 P 70

E E 80 I- L $3 50 e E 40 I- 5 30 z ‘0 P 20 e c.

10

0

mnl Biological Theme8

I Tools

Reflection + Reflection - Control

FIG. 3. Proportion of subjects achieving solution on the third problem as a function of Age, Reflection Condition, and Materials.


Whereas there is no significant difference between the Reflection and No Reflection conditions for 3-year-olds learning biological themes, there is a significant difference for the tool use stories, x2(1, N ,= 60) = 9.88, p < .Ol . Three-year-olds learn to learn about analogical transfer more readily with the biological themes material. This could be because the materials are inherently more interesting or because at a high level of abstraction the biological themes shared an action (change appearance) while the tool pairs did not (stack, swing, pull, etc.).

LEARNING BY EXAMPLE

Study 4

In the previous studies children were required to transfer a rule on the basis of previous examples. In the next set of studies, we examine a form of explanation-based learning from example. There is considerable interest in the field of Artificial Intelligence in expert systems that learn on the basis of a single example (DeJong & Mooney, 1986; Mitchell et al., 1986). Such systems work by elaborating on why the example in question sat- isfies the conditions of the concept under study. Explanation-based or analyses-based systems (Lewis, 1986) attempt to build generalizations by analyzing the essential features of a single example rather than attempting to extract the commonalities of a number of examples, as is the rule in similarity-based systems (Lebowitz, 1985). Similarly, recent work in cognitive psychology has been concerned with how adults use examples when learning from texts in such domains as computer programming (Le Fevre & Dixon, 1986; Pirolli & Anderson, 1985; Reder, Chamey, dz Mor- gan, 1986). The central issues concern (a) whether adults can generalize on the basis of one versus many exemplars of the rule (Kieras & Bovair, 1986); (b) whether they spontaneously use examples as a basis for generalization (Pirolli & Anderson, 1985); and (c) whether a statement of the general rule helps them use examples (Sweller & Cooper, 1985). None of this work has been conducted with children. In the next set of studies we examine 4-year-olds’ generalizations of biological mechanism on the basis of a single example.

Method Subjects. Fifty Cyear-olds (mean age-4 years 4 months) were recruited for this study.

Twelve were assigned to each of the three experimental conditions and 10 were assigned to a control group. Four were dropped from the study because they would not listen to the stories. There was an equal number of boys and girls in each group.

Materials. Six stories were designed for this study. Details are included in Table 5. Three stories illustrated the mimicry mechanism: the crested rat (skunk), the hawkmorh caterpillar (poisonous snake), and the Capricorn beetle that opens its wings to look like a wasp. The three remaining stories illustrated a second theme, natural pest conrrol, or biological de- terrents. These animals are exploited by humans to destroy unwanted pests, thus providing

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a natural biological solution rather than a chemical one. pilot data had shown that 4- year-olds could readily understand these examples when explained with reference to the well known cat-mouse analogy: The ladybug that farmers use to kill little white bugs (aphids) that grow on hops and orange crops; the manatee, a large water mammal moved by boat owners to Florida’s inland waterways because they eat the weeds that clog the river and hinder pleasure boating; and the purple martin, a bird that eats mosquitos.

Short stories were written about these animals. The stories contained problems for the children to solve via analogy. Each story included two irrelevant facts together with the critical information. For example, the purple martin story contained the critical information (separated by another fact) that (a) purple martins are birds that like to eat mosquitos, and (b) purple martins will live in man-made bird houses, but in the story it was not explicitly stated that the gardener could get rid of his mosquito problem by building a house for purple martins. Children were asked three questions about the story including the critical question, “How could the gardener get rid of his mosquitos ?” A correct answer would be like Jere- my’s, “well he could build a house for these purple martins at the bottom of the garden . . . but I think Raid is best-but it’s just like the others we talked about, like the ladybugs eating the farmer’s bugs-we talked about this.”

In the preceding studies, the stories were dissimilar in that both the animals and their specific mechanism of defense were unique. In order to further reduce surface similarity among stories, we introduced a specific predator or pest for each story so that no general term like “enemy” or “pest” could be used to trigger similarity at the surface level. In addition, the verbs used in the questions to tap the mechanisms were different from those used in the stories and different across stories. That is, in the mimicry question, the verbs used were trick, pretend, or fool the (named) predator and for natural pest control, the verbs used were want, like, or have natural pest controller (named) in their gardens, rivers, etc.

Procedure. The children were assigned to one of four conditions of a 2 x 2 design: Rule and Example, Present or Absent. The children in the Rule and Example condition were told the general rule: There are animals that protect themselves from enemies by looking like more scary animals or that there are animals who are friends to people because they eat nasty pests. They were also given the lirst problem as an explicit example of that rule, i.e., here’s an example like that, it’s the purple martin, it eats mosquitos, etc. Children in the Rule Only condition received only the general rule and no example. Children in the Example Only condition received the fmt problem with its specific solution but no general rule; the experimenter was careful not to state the high level abstraction (e.g., mimicking), only the current specific solution (look like a snake, etc.). And the remaining children served as a control, receiving neither examples nor rules, just an irrelevant story. Then all children were presented with the fmt transfer story as a problem to solve with no mention of problem similarity. This was followed by a second transfer problem.

Results

The proportion of correct solutions to the first transfer problem and the first theme encountered is shown in Fig. 4. The overall effect of conditions was reliable, x2(3, N = 46) = 17.58, p < .OOl. Children receiving Examples outperformed those that did not, x2(1, N = 46) = 14.68, p < .OOl. But the effect of having or not having a general Rule was not reliable, x2( 1) = 2.10, neither was the interaction of Rule x Examples x2 = .8.

The same pattern was repeated on the second theme. There were no significant differences between themes. The proportion correct for Rule


R”‘e Example m Rule mn

Exam&m Control m

I: STUDY 4 STUDY 5 STUDY 8

CONDITIONS

FIG. 4. Proportion of subjects solving the fast transfer problem in Studies 4, 5, and 6 as a function of condition.

and Example, Example, Rule, and Control was 1 JO, .94, .35, and .O, respectively. The overall effect of condition was reliable, x2(3, N = 46) = 31.22, p < .OOl. Students receiving examples scored extremely well and outperformed those who did not, x*(1, N = 46) = 28.55, p < .OOl. The interaction was not significant.

Turning to the second transfer problem (collapsed across theme), performance was again excellent with performance of 100,100,67, and 30%, respectively, for the Rule and Example, Example Only, Rule Only, and Control groups. This effect was reliable, x2(3, N = 46) = 19.80, p < .OOl. The difference between the Example Only and Rule Only conditions was reliable x*(1, N = 24) = 4.80, p < .05, but that between the Rule Only and Control was not. Having examples of the theme is better than having the abstract rule.

Study 5

Study 5 is a repetition of Study 4 with the exception that the stories were made more difftcult by the addition of more irrelevant facts (four vs two) because of the very high level of performance of the children in the Example Only condition. This near ceiling performance could have masked the additive effect of having both the rule and the example.

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Method Subjects. Forty-two Cyear-olds were selected from local day-care centers. There were

approximately equal numbers of boys and girls in each condition. The mean age was 4 years, 9 months.

Materials. These were the same as in Study 4 with the exception that two additional irrelevant facts were added to the stories.

Procedure. The procedure was identical to Study 4 with the exception that the children worked with only one of the two possible themes, half receiving mimicry and half working on natural pest control and they received only two of the possible three exemplars, forcing them to abstract the similarity on the basis of one example only.

Results

The results are shown in Fig. 4, together with the comparable data (Theme 1) of Study 4. The added irrelevancies did reduce the level of transfer considerably, but the pattern of results remained the same. The overall effect of conditions was reliable, x2(3, N = 40) = 8.99, p < .Ol. Children receiving examples outperformed those who did not, x2( 1, N = 7.48), p < .Ol, but the effect of having or not having a rule was not reliable, and neither was the interaction.

Discussion

Taken together the results of Studies 4 and 5 suggest that examples are more useful in promoting transfer than the provision of an explicit statement of the general rule. Note, however, that in both studies the abstract rule was provided by the experimenter, not the child. We have no means of knowing whether the child listened to, or understood, the rule as stated. Several recent studies of text learning suggest that adults rely on example information and disregard instructions (Le Fevre & Dixon, 1986; Sweller & Cooper, 1985). Particularly relevant is a series of studies by Reder et al. (1986), where it was found that externally provided information about examples was by no means as useful as elaboration of rules provided by the subjects themselves.

In Study 6 we examined the spontaneous elaboration of children leaming the biological themes. We sought to find out whether (a) the children could come up with an explanation of the biological theme on their own; (b) if so, at what level of abstraction; and (c) whether a child-produced explanation would influence transfer, whereas the experimenter-provided explanation did not.

Study 6

In Study 6 we looked at the efficiency of transfer given the status of children’s spontaneous recall, In a previous study using a single novel tool use solution, Brown et al. (1986) found that children who spontaneously recalled the common goal structure of stories transferred that goal


structure across stories with differing surface features, whereas children who concentrated on interesting but peripheral details in their recall did not transfer so readily, even though they understood the goal structure. Here we examined whether 4-year-olds who spontaneously recalled both the general rule “look scary” and the specific instantiation of that rule “be a snake” would outperform those who recalled the rule only, the example only, or neither piece of information.

Method Subjects. Forty-seven 4-year-olds, with a mean age of 4 years, 7 months were selected

from local day care centers. There were approximately equal numbers of boys and girls in each group.

Materials. The more ditficult materials from Study 5 were retained. Procedure. All subjects were treated the same. They received two stories from either the

mimicry or natural pest control theme. The first story contained several irrelevant facts and an explicit statement of the theme “helpful to humans because they get rid of harmful (nasty) pests.” The fust story also contained an explicit statement of why the particular example was an instance of that theme, e.g., “ladybugs get rid of little bad white bugs that eat the farmers’ crops” (corn substituted if children did not know the word crops). After hearing the story, the children were asked for spontaneous recall (tell me all about the story, tell me the best part of the story) before proceeding to the transfer problem. In the second story, the transfer problem, they needed to supply the theme, which was not directly stated, and infer the animals’ particular solution from the relevant pieces of information (that manatees eat water weeds, and that water weeds get in the way of boats).

Results

The results are shown in Fig. 4 together with the comparable data from Studies 4 and 5. The major difference is that whereas in Studies 4 and 5 the children were assigned to the four conditions; in Study 6, the data are opportunistic, i.e., based on children’s rated recall. Children were placed in the Rule and Example condition if they spontaneously reproduced both the general rule “look like a more scary animal” and the specific example “looks like a poisonous snake”; 32% of children recalled these details. Another 34% recalled the specific example, but did not mention the general rule; they were labeled the Example group. Only 15% of children recalled the rule, but did not give specific details of the example, and the remaining 1% of children recalled neither the rule nor the example, concentrating on the irrelevant details such as the fact that the manatee weighs 2000 pounds and is eaten by sharks and how can sharks eat a 2000-pound fish!

First, it is clear from Fig. 4 that children who spontaneously recall the theme and the example are performing better than both the remaining children of Study 6 and their counterparts in Study 5 who had the rule and example provided by the experimenter. The children who extracted for themselves the critical information of the concept and a specific instan-

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tiation transferred readily to a new instance. The overall effect of conditions was reliable, x2(3, N = 21.72), p < .OOl, but none of the pair-wise comparisons were. Again the advantage of having an explicit statement of the rule, in addition to the example, is not significantly better than having only examples, but the trend in all three experiments is in the right di- rection. Collapsing across groups, subjects who remembered the details of the example outperformed those who did not, x2(1, N = 10.45), p < .Ol.

Study 7

One problem with Study 6 is that we have no means of knowing whether the children who did not recall the example and rule had indeed encoded both pieces of information in the first place. In Study 7, we introduced an explicit prompting condition where children were required to state the general rule and provide an explanation of why the particular example in question was an example of that rule. This procedure is similar in spirit to explanation-based learning systems of AI that learn by constructing an explanation of why an example is an instance of the concept it exemplifies. The similarity is only superficial, however, in that most AI systems (DeJong 62 Mooney, 1986; Mitchell et al., 1986) have a great deal of knowledge about the domain in question and the goal structure of that domain (see, however, Lewis, 1986). The 4-year-olds, however, do not know about mimicry before entering our experiments. In Study 7, then we tested whether children can generalize on the basis of one instance if they are required to provide a rationale for why the example is an instance of the concept to be generalized.

Method

Subjects. Forty-seven 4-year-olds were selected from local day-care centers. Their mean age was 4 years, 9 months. Approximately equal numbers of boys and girls were in each group.

Materials. Three versions of the mimicry themes were constructed that included the critical facts, that hawkmoth caterpillars can look like poisonous snakes, and that birds love to eat caterpillars, but no specific mention of the theme or problem solution (look like a snake to scare predators) was made.

Procedures. The children were divided into three conditions. Twenty-one children were asked to listen to the fust story and were then asked two questions about it. The fust questions were designed to see if children could come up with a reason why a caterpillar might have the property of looking like a snake-“why would a furry caterpillar want to look like a snake?” The second question probed more explicitly for this information-“What could the furry caterpillar do to stop the big birds from eating him?”

Sixteen of the remaining children were told the reason why the caterpillar looks like a snake by the Experimenter. Finally, 10 children served as a control neither receiving nor being asked to produce a reason for the strange fact of snake resemblance.

After answering questions on the first story, the children received two more stories with


(a) no mention that they were similar and (b) no mention of the theme “look dangerous” or the importance of the markings.

Results

Consider first the 21 children in the condition in which the subjects must explicate the rule. Only 6 were able to do so on the basis of the open-ended question concerning the potential significance of the markings. All 6 (100%) transferred to problem 2. Thirteen of the remaining children did answer the second question explaining that looking like a snake would scare the bird away, thus inventing the mimicry solution; 85% of these transferred to problem 2. The remaining children who could not come up with an explanation failed to transfer. Thus 85% of subjects producing some explanation transferred to the next problem, whereas children not producing explanations did not.

Consider next a comparison of the conditions in which either the subject or experimenter provided the explanation of the mimicry theme. The data are shown in Fig. 5. On the first transfer problem, the difference between conditions was reliable x2(2, N = 35) = 18.28, p < .Ol. Subject explanations produced significantly better transfer than experimenter- provided explanations, x2( 1, N = 35) = 5.51, p < .05. The control chil-

TRANSFER PROBLEM 1 TRANSFER PROBLEM 2

SUBJECT CONTROL SUBJECT CONTROL EXPERIMENTER EXPERIMENTER

EXPLANATIONS

FIG. 5. Proportion of subjects in Study 7 solving the first and second transfer problems as a function of providing or receiving explanations of why the exemplar is an example of the rule.

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dren did not transfer, as they had learned nothing (no one provided an explanation of the markings). On the second transfer problem, the trend is repeated. The overall effect of conditions was reliable, x2(2, N = l&36), p < .Ol. The difference between the subject- and experimenter- provided explanations is significant, x*(1, N = 4.69), p < .05, and the experimenter-provided condition is significantly better than the control, x*(1, N = 5.85), p < 4.69.

Discussion

Taken together, Studies 5, 6, and 7 demonstrate the efficacy of having learners generate explanations of why an example is an instance of a concept. When this information was provided by the experimenter, it was no more effective than examples alone. However, when the justification was spontaneously recalled by subjects or produced by the subject as a result of prompting, transfer of the general rule to new instances of the concept is greatly enhanced.

GENERAL DISCUSSION

Preschool children can form a mind set to look for analogous solutions to problems that differ in surface features but share deeper relational commonalities. The learning to learn effect is rapid and dramatic. It occurs even when the problem pairs are not adjacent. Not only can children learn to apply a solution that they have just seen demonstrated, but they can select the appropriate analogy from a stream of past experiences.

Children as young as 3 years of age can learn to apply a new found rule by their third experience of analogical transfer, and for 4-year-olds, the effect is noticeable by the second experience. Four-year-olds show the learning to learn effect without being prompted; 3-year-olds benefit from instructions to discuss similarity. Note, however, that 3-year-olds spontaneously mention problem similarity when asked to teach the problems to a puppet, even though they are under no constraint to do so. And when they do, they perform equally as well as children who are told explicitly that the problems are the same, or who are asked to discuss similarity.

Exposing children to a variety of transfer experiences teaches them to search for underlying commonalities. This finding takes us beyond previous studies of analogical transfer, wherein children were told to concentrate on structure, and where their attention was directed to one and only one structural similarity (Brown et al., 1986; Holyoak et al., 1985). Here the children must form a set to transfer per se, whereas in previous studies they may have learned a single rule. For example, consider this interaction between an interviewer (M. J. Kane) and Billy, a 4-year-old exposed to three versions of the Genie story introduced by Holyoak et al. In the stories, a protagonist solves each problem by rolling a sheet of paper


into a tube with which to convey precious items across an obstacle (see Brown et al., 1986). Billy, having heard the Genie problem, now must figure out a second problem, how an Easter Bunny can get eggs across a river.

B: He could walk across. MJ: No, he can’t walk over water, nobody can. B: He could go around it. MJ: No, he’s gotta get across the water ‘cause it’s too far for him to go

around. B: Roll this thing up (points to paper) and then do it. MJ: Are you kidding? How did you think of that? B: ‘Cause I knowed it.

Before being faced with the third problem he spontaneously offered the following:

MJ: I’ve got another story for you. OK? B: But they all have problems. MJ: You’re right, every story is a problem. That’s why we are all here. B: And all you need to do is get this thing rolled up? I betcha!

In other words, Billy has learned that whatever the problem, he needs only to roll the paper into a tube, and it is this simple rule, and this alone, that he must transfer; he doesn’t even need to see the problem. In contrast, in the present study, the children did not know what solution they would encounter from pair to pair; they only knew they would have to look for the analogy. Set to look for analogies, they found them.

Preschool children are adept at learning from examples; under certain circumstances only one example suffices. If children spontaneously recall, or elaborate on why an example is an instance of a deeper relational mechanism, or if they are led to such elaborations by probing questions, they transfer readily. Elaborations and explanations provided by the subjects themselves are more effective in promoting transfer than those provided by the experimenter, an effect reminiscent of the use of self- produced elaborations in adult learning (Reder et al., 1986). Explanation- or analysis-based learning theories (DeJong & Mooney, 1986; Lewis, 1986) developed to explain machine learning do have psychological reality. Children who can explain examples learn.

“Why explain things during learning? It appears that explanations or- ganize knowledge about procedures in a way that supports generalization” (Lewis, 1986, p. 36). We argue that explanations force the subject to represent the problem in terms of a generalized mental model (Gentner & Stevens, 1983; Johnson-Laird, 1980) or a situation model (van Dijk & Kintsch, 1983), that is, a flexible schema allowing for a collection

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of similar situations, thus providing the proper basis for reasoning by analogy (Brown et al., 1986).

These studies also highlight the importance of reflection, one important form of metacognition (Brown, 1975, 1978; Brown, Bransford, Ferrara, & Campione, 1983; Flavell, 1977; Flavell & Wellman, 1977). They illustrate the importance of understanding, or knowing what you are doing while learning. Children who can explain examples and extract higher level commonalities understand what they are learning and hence transfer readily. Conditions that prompt the child to talk about, or teach, problem similarity all have a dramatic effect on learning; indeed, children who spontaneously choose to concentrate on problem similarity perform equally as well as children explicitly told to look for such similarity. Note that four- and five-year-olds do not need prompts to reflect, at least not on these simple problems, presumably because they are making comparisons on their own volition, a claim supported by their spontaneous verbaliza- tions .

Preschool children are not extreme Thomdikians: they can transfer on the basis of underlying structural similarity; they are not totally depen- dent on surface features to mediate transfer. In both the tool and animal scenarios, the problems contained neither object (protagonist) similarity (Gentner & Lander, 1985; Ross, 1988) nor mechanism similarity (looks like a snake). Regularity across problems was at the level of an abstract rule (mimicry). Although physical similarity obviously provides a crutch for young children’s learning, it also does so for older children (Gentner & Toupin, 1986) and adults (Anderson, 1987). Surface similarity is important for accessing information (Gentner & Lander, 1985), for reminding learners of previous examples that they might use, at least in the initial stages of learning (Anderson, 1987; Ross, 1988). Children are no different in this respect than adults. Thus, developmentally, we support a lack of knowledge hypothesis rather than a developmental stage or preference hypothesis. Children rely on appearance matches in transfer usually because they have no other basis on which to rely, as indeed, do novices learning in complex domains (Anderson, 1987; Chi et al., 1981; Pirolli & Anderson, 1985; Ross, 1988). And this tendency to fall back on perceptual similarity is not a bad strategy. Appearances usually are important. As Medin and Ortony (1988) point out, surface features are often constrained by deeper structural meanings; appearances are usually not deceiving; surface similarity is usually correlated with deep structural similarity; and organisms are sensitive to just these kinds of correlated relations that lead to the deeper and central properties. Because of these correlated relations, sensitivity to surface features has a high probability of paying off. Noting stable similarities among surface properties might act as a crutch to new learning while children are differentiating the core structures


within their emergent theories (Carey, 1985). For young children, and novices who have not yet differentiated the deeper structure, appearance matches serve as a fallback option when theory fails.

Dependence on surface similarities is useful but fallible, however, as all surface similarities do not correlate with deep structure. Appearances, as in the case of whales and fishes, can be misleading. If the child is captured by superficial features that are not rooted in a stable casual explanation, learning should be fleeting and fragile. The typical pattern of laboratory transfer suggests that it is just such momentary partial understandings that are being captured. Rapid, transitory judgments in the absence of causal explanation are not the basis for sustained learning or conceptual change (Brown, 1988).

We have no compelling explanation for the developmental effect found in these and other studies of laboratory transfer, but findings of developmental increases in transfer are ubiquitous (Brown, 1988; Brown & Cam- pione, 1981, 1984; Gentner & Toupin, 1986; Holyoak et al., 1984). Ifit is true that children readily show analogical transfer under appropriate conditions, what is the explanation of the persistent developmental trend?

The most commonly preferred explanations are (1) lack of knowledge, particularly coherent explanations of the domain in question; (2) differences in basic mental capacity, a moot point at this time; (3) ineffective general processing, or learning strategies; and (4) metacognitive difficulties, i.e., the ability to think about one’s mental representations and in- ferential processes (Brown et al., 1983). Problems with these factors: knowledge, capacity, strategies, and metaconceptual difficulties, could mask actual competence in the analogical transfer process itself.

The superiority of older children in laboratory transfer tasks holds true even when care is taken to tailor the task difficulty to the narrow age ranges under consideration, even when neither the young nor the old have the requisite specific knowledge to solve the problem. Yet with minimal prompts, 3-year-olds can proceed merrily through a series of problems, after experiencing the first solution, so it is difficult to imagine that the tasks are differentially overloading the information processing capacity of the very young. If it is not knowledge, because all are equated for their lack of it, nor overloaded capacity, then what is responsible for the greater efficiency of the relatively older groups?

Once knowledge and capacity are ruled out, learning strategies and metaconceptual competence still remain; and we believe it is advances in these general factors that underlie the pervasive development trend. One explanation is that the greater efficiency of the older children reflects the fact that they can perform for themselves the type of help that we provide to enhance performance. They are more capable of reflecting on their problem solutions, they expect to extract a general rule, they look for the

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rules of the game (Brown et al., 1983; Flavell, 1977). Efficient learners prepare for transfer by engaging in reasoning processes aimed at elaborating knowledge. With experience, efficient learners develop a mind set to regard new problems, not as isolated examples, but as instances of a general class. Efficient learners come to expect what they learn to be relevant elsewhere. Efftcient learners perform thought experiments in which they actively seek out appropriate analogies. In short, efftcient learners understand some of the principles involved in learning and reasoning; they have a greater metaconceptual grasp of the domain ‘ ‘learning. ’ ’

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preschool children can learn to transfer: learning to learn and learning from example

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