Tag Archives: exchanges

Warneken: Young children share the spoils after collaboration

Warneken, F., Lohse, K., Melis, A. P., & Tomasello, M. (2011). Young children share the spoils after collaboration. Psychological Science, 22(2), 267–73. http://doi.org/10.1177/0956797610395392

Interesting paper.

1) The authors postulate that the relationship between joint collaboration and sharing is crucial for understanding the origins of equality, both in ontogeny and phylogeny. Therefore, they investigate how children actively divide rewards after working for them in a collaborative problem-solving task.

Most studies on sharing involve windfall situations, in which resources are given to the children by a third party, with no work or effort involved. Moreover, many studies use a forced-choice paradigm with predefined allocation options, which does not allow for an assessment of how children themselves would actively negotiate over how to distribute resources with another person.

In contrast, Warneken et al.’s research is guided by the notion that people often have to work toward obtaining resources, and that they distribute those resources actively, rather than choosing individually between predefined options. Previous studies, they say, have not shown how children share resources in situations that might be the cradle of equality: actual joint collaborative activities with a social partner.

2) The experiment closely resembles sharing experiments with chimpanzees and other non-human primates. Warneken et al test children in dyads. Children have to perform a task together: they have to pull from both ends of a rope at the same time in order to bring a box close to them. In this way, they are able to get a reward (such as stickers or candy that have been placed in the box). In one condition, the box has two holes far apart, so that each child can get her reward without interference from the other participant. In a second (“clumped”) condition, the box has only one hole, and therefore only one child can access the rewards at a time.

3) Warneken et al. found that neither the reward type nor the opportunity to monopolize rewards in the clumped condition interfered with the children’s collaboration. 3 year-olds collaborate successfully in situations in which resources can be monopolized. The collaborative abilities of young children, compared with those of chimpanzees, are not constrained to the same extent by a tendency to monopolize resources.

Children predominately produced equal shares. They shared rewards equally most of the time, even when rewards could be monopolized more easily (clumped condition). At an age when children are just beginning to skillfully collaborate with peers, they already engage in sharing behavior that results in equitable outcomes.

4) What does it all mean? Competition over resources, the authors claim, is mitigated in human children (when compared with chimpanzees and other primates) by an emerging sense of equal sharing of the spoils, which enables successful collaboration even early in ontogeny. Thus, the authors claim that this study supports a Tomasello-like evolutionary hypothesis, according to which the emergence of cooperation is due not only to cognitive and behavioral skills, but also to a reduction in competition over resources. Competition over resources is mitigated in human children by an emerging sense of equal sharing of the spoils, which enables successful collaboration even early in ontogeny.

5) According to this study, children are capable of equitable distributions a very early age. Although many studies place the origins of equality at around 5, 6 or even 7 years of age, it all depends on how the concrete distribution problem is presented to the children. Warneken et al. present children with a collaborative, non-competitive situation. In addition, in this study the peer is present; the dyad works together in a problem solving activity (compare this with economic games that are played by a single present individual and an absent, anonymous, “invisible”). Even more, some of the dyads comprise children who know each other well, since they attend the same day-care center (they are not one-shot interactions, as in most economic games). All this seems to help even 3 year-olds to produce equitable outcomes early in development. The authors reach the conclusion that, perhaps, children learn to acknowledge each other’s right to gain equal resources in situations in which they collaborate to produce a mutually beneficial outcome that one person acting alone would not be able to achieve (this result is not proven by the experiment, in my opinion).

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Dialogue of the deaf

Dialogue of the deaf

I had a stimulating discussion with a neuroscientist the other day. I tried to explain to her that my interest in children’s cognitive development is linked to my interest in epistemology, that is, to what I refer to in this blog as the normativity of thought.

For example, I argue that researchers who try to explain children’s knowledge of math from a nativist point of view, can only explain the starting point of cognitive development. The starting point is innate mathematical knowledge, which is mostly implicit, and basically consists in an ability to identify the numerosity of collections of objects found in the outside world. In other words: researchers have shown that animals (humans included) have the innate ability to assess the size of a collection of perceived objects (for example, they can notice that a collection of 15 pebbles is greater than a collection of 10 pebbles). They can also discriminate among exact quantities, but only when dealing with small sets (two, three, and perhaps four objects). Also, some animals and human babies can perform elementary arithmetic operations on small sets (adding two plus one, subtracting one from two, etc.) I am referring here to studies by Dehaene (2011), Izard, Sann, Spelke, & Streri (2009), Spelke (2011), and many others.

This basic capacity is certainly different from fully-fledged “human math.” The latter involves, at the very least, the symbolic representation of exact numbers larger than three. We (humans) can represent an exact number by saying its name (“nine”), or by using a gesture that stands for the number in question (depending on the culture, this might be done by touching a part of one’s body, showing a number of fingers, etc. – see Saxe ( 1991) and also http://en.wikipedia.org/wiki/Chinese_number_gestures). And, of course, we can write down a sign that represents the number (for example, with using the Arabic numeral “9”).

Scholars agree on the fact that advanced math is explicit and symbolic, and that it builds on (and uses similar brain areas to) its precursor, innate math. Once they operate on the symbolic level, humans can do things like: performing operations (addition, subtraction, multiplication, division, and others), demonstrating mathematical propositions, proving that one particular solution to a mathematical problem is the correct one, etc. To sum up: our symbolic capacities allow us to re-describe our intuitive approach to math on a precise, normative, epistemic level.

Now, here’s when it gets tricky. I argue that the application of algorithms on the symbolic level is not merely mechanical. Humans are not computers applying rules from a rule book, one after the other (like Searle in his Chinese room). Rather, as Dehaene (2011) argues, numbers mean something for us. “Nine” means nine of something (anything). “Nine plus one” means performing the action of adding one more unit to the set of nine units. There is a core of meaning in innate math; and this core is expanded and refined in our more advanced, symbolic math.

When executing mathematical operations (either in a purely mental fashion, or supported by objects) one gets a feeling of satisfaction when one arrives to a right (fair, correct, just) result. Notice the normative language we apply here (fair, correct, right, true, just). We actually experience something similar to a sense of justice when both sides of an equation are equal, or when we arrive to a result that is necessarily correct. (Note to myself: talk to Mariano S. We might perhaps do brain fMRIs and study if the areas of the brain that get activated by the “sense of justice” in legal situations, also light up when the “sense of justice” is reached by finding the right responses in math. If a similar region gets activated, that might suggest that there is a normative aspect to math that corresponds to the normative aspect of morality).

For me, then, the million dollar question is: how do humans go from the implicit, non-symbolic, automatic level to the explicit, symbolic, intentional and normative level? What is involved in this transition? What kind of biological processes, social experiences and individual constructions are necessary to achieve the “higher,” explicit level? (These are interesting questions both for the field of math and for the field of morality). And my hypothesis is that this transition necessarily demands the intervention of a particular type of social experience, namely, the experience of the normative world of social exchanges and rules of ownership (I’ve talked a little about such reckless hypotheses in other posts of this blog).

Now, when I try to explain all this to the neuroscientist, I lose her. She doesn’t follow me. For her, human knowledge is the sum of a) innate knowledge and b) learning from the environment. Learning is the process by which our brain acquires new information from the world, information that was not pre-wired, that didn’t came ready to use “out of the box.” Whether such learning involves a direct exposure to certain stimuli that represent contents (a school teacher teaching math to his or her students) or a more indirect process of exposure to social interactions is not an interesting question for her. It doesn’t change her basic view according to which there are two things, and two things only: innate knowledge and acquired knowledge. What we know is the result of combining the two. And this is the case both for humans and for other animals. Period.

Something similar happens when I talk to her about the difference between “cold processing” and “hot processing.” We were discussing the research I am conducting right now. I interview children about ownership and stealing. In my interview design, children watch a movie where one character steals a bar of chocolate from another, and eats it. The interviewer then asks the child a series of questions aimed at understanding her reasoning about ownership and theft. Now, the movie presents a third person situation. This means that the child might be interested in the movie, but he or she is not really affected by it. Children reason about what they see in the movie, and sometimes they seem to say what they think it’s the appropriate thing to say, echoing adults’ discourse. Because, after all, the movie is fiction, not the real world.

I believe that normativity emerges not from absorbing social information that comes from external events (watching movies, attending to teachers’ explanations) but from children’s real immersion in first person, real world, conflictive situations. When a child is fighting against another for the possession of a toy, there are cries and sometimes there even is physical violence. These encounters end up in different ways; sometimes children work out a rule for sharing the scarce resource, sometimes they just fight, and sometimes an adult intervenes and adjudicates in the conflict. The child’s reactions during these events is not dictated by cold reasoning but by deeper impulses. It is in these situations where we should look for the emergence of our basic normative categories, such as reciprocity (both social and logical, or “reversibility”), ownership (or the relationship between substance and its “properties”), quantity (used to implement equity and equality), etc.

But, again, my biologist friend does not feel that the distinction between the impulsive, intense, hot reactions we experience when involved in real conflicts and the kind of third person reasoning that is triggered by movies and artificial stimuli is an important one. In both cases, she argues, it’s the same cognitive system that is at work. What we think about third person characters is probably similar to how we reason about ourselves (thanks to our capacity for empathy, our mirror-neurons, etc.)

I don’t know who’s right and who’s wrong here.

 

Dehaene, S. (2011). The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition. The number sense How the mind creates mathematics rev and updated ed (p. 352). Oxford University Press, USA. Retrieved from http://www.amazon.com/dp/0199753873

Izard, V., Sann, C., Spelke, E. S., & Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Science, 106(25), 10382–10385.

Saxe, G. B. (1991). Culture and Cognitive Development: Studies in Mathematical Understanding. Hillsdale: Lawrence Erlbaum Associates.

Spelke, E. S. (2011). Quinian bootstrapping or Fodorian combination? Core and constructed knowledge of number. Behavioral and Brain Sciences, 34(3), 149–150.

 

Clarification on the purpose of my planned experiment on “practical math”

What follows is the response to some questions my friends Philippe and Samar raised about the experiment I describe here (previous post).

1) How is the normative context you are proposing different from a school math context?

I try to embed math problems in narratives that remind children of everyday, familiar situations that involve observance or transgressions of exchange and distribution rules. Such narratives, I believe, will awaken children’s sense of justice and motivate them to balance a situation that they see as unbalanced or unfair (“A gave a present to B but B didn’t make a matching present to A”, “A stole something from B”, etc.) Such narrative contexts should remind children about the institutions and rules or reciprocity that govern exchange and distribution. So, this is very different from the formal, instructional school context.

I’m not primarily focused on the educational applications. My questions are theoretical. I’m interested in mapping the social aspects of human cognition. If my work gets the desired results, then the educational applications might follow… but that’s not a primary goal for me. The experiment aims at proving a theoretical point.

2)  Do you think that the social/normative context of math problems would boost children numerical competence?

Yes, my hypothesis is that the social-normative context of these math problems will probably improve children numerical competence. But I would not expect any deep or long term effects from just one session. My idea is as follows: if we can use this one session to show just a local effect of the narrative context on how children construe and solve these problems, this is relevant enough. This would prove that social meanings are transferred to the mathematical domain and have an impact on children’s performance. I think that proving such local effect is much simpler than doing a longitudinal study (which might be a second step in the research). I also proposed to “do some standardized numeracy tests (perhaps those used by Opfer & Siegler, Dehaene, Piagetian conservation tests, etc.) right after the main task in order to evaluate if each of these normative contexts has “sensitized” the child to quantities in a special way.” In other words, we would not be testing for any lasting effects, but we would test numerical competence and/or quantity conservation right after the main experiment, to see whether this “sensibility” to number gets transferred to different problems. So this would only test for immediate effects, but we are interested in the child’s performance in a second, apparently unrelated problem, in the domain of math, to see if there is a “spill-over” from one situation to the other.

3) Why should normative and social context as provided in the narrative improve children’s performance?

Math problems that involve some kind of “equalization” between different parties are social in nature. This type of math was created historically to deal with such social problems (barter and purchase, paying back, getting even, managing debt). The history of math seems to go hand in hand with the history of human exchange and distribution systems. For example, the popularization of coins and the establishment of a class of merchants seems to happen at the same time as (and probably facilitate) the emergence of formal arithmetic. Calculus (developed simultaneously by Newton and Leibniz) is invented at a time when the first stock exchanges are being created.

We are not merely providing children with a social metaphor in this experiment, we are re-embedding math problems in their original social context. It’s the meaningfulness of the situation that should impact on children’s performance. This is the idea I want to test.

4) Where’s the novelty of your approach? 

Most current researchers (Dehaene, Opher, Siegler, Spelke, Lourenco, among many others) are interested in the innate, Approximate Number System (ANS) that humans share with other animals. Although there are differences among authors in the details, there is consensus that such a system is a pre-condition for the development of symbolic number and arithmetic (which are unique to humans). These authors show that symbolic number builds upon such innate capacity but they don’t provide good explanations about how we go beyond the ANS and up to human math. They mention “culture” but they treat culture as a mere collection of arbitrary conventions, technologies and techniques. In the case of number, culture is seen as providing a more or less fast and effective set of arbitrary procedures to perform calculations.

So, again, my immediate aim is not so much to discover the best strategy for training kids or to improve academic performance in the long term, but to prove a theoretical point about the social nature of math.

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.

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.