Tag Archives: reciprocity

Thinking about an experiment on “practical math” in normative contexts

I am trying to think about an experimental situation that would allow me to test how normative-institutional contexts impact on children quantitative reasoning. Ideally, it has to be an easy experimental task that can be tested quickly with children from different cultures. What follows is a half-baked draft. Your feedback and criticism is most welcome.

So this is the idea… Children (ages 4 to 7) are interviewed individually. During the interview, they are shown a series of very short puppet plays. After each play children are questioned about the best way to solve a problem that arose in the play. Children are required to offer quantitative answers to such problems; for example, “how much money does character A have to pay character B to get even?” or “How many blocks does character A need to add in order to complete the building?”, etc.  The narratives are different in nature. Some narratives provide a social and normative context to the problem, in the sense that they highlight certain social rules children need to take into account in order to respond appropriately to the situation. Other narratives, by way of contrast, highlight “technical” or “engineering” problems, and involve means-ends reasoning. They problems they involve are similar to the normative problems in their mathematical content, yet the narrative context is markedly different.

Examples:

A1: “Negative reciprocity and reparation”. Character A has a bag with three candy bars. Character A shows the bag to character B and tells her that she loves candy bars and that she plans to eat them with her friends the next day. Character A goes to sleep. Character B steals the bars and eats them. Character A wakes up and finds character B stole the candy, and asks character B to return them. Character B says she doesn’t have the candy anymore but that she can offer character A some money to make up for the stolen candy. She opens a purse and drops some coins and bills on the table. The child is asked to choose the coins and bills character B has to hand over to character A in order to get even. They child is questioned about how she made that decision; and how she calculated how many bills and coins that character B must give character A.

A2: “Destruction and reconstruction”. The child is shown a tower formed by six big blocks. The child is told that a powerful storm and strong winds hit the building during the night and broke the three upper stories of the building. She’s then given a number of smaller blocks of different sizes and is asked to rebuild the tower so that it is as high as it was before the storm. The child is questioned the criteria she used to select the blocks and to decide how many blocks to use.

B1. “Positive reciprocity”. Character A visits character B and shows up with a present: a stack of stickers or trading cards. Each character returns to her own home. Then character B says that character A was really nice and that she would also like to give her a present to “get even”. The child is asked to help character B prepare her present. She is shown a cup and a collection of marbles and is told to fill the cup up until there are enough for A’s present. The child is also asked about how she decided how many marbles to give; i.e. to justify her decision.

B2. “Bridging the gap”. The child is shown a model of a river. On the river there is half bridge built with legos. The bridge starts on one shore and goes only half-way over the river. The child is asked to pick the lego pieces that she would need to build the other half of the bridge. The set of lego pieces the child can choose from have a different size than the ones used to build the first half of the bridge.

All four situations involve some kind of addition and subtraction of different units; they also involve compensating different dimensions of problems (values of the goods exchanged, sizes of different objects, etc.) A1 and B1 are “social” and “normative”: they involve the concept of justice; A2 and B2 are “technical”: they involve a kind of means-ends reasoning.

One possibility is to give situations A1-B1 to one group and A2-B2 to a different group. One could then compare the reasoning and argumentation of children who are given a “normative” vis- à-vis a “technical” narrative. To this end, one might use the theory of argumentation and other tools of discourse analysis. One could also do some standardized numeracy tests (perhaps those used by Opfer & Siegler, Dehaene, Piagetian conservation tests, etc.) after the main tasks in order to evaluate if each of these normative contexts has “sensitized” the child to quantities in a special way; i.e. if the children who just completed the “technical” problem perform better or worse than the children who did the “social-normative” problem.

Another possibility is to give the same children all four situations so as to compare the features of quantitative thinking in technical vs. normative contexts in the same children.

Still thinking…

“Let’s trade” and “my turn”

My son L. is 3y 1m old. He’s started recently to use the expression “let’s trade” (“te cambio”). That is: he produces speech acts aimed at swapping objects with another person. For instance, he gives away his glass of milk in order to obtain a yoghurt cup I have. We exchange goods. He seems to understand that the proto- contract we thus celebrate involves the mutual surrender and handing over of possessions. The rules of reciprocity are no doubt regulating this interaction. Which doesn’t mean that the child can understand conceptually, let alone articulate, such rules.

In addition, when playing with other children, L. knows how to claim his turn to use a toy (shouts “¡Turno mío!”). He also uses this expression in other contexts; for instance, to demand his turn to drink mate (in a mate round shared with adults). Again: his understanding of the reciprocity rules involved is perhaps incipient. But L. is clearly starting to master the rhetorical forms that allow efficient access to the desired objects.

My hypothesis: the child first masters the rhetorical forms, and only later the conceptual content. Piaget’s prise de conscience (the conceptual, explicit insight) is the final product of a process that starts with immediate, un-reflected action. The process goes from the periphery of action to the center of explicit, conceptual thinking. Differently from Piaget, however, in the periphery I do not see the actions of an organism but the utterances of a retor.

Ritualized exchanges at three years of age

My son L. is taking a bath. He’s 3 years – 1 month. After playing around in the water for a while, he says “I’m a fish”. Then looks at me and says: “I am a penguin.” I reply: “Hello, penguin”. He: “Nice to meet you”. Then he adds: “I pay” (extends his hand as if giving me money). I extend my hand and say: “Here is your change.” Then he says: “Here’s a gift” (and again extends his hand). So I say, “Oh, what is it?” He answers: “A perfume”. He then gives me several more presents, sometimes saying that the gift is “a perfume”, and at other times saying it’s “a surprise”.

I find this sequence very interesting. Our interaction comprises a continuous series of conventional behaviors that are typically used to start social exchanges and to keep them alive. So we go from “greetings” to “payment,” and then to “gift-giving”. Children, of course, do not understand payments as a way to deliver a certain amount of monetary value in the context of a sale or some other economic contract. Rather, they ​see payment as a ritualized exchange, in that sense similar to gift-giving or greeting rituals (as we know from the research in the area of children’s economic notions, such as Berti and Bombi’s, Delval’s, Jahoda’s and Danziger’s among many others). All the actions performed by Leon are instances of ritual exchanges, realized with a purely associative purpose, that is: he interacts in order to keep me engaged in interaction.

On L. Marshall’s “Sharing, talking and giving”

Just finished reading “Sharing, talking and giving” (Marshall, 1961). Great article. As the author summarizes it: “This paper describes customs, practised by the !Kung Bushmen in the Nyae Nyae region of South Africa, which help them to avoid situations that are likely to arouse ill will and hostility among individuals within the bands and between bands. Two customs which seem to be especially helpful and which I describe in detail are meat-sharing and gift-giving. I mention also the !Kung habits of talking, aspects of their good manners, their borrowing and lending, and their not stealing.”

A couple of details were interesting for me:

Taking possession: When they hunt, “The owner of the animal is the owner of the first arrow to be effectively shot into the animal so that it penetrates enough for its poison to work. That person is responsible for the distribution”. Note: the owner is not the head of the band, or the person who organized the hunt, or the person who shot the arrow. The owner of the animal is the owner of the arrow (who often is not even be part of the hunting expedition). Ownership of the tool (arrow) becomes ownership of the hunted animal.

Associative reciprocity: !Kung Bushmen make presents. And the motives for this “are the same as in gift-giving in general: to measure up to what is expected of them, to make friendly gestures, to win favour, to repay past favours and obligations, and to enmesh others in future obligation. I am sure that when feelings of genuine generosity and real friendliness exist they would also be expressed by giving”. A nice list that sums up what I mean by “associative reciprocity”. As Demi, a !Kung informant, tells the anthropologist: “a !Kung never refuses a gift. And a !Kung does not fail to give in return. Toma said that would be ‘neglecting friendship’.”

Marshall, L. (1961). Sharing, talking, and giving: Relief of social tensions among! Kung Bushmen. Africa, 31(3), 231–249.

Out of reciprocal exchanges, morality emerges

More Rochat:

Children between three and five years develop an understanding that they are potentially liable and that they are building a history of transactions with others. Needless to say, parents and educators foster this development in all cultures, but this fostering is essentially the enforcement of the basic rules of reciprocity, the constitutive elements of human exchanges. Children are channeled to adapt to these rules they depend on to maintain proximity with others. From this, they begin to build a moral space in relation to others, a moral space that is essentially based on the basic rules of reciprocity.

Again: Rochat, P., 2009. Others in Mind: Social Origins of Self-Consciousness. New York: Cambridge University Press, p. 180.