British Journal of Educational Psychology (1998), 68,351-311 0 1998 The British Psychological Society

Printed in Great Britain

Third graders’ acquisition of knowledge of banking: restructuring or accretion?

Anna Emilia Berti* and Maria Grazia Monaci University of Padua, Italy

Background. Some scholars maintain that similar processes intervene in children’s cognitive development and in the history of science. According to Carey (1985), radical conceptual restructurings taking place during ontogene- sis are the counterpart of scientific revolutions. Other authors object that individual cognitive development is only of an incremental type and shows no resemblance to scientific revolutions.

Aims. The main aim was to investigate whether a radical restructuring in children’s conceptions of banking can be produced in a short time through explicit teaching.

Sample. A total of 58 third grade middle-class children participated.

Method. A curriculum on the notion of banking (involving deposits, loans, interest, and their relations) was implemented in a third grade class of 25 children. The curriculum lasted about 20 hours, distributed over two months. Two post-tests were carried out - a week and four months later - on both the experimental and the control group who received no training.

Results. Most children in the experimental group acquired and retained an understanding of banking. Only very limited progress was shown instead by the control group.

Conclusion. The comparison between children’s conceptions before and after teaching suggests that a conceptual restructuring had occurred. The way this result was achieved shows that restructuring should be viewed as the end product of changes of an incremental type rather than as a distinct process.

A growing number of developmental and educational psychologists argue that cogni- tive development and cognitive learning mainly consist in changes taking place within distinct and largely independent theory-like conceptual domains. According to some scholars (e.g., Carey, 1985; Gopnik & Wellman, 1994; Vosniadou & Brewer, 1992; Wellman, 1990) similar processes intervene in children’s cognitive development and in the history of science. In both cases there are different degrees of change, from the

*Correspondence and requests for reprints and related material should be addressed to Professor Anna Emilia Berti, Dipartimento di Psicologia dello Sviluppo e della Socializzazione, via Venezia 8,35131 Padova, Italy. E-mail: aeberti@psico.unipd.it

358 Anna Emilia Berti and Maria Grazia Monaci

simple addition or deletion of beliefs, which has been called ‘accretion’ (Carey, 1991; Vosniadou & Brewer, 1987), ‘enrichment’ (Spelke, 1991) or ‘accumulation of knowl- edge’ (Carey, 1985), to the restructuring of a cognitive domain.

According to Susan Carey, there are two kinds of restructuring, a weak and a radical one. Weak restructuring has been identified by comparing the performances in various tasks by experts in a relevant knowledge domain (such as physics, chess, or medicine) with those of intermediates and novices (Chi, Glaser & Rees, 1982). These comparisons have highlighted two main differences between the conceptual systems of experts and novices: ‘First, experts represent different relations among concepts (as in the change from “no motion without a force” to “no acceleration without a force”). Second, patterns among these new relations motivate the creation of new, abstract concepts and schemata that either are not represented by novices at all, or are not very accessible to them’ (Carey, 1985, p. 3). However, novices’ and experts’ systems of knowledge share many concepts. For instance, in the domain of physics ‘nodes corresponding to concepts such as force, energy, and so on can be identified in both systems, and the terms for these concepts either are identical or can easily be translated from one system to the other’ (Carey, 1985, p. 4).

The strong or radical restructuring has been identified by examining the history of sciences. When a scientific revolution occurs, ‘successive theories differ in three related ways: in the domain of phenomena accounted for, in the nature of explanation deemed acceptable, and even in the individual concepts at the center of each system’ (Carey, 1985, p. 4). As an example of these differences Carey proposes a comparison between Aristotle’s and Galileo’s theories of mechanics.

According to Carey, both weak and radical restructuring occur in individual cogni- tive development. They are testified by two different kinds of evidence. The first regards the conceptual systems of children at different age levels. For instance, the comparison between 5- and 10- year-olds’ concepts of animals and body functions shows that, unlike older children, younger ones do not yet possess the concept of a living being and interpret processes such as eating, breathing, growing, etc., in psycho- logical rather than in biological terms. Therefore, ‘the kind of conceptual reorganisation children experience during these years is at least as radical as the conceptual reorganisation adults experience when gaining expertise in some domain’ (Carey, 1985, p. 187).

The second kind of evidence suggesting restructuring is about resistance to change, as presented in educational studies (mainly in the field of physics) which report failures to learn or the long time needed to learn. According to Carey, ‘the reason that students’ misconceptions are so resistant to tuition is that learning mechanics requires a theory change of the sort achieved by Galileo’ (Carey, 1985, p. 7). Therefore, ‘Restructuring . . . is not accomplished by a few hours, or even many hours, of instruction’ (Carey, 1985, p. 192). Resistance to change appears in this view to be due to intrinsic characteristics of the knowledge acquisition systems. ‘The systems facilitate incremental addition of factual information but are resistant to wholesale abandonment of information. There is a strong inertial component that resists knowledge restructuring’ (Duschl, Hamilton & Grandy, 1990, p. 231).

A similar explanation has also been proposed for the data showing the distance in years between the most mistaken ideas and the more correct ones often found in cross-

Restructuring in children’s conceptions 359

sectional developmental studies of children’s supposedly spontaneous conceptions. For instance, Wellman (1990)’ commenting on children’s theories of the mind, states: ‘If the history of science is any guide at all, then changing such preconceptions requires a long period of accommodation and transitions, at times conceptual revolution’ (p. 146).

The parallel between children’s cognitive development and learning and the history of science has been challenged on different grounds. Harris (1994) has reviewed several differences between the collective activity of the scientific community and the cognitive processes of individual children and lay adults. Caravita & HalldCn (1994) have discussed some differences between a scientific community and a school class. Thagard (1992), after a detailed analysis of conceptual systems and the changes they can undergo, has highlighted the differences between scientific revolutions and the changes identified by the cross- sectional studies of Carey and other proponents of similar views. While scientific revolutions consist of the replacement of a whole conceptual structure with a different one, children’s cognitive development and students’ learning involve only piecemeal addition and deletion of concepts and beliefs. In this view, the difference between what Carey labels as ‘restructuring’ (both of the weak and radical type) and ‘accretion’ or ‘enrichment’ appears to concern the grain of analysis rather than the nature of the process, thus suggesting that restructuring could be nothing but the result of a sequence of changes of the accretion type.

Resistance to instruction can be explained in different ways other than by assuming that an inherently time consuming type of change is involved. Apart from motivational and contextual factors, (examined by Pintrich, Marx & Boyle, 1993), the notions taught might: a) presuppose the possession of a great amount of prerequisite knowledge (GagnC, 1985) or background knowledge (Chinn & Brewer, 1993) that the learner does not already possess; b) be constructed through the contemporaneous activation of several notions, thus exceeding the processing capacity of the learner (Case, 1985); c) involve the abandonment of deeply entrenched beliefs, that is beliefs that have a great deal of evidential support, or that participate in a broad range of explanations, or that satisfy strong personal or social goals (Chinn & Brewer, 1993). The relevant beliefs are not only those about the class of phenomena taught but also those about related phenomena and epistemology and ontology (Vosniadou, 1990). People are very reluctant to abandon entrenched belief, preferring to ignore, reject, or reinterpret information which does not fit (Chinn & Brewer 1993). Physics turned out to be a domain with a wealth of misconceptions entrenched in observation (Champagne, Klopfer & Anderson, 1980; McCloskey, Washburn & Felch, 1983; Vosniadou & Brewer, 1992). d) Many of the students’ preconceptions, especially in the physical domain, might take the form of procedural knowledge, that is knowledge of how to act, which is by its nature automatically and unconsciously used, and difficult to change (Hashweh, 1986).

In the field of cognitive development, factors a) and b) of the above list have been stressed more when explaining the distance in years from one conception to a different and more correct one, or the long time it takes to acquire certain abilities. Indeed, several major theories represent cognitive development as a gradual construction of complex abilities and abstract concepts. This occurs through the progressive differ- entiation and hierarchical integration of more elementary and concrete skills and concepts within a particular task domain, and their subsequent generalisation to other

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domains (Case, 1985; Fischer & Farrar, 1987; Flavell, 1963). However, the other factors could also apply. Lastly, when children are not formally taught about a certain topic, the long persistence of incorrect conceptions could be due to the lack of opportunity to receive information about the topic or reflect on it.

In order to check if it is the true nature of the processes making up conceptual restructuring, rather than other factors, which requires time and provokes resistance, intervention studies are needed, implementing curricula on notions so distant from children’s preconceptions that their acquisition could be seen as an instance of radical restructuring. To carry out such studies, conceptual domains meeting the following demands should first be identified: a) in the absence of explicit teaching they should develop through stage-like sequences, with lower and higher levels so distant from each other as to suggest different ontologies and explanations; b) misconceptions character- ising their lower developmental stages should not rely mainly on perception, which is a powerful source of entrenchment; c) the misconceptions should not have the form of procedural knowledge; d) the domains should be made up of subdomains that can be easily singled out and taught independently from one another, so that learners are not overwhelmed by a huge amount of information and the role of knowledge accretion and restructuring can be disentangled.

The domain of economic institutions meets the above requisites for the following reasons: a) cross-sectional studies on children’s economic understanding (reviewed by Berti & Bombi, 1988; Furnham, 1996) have shown sequences including striking misconceptions and great, qualitative differences between the ideas expressed by the youngest and oldest subjects; b) mistakes appear to arise from interpretation of what is observed, rather than from observation. For instance, the perception of a person driving a bus is veridical. The mistake is in the inference, drawn by many children, that the bus driver is also the owner of the bus (Berti & Bombi, 1988); c) misconceptions regard institutions about which one has limited fist hand experience; they are there- fore unlikely to have a procedural form; d) individual subsystems such as the factory, shop and bank can be taught separately, thus testing if concept restructuring is possible when it does not involve the acquisition of a lot of new information.

Due to the above characteristics, economic concepts appear particularly tailored to an examination of the severity of changes a conceptual structure can undergo as a function of its distance from the notion taught, without interference from extraneous factors such as misleading observation, the procedural form of the cognitive structure to be changed, and the amount of information to be learned.

The economic subsystem considered in the present study is banking. According to the literature (Berti & Bombi, 1988; Jahoda, 1981; Jahoda & Woerdenbagch, 1982; Ng, 1982; Takahashi & Hatano, 1989,1994; Wong, 1989) children’s conceptions of banking in the absence of formal teaching develop following a stage-like sequence. Preschoolers and kindergarten age children either do not know the bank or think that it is a place where anybody can go and get money. From age 6/7 to 9/10 years children say that only people who have previously deposited money can go and get it. At 9/10 children know that the bank also lends money but they do not relate deposits to loans. The deposit money is locked in a safe in separate envelopes or boxes and is not touched again until it is returned to its owner, whereas loan money is obtained from external sources, such as the state or local council. Only at about 11/12 do children make the connection

Restructuring in children’s conceptions 361

between deposits and loans. At these levels, knowledge about interest is fragmentary. Lastly, children are aware of interest on both deposits and loans and connect them, stating that the bank can pay deposit interest thanks to the interest that it receives, in turn, from loans. However, in western countries only a small minority of adolescents at the ages of 14 to 16 recognise that loan interest is higher than deposit interest, thus allowing banks to pay their employees and earn a profit (USA: Wong, 1989; Italy: Berti & Bombi, 1988; Great Britain: Jahoda, 1981).

Some characteristics of the above sequence suggest that knowledge restructuring rather than mere enrichment is involved: 1) The transition from the most incorrect conception to the correct one is very slow and gradual. 2) In the transition from one level to the next, new relations between concepts are introduced: the relations between the money taken from the bank and that previously deposited, deposits and loans, loan interest and deposit interest, bank earnings and the difference between loan interest and deposit interest. 3) In the most advanced conception, the superordinate concept of interest, intended as ‘money paid to keep somebody else’s money for a certain time’, appears. These three characteristics suggest that the transition between levels involves at least a weak restructuring. The two subsequent characteristics suggest that even radical restructuring occurs: 4) There are changes in individual concepts. For instance, the bank, initially conceived as a place where money is kept safe, becomes an institution providing for the circulation of money. 5) The domain of phenomena explained by the conceptions also changes. Thanks to the difference between deposit and loan interest the source of money for bank employees can be identified.

If the above analysis is correct, leading children from the lower to the higher levels of the sequence on banking means producing a radical restructuring. If this could be achieved in a short time by teaching all the individual concepts and relations involved step by step, it would be shown that differences in nature between radical restructuring and enrichment do not exist.

Attempts to teach the notion of banking have already been successfully performed with Italian fourth and fifth graders (of 9 to 10 and 10 to 11 years of age respectively). Fifth graders (most of whom did not know about interest and did not relate deposit and loans) showed significant improvement at a post-test carried out two weeks after one lesson (Berti, 1993) or a couple of lessons on banking (Berti 1994, Study 1). A percentage of 62 per cent and 65 per cent of children in the two studies reached the highest level in the sequence. Fourth graders participated in a much longer inter- vention, lasting 18 hours distributed over three months, which was aimed at teaching not only banking but also the notion of shopkeepers’ profit (Berti, 1994, Study 3). These children showed significant improvement at the end of the curriculum (with 76 per cent of them, versus none at pre-test, knowing deposit and loan interest and their relation). Further, they also showed substantial conservation of what had been learned, in a follow-up study carried out eight months after the intervention. However, a significant regression was found in the notion that bank employees are paid with loan interest, which had shown the least progress after the interventions, thus appearing the most difficult to learn.

Much less successful had been an attempt to teach banking in a couple of lessons to third graders (8 to 9 year-olds), which led only 13 per cent of them to understand deposit and loan interest and their relation (Berti, 1994, Study 2). Due to the short

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duration of the intervention (only two hours in all) it was not possible to check if this was a consequence of the large amount of information being distributed over a short time, or to children’s resistance to abandon their conception of ‘strict reciprocity’ according to which you must return exactly the same as you borrow (Jahoda, 1981).

In the present study, bank functions have been taught to Italian third graders, that is at the lowest grade at which this topic can be dealt with, given that at lower grades children have not yet been taught the prerequisite arithmetic skills and notions, at least in Italy. In contrast to the previous studies, which examined or taught only deposit, loans, interest, and their relations, other aspects of banking, such as automatic teller and cheques, have been considered. Taking profit from the previous studies and the hindrances to understanding they have highlighted, a further aim of the present investigation was to improve the curriculum already tried with fourth graders, so that the great majority of children involved could learn all the notions taught. Finally, unlike the above studies, which adopted only a pre- post-test design, the present study also comprised a control group.

Method

Participants The experimental group was one third grade class attended by 25 children (16 girls and nine boys). The control group was made up of two third grade classes, attended by a total of 33 children (12 girls and 21 boys). All the children lived in a small Italian town and were from a middle class background. Their average age, at the beginning of the study, was 8 yrs 4 months.

Design The study was divided into four parts: 1) pre-test, a semistructured interview on banking, carried out with all the children about one week before starting curriculum implementation; 2) curriculum implementation (two units a week for five weeks) only with the experimental group; 3) post-test carried out with all the children about ten days after the end of the curriculum; 4) delayed post-test, again involving all the children, four months after the fist post-test. Both post-tests consisted of the same questions as the pre-test. Only the amounts of money mentioned in the questions about deposit and loan interest were changed. Each test session lasted about 25 minutes. Children were tested individually by a female interviewer in a quiet room. Interviews were recorded and transcribed. Due to budget limitations, it was not possible to engage an interviewer blind to the intervention status of the children. However, the inter- viewer was experienced in semi-structured interviews and trained not to ask leading questions.

Interview on banking We describe here the points asked about. Question order and wording depended on children’s answers and on the words they used themselves.

Children were first asked if they had ever seen cheques or heard of them. If they said yes, they were asked about the function of cheques, why people sometimes use cheques instead of money, how somebody managed to have cheques. Next, the interviewer told

Restructuring in children’s conceptions 363

of a person paying for a refrigerator with a cheque, and asked the children what the shopkeeper does with this cheque. If they said that he or she takes it to the bank and receives back money, they were asked where that money came from. Similarly, children were asked about what automatic tellers are, where the money comes from, what people have to do in order to have it.

Then questions about what the bank is and what it is for followed. When children said that the bank is to put money in, they where asked how the money is kept, everybody’s all together or in separate containers; why people take money to the bank; what the bank does with that money, what current and saving accounts are. Children’s knowledge of interest was explored by describing a person who took 10,000 lire to the bank and after one year went to the bank to get all her money back. Children had to guess how much money she would get and why. It should be recognised that 10,000 lire is a very small amount (about &3), but pilot interviews showed that third grade children could not manage larger numbers. If children mentioned interest, they were asked where the bank gets the funds to give this extra money.

If children did not spontaneously mention bank loans, they were explicitly asked if people can borrow money from the bank. Then it was assessed how the bank gets the money for loans. Next, knowledge of loan interest was examined by describing a person who borrowed 10,000 lire from the bank and after one year paid the money back. The children were asked how much money she would have to pay back. If children mentioned both deposit and loan interest, they were invited to compare the two amounts with the following questions: ‘Let’s see again how much more money the bank can give you if you deposit 10,000 lire for one year. If you borrow 10,000 lire for one year, how much more do you have to give back? Why?’ The interviewer repeated the amounts mentioned by the child highlighting their relation (same, or one greater than the other), to make sure that she meant what she said, and asked her to explain the reason. Lastly, children were asked who pays the people working in the bank and how the money is found to pay them.

Curriculum on banking The curriculum on banking was planned according to the directions of the literature on conceptual change (Strike & Posner, 1985; Vosniadou, 1990) and included several activities such as class discussion, lessons, arithmetical exercises, text reading.

The purposes of class discussions were to make children aware of both their conceptions and the possible difference between theirs and other children’s concep- tions, and to learn from their peers’ answers when some children were more knowledgeable than others. Further, by linking notions taught in class with the beliefs children had constructed from pieces of knowledge collected outside the school, discussions were intended to prevent those notions from becoming inert knowledge, stored in a separate memory (Renkl, Mandl & Grueber, 1996).

The lessons were aimed at teaching children the notions that had not emerged from the discussions. When these notions were quite different from children’s conceptions, this difference was highlighted, in order to prevent children from either missing or misunderstanding it (Vosniadou, 1990). The assumptions underlying children’s miscon- ceptions were also taken into account, so that the notions taught could be fully understood. For instance, it was said that, differently from what most children believed,

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the banks need not keep each person’s deposit money in different containers, because people are not worried about getting back the very same money they had deposited, but only the same amount. So, all the bank needs do is keep a note of the money deposited by each person, writing the amount in a book or computer.

The notions taught in the class were presented in short texts which children could read and study, and whose comprehension was checked through open and closed written questions. Arithmetical exercises were needed to have children practise with the notion of interest. At the same time, they helped linking arithmetic with everyday problems and social studies. The content of the curriculum is presented in Table 1.

Scoring Answers on each topic of the interview were scored as correct, incorrect, or ‘don’t know’. Correct answers were those stating the contents listed in the first column of Table 2. Incorrect answers were those diverging from them which will be described in the Results. One person scored all the protocols. A second person scored ten protocols. The two judges reached a percentage agreement of 98 per cent.

Results

The percentage of correct, incorrect and ‘don’t know’ answers given by children from experimental and control groups at pre-, post-, and delayed post-tests are presented in Table 2. Between-group comparisons of frequency of correct answers at pre-test (as opposed to incorrect and ‘don’t know’ merged) were carried out by means of chi- squares. Within-group comparisons were carried out by means of the McNemar test.

As shown in Table 2, at pre-test children either expressed correct conceptions about some points or answered ‘don’t know’, while diffuse misconceptions emerged about other points. Bank deposits and loans turned out to be the topics known by the majority of children both from the experimental and control groups. However, although when explicitly asked the majority recognised that you can borrow money from the bank, differently from deposit, only a minority of children spontaneously mentioned loans when asked about what a bank is for ( N = 3). Cheques, automatic tellers and how banks find the money for loans and their employees’ wages were the topics about which the majority of children had no ideas (as revealed by the frequency of ‘don’t know’ answers). Various widespread misconceptions were expressed about the other topics. According to the majority of children, each person’s deposit money is kept separately and is not touched until its owners come to claim it; people who leave their money at the bank receive back exactly the same amount as deposited if not less (as stated by a couple of children) because you have to pay for the custody; similarly, people borrow- ing money from the bank must give back the same amount as they received. Other wrong conceptions, expressed by a minority of children, are the following: money for cheques comes from the money that the bank itself makes, or the deposits of other people - not those who signed the cheques, or is given by the local council; money for loans comes from sources such as a money factory, the local council, tax; deposit interest and bank employees are paid with tax or deposit money.

At pre-test, children from experimental and control groups showed on the whole the same pattern of answers with the only exception of one unexpected difference: the

Restructuring in children’s conceptions 365

Table 1. Structure of the curriculum on banking ~~ ~

Unit number Concepts to be taught Instructional intervention, students’ Length activities

1 2 hours

2 2 hours

3 2 hours

4 2 hours

5 2 hours

6 1 hour

7 1 hour

8 2 hours

9 2 hours

10 2 hours

11 2 hours

- Each person’s deposit money is not kept separate from the others. - The main functions of the bank are to keep deposit money and to lend money.

- The bank uses the money deposited to give loans. - Extra money, that is interest, is given to people who deposit their money in the bank.

- The longer people leave their money in the bank the more money they receive as interest.

- Different types of deposit: current and saving accounts. - Automatic teller and cheques are means of getting money from one’s own current account.

- Rehearsal of the notions already taught.

- Loan interest.

- Loan interest is higher than deposit interest. This allows the bank to pay for its expenses and to make a profit.

- The interest paid by those who borrow money from the bank depends on how much money has been borrowed and for how long.

- Rehearsal of the notions already taught. - Banks’ expenses.

- Analogy between banks and shops.

- Checking children’s learning.

- Class discussion. - Teacher explanation.

- Class discussion. - Teacher explanation.

- Class discussion. - Arithmetic exercises: calculating deposit interest as a function of the amount of money deposited and the time it is left in the bank.

- Class discussion. - Study a short text. - Answer open-ended questions.

- Discussion. - Arithmetic exercises. - Role play: receiving automatic teller and cheques from a bank; using them to pay at shop.

- Discussion.

- Class discussion. - Teacher explanation.

- Teacher explanation. - Arithmetic exercises: calculating loan interest as a function of the amount of money borrowed and the time it is kept.

- Answer open-ended questions. - Arithmetic exercises. - Multiple choice questionnaire. - Class discussion.

- Class discussion. - Teacher explanation. - Making up a board comparing banks and shops.

- Multiple choice questionnaire. - Open-ended questionnaires. - Arithmetic exercises.

366 Anna Emilia Berti and Maria Grazia Monaci

experimental group turned out to be less knowledgeable about the automatic teller. At the first post-test, all the children in the experimental group showed great progress, with percentages of correct answers ranging from 68 per cent to 100 per cent. This

Table 2. Percentage of correct (incorrect /don’t know) answers given by children from experimental and control groups at pre-, post- and delayed post-tests.

Experimental group Control group (N = 25) (N = 33)

Content examined pre-test post-test delayed pre-test post-test delayed post-test post-test

A cheque is for paying 44,(0/56) 92 (018) 58(0/42) 60,(0/39) 70(0/30) The money for a cheque 12,(12/76) 72,,(8/20) 88(4/8) 24,(21/54) 30,(18/51) 48,(12/39) comes from the deposit of the person who pays it

paying or for getting money Automatic teller money 20,(0/80) 96,,(0/4) 96(0/4) 60,(0/60) 57,(0/42) 67(0/33) comes from its owner’s deposit The bank keeps deposit 64,(36) 100, 100 79,(21) 87(13) 96,(4) money* Everybody’s deposit 20,(80/0) 96,,(4/0) 100 33 (54/12) 24( 73/3) 18( 82/0) money is kept altogether Deposit money increases 12,(78/10) 100,b 100 30(64/6) 36,(64/0) 36(64/0) The bank lends money 76,(24/0) loo&, 100 48(43/9) 51,(49/0) 67(33/0) Loan money comes from 24,(8/68) 84,,(0/16) 80(4/16) 18(0/82) 12,(9/79) 25(0/75) deposit money Those who borrow money 4,(96/0) 96,,(4/0) 96(4/0) 12(88/0) 18,(82/0) 21(79) from banks have to give back more The bank pays deposit 0,(0/100) 68,b (20112) 68(24/8) 0(6/94) Ob(6/94) 0(30/70) interest with the interest it gets from loans Loan interest is higher O,(O/lOO) 92,,(8/0) 84(12/4) 6(0/94) 12,(0/78) 15(0/85) than deposit interest Bank employees are paid 0,(32/68) 72,,(16/12) 76(20/4) 6(39/54) 3,(39/58) 6(39/54) with the money the bank gets from loan interest

Note. Matching letters in the same row differ significantly as shown by chi squares (comparisons between experimental and control groups) or McNemar (comparisons within groups), p < .01 (Roman) or p < .05 (italic). The first figure in brackets indicates the percentage of wrong answers. The second figure indicates the percentage of don’t know answers or children not asked a certain question because of the absence of prerequisite knowledge, as for instance the source of money for loans with children not knowing about bank loans.

the figure in brackets indicates the number of children who mentioned bank functions different from keeping money, such as loans, payment of tax and bills.

The automatic teller is for 20,(0/80) loo& 100 60,(0/60) 64,(0/36) 73 (0/27)

*Incomplete rather than incorrect answers were found concerning the banks’ functions, so

Restructuring in children’s conceptions 367

caused significant differences both in the within-group comparison with pre-test (McNemar) and in the between-group comparison with control children’s perfor- mances at post-test (chi-square). Delayed post-test showed no significant regression after four months in the experimental group, thus pointing out that the achievements were very stable. In the control group, no significant difference between pre- and post- test, and between post- and delayed post-test emerged, while a couple of significant differences were found between pre- and delayed post-test regarding knowledge of bank deposits and the source of money to pay cheques.

Conclusion

This study has shown that a curriculum on banking produced stable changes in conceptions of banking for third grade children who did not know about some of the bank’s services and showed misconceptions about others. At pre-test, the majority of these children had little knowledge of cheques and automatic tellers; they believed that each person’s deposit money is kept separate from the others’, while money for loans comes from different sources, and that people who deposit or borrow money from the bank receive or have to pay back the same amount as deposited or borrowed. Some children expressed wrong ideas about the source of money for bank loans and payment of bank employees, while the majority gave ‘don’t know’ answers. At the two post-tests, the first ten days, and the second four months, after the intervention, most children appeared to have filled their knowledge gaps and revised their wrong conceptions. They knew what cheques and automatic tellers are and where the money needed comes from. They connected deposits to loans, knew and connected their interest, knew that deposit interest is lower than loan interest and that their difference allows the bank to pay its employees and other expenses.

With respect to the previous study involving third graders (Berti, 1994, Study 2), these data show that also at 8 to 9 years of age children can be led to an understanding of banking, provided that all the knowledge involved is supplied step by step through a long-lasting intervention. Therefore, even at that age children’s learning of the notion of interest does not appear to meet any resistance by strongly held principles of strict reciprocity. With respect to the study involving fourth graders (Berti, 1994), these data show that the notion of bank employees being paid with loan interest, which in that study was taught less successfully, can also be learned very well provided that children’s attention is called to it and their misconceptions explicity challenged.

In the absence of teaching, conceptions of banking changed instead very slowly. Within the six months required to accomplish this study from the pre- to the delayed post-test, the control group showed very little progress, becoming more knowledgeable about the source of money to pay for cheques, and bank loans. No progress or even small regression occurred in other notions, namely those about interest, the link between loans and deposit money, and the source of money for bank employees. Comparison between the notions showing progress and those showing no progress or even small regression suggests that the latter are more relational in nature and more remote from children’s experiences. While children may witness a person paying or receiving cheques, or overhear parents talking about the opportuneness of asking for a bank loan, they have little possibility of coming across payment of bank employees or

368 Anna Emilia Berti and Maria Grazia Monaci

hearing about how the bank obtains money to lend. The great advance made by the experimental group suggests that the lack of progress in the control group is due to the limited opportunities of having relevant experience or receiving pertinent information within the six-month time interval of the investigation, rather than to the fact that more time is needed for those notions to develop by restructuring pre-existing concepts.

According to the analysis presented in the Introduction, the changes occurred in the experimental group correspond to a conceptual restructuring, at least of the weak type. They were yielded by an intervention during which children’s misconceptions were explicitly disconfirmed and new knowledge was gradually introduced. This suggests that conceptual restructuring is not a distinct process, but the end result of a sequence of more elementary processes of addition and deletion of rules and concepts, as suggested by Thagard (1992). The curriculum which brought about the change, although distributed over five weeks, required a total of about 20 hours, part of which was spent in arithmetic exercises. This means that, contrary to what was stated by Carey (1985), when factors such as entrenchment and lack of background or prerequiste knowledge are not involved, conceptual restructuring does not need much time to take place.

Although much shorter than the time needed to produce concept restructuring according to Carey (1985), the 20 hours spent to teach banking to third graders was much longer than the single hour or couple of hours it took to teach this topic (even if not with the same rate of success) to fifth graders. The additional time spent in the third grade was partly due to the broader scope of the intervention, which comprised also notions of the cheque, automatic teller, different kinds of deposit. Further, part of the time was spent in arithmetical exercises. Similar to the third graders of the present study, most of the fifth graders did not connect deposits and loans and did not know about interest, but differently from them they were more skilled in arithmetic (Berti, 1993,1994, Study 1). Thus it appears that, in the case of explicit teaching, what takes time is the acquisition of prerequisite knowledge, rather than the restructuring of the conceptions of banking per se.

The progress following our intervention has being striking if compared with the resistance to learning, or regression to naive conceptions after learning, highlighted when other topics were investigated (see Eylon & Linn, 1988; Gardner, 1991). This suggests that in those cases other factors, different from the requirements for restruc- turing, had hindered or prevented conceptual change. The study of factors such as cognitive load, lack of prerequisite or background knowledge, and the various sources and types ,of entrenchment, might prove to be more fruitful than the tenet that some types of cognitive changes are similar to conceptual revolutions, thus taking a long time to accomplish.

Striking progress has been highlighted also by other studies on the teaching of economic notions. They have shown that successful learning takes place when children already possess the prerequisite knowledge (Berti, 1992), or their preconceptions are challenged and all necessary information is gradually provided in involving environ- ments and by promoting active participation (Ajello, Bombi, Pontecorvo & Zucchermaglio, 1986, 1987; Kourilsky & Carlson, 1996). Correspondingly, failure in learning appears to be due to a poor fit between children’s previous knowledge and the information made available at school (Berti, 1991). This suggests that some factors

Restructuring in children’s conceptions 369

hindering knowledge restructuring in other domains - such as, for instance, in the case of physics, the entrenchment of beliefs due to perceptual experience - are not operating in the domain of economic (and possibly societal in general) institutions. The relative ease with which children learn about economic topics adds to the arguments of the proponents of more instruction about society during elementary school (some of which are reviewed in Ahier & Ross, 1995).

Children’s understanding of an economic subdomain does not involve that this knowledge be applied to other subdomains. We do not expect that the participants in our study transfer their understanding of bank interest to the relations between a factory’s costs and revenue. Indeed, third graders’ knowledge of factories is very poor (Berti, Bombi & Lis, 1982). A training study on the notion of shopkeeper profit (which, according to cross-sectional studies, is acquired at about 9-10 years, see Berti & Bombi, 1988) has shown that third graders do not generalise the notion of profit from the shop to the factory (Berti, Bombi & De Beni, 1986). Abstract economic notions, such as costs, profit, or enterprise, thus appear to be constructed through generalisation from more concrete ones, similar to how it has been suggested for other kinds of skills and knowledge (Fisher & Farrar, 1987). In order to lay the foundation for the teaching of those abstract notions, the instruction about individual subsystems, such as bank, factory, shop, etc. could be started as early as elementary school years.

While the notion of shopkeepers’ profit was successfully taught to third graders who already possessed the prerequisite arithmetic skills in only one lesson, in the present study it took 20 hours to teach the notion of banking at the same school level. Should this notion be retained in a third grade curriculum nevertheless? Or should that great amount of time be more profitably spent teaching children more fundamental skills, such as writing and arithmetic? Considering both the key role of the bank in the economic system, and the pivotal role of children’s widespread misconceptions of banking in supporting their misconceptions of other economic institutions (see Berti & Bombi, 1988), we think that children’s understanding of banking should be promoted as early as possible. Further, it should not be forgotten that some of the hours needed to teach banking were in reality spent on arithmetic exercises, which allowed children to practise operations which in any case they would have had to practise (even if not calculating interest). Banking, besides being an interesting topic itself, could also be a context for exercising arithmetic skills meaningfully.

Acknowledgments

This research has been supported by grant CNR 94.03768.CT.08. We are grateful to Alberta Bordin, who implemented the curriculum in her class, and to the pupils of the schools Marconi and Maria Ausiliatrice in Montebelluna, who participated in the study. Some of these data were presented as a poster at the Conference ‘The Growing Mind’, Geneva, September 14-18,1996.

370 Anna Emilia Berti and Maria Grazia Monaci

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(Manuscript received I3 October 1997; final version 1 December 1997)