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The Development of Equity and Logico-Mathematical Thinking

1978; Wiley; Volume: 49; Issue: 4 Linguagem: Inglês

10.1111/j.1467-8624.1978.tb04072.x

1467-8624

Jay Hook,

Pragmatism in Philosophy and Education

ion, me more than you, out of its concrete work context, that is, relative reward. The implication of unidimensional theory for moral education is that such a child can understand the nominal notion that, for him, work and reward are associated, but he cannot handle the ordinal notion that persons who do more work get more reward. The implication for research into the causes of the work-reward link is that the concept (the dependent variable) is best studied: When work is present, reward is present. In addition to making reward allocations irrelevant to work, the 5-year-olds, as hypothesized, kept more for themselves than they contributed to their dyad partners. However, in the postexperimental interview, they assigned vignette characters equal rewards, no matter what the characters' relative work. This suggests that the 5-year-olds' actual allocations had a greedy basis, inconsistent with their detached judgments of what is fair. Also, in the postexperimental interview, only five of 27 5year-olds accurately recalled either the amount of work they and their partners had done or the rewards each had been allocated. In fact, their recollections seemed almost randomly distributed through, and even outside of, the possible ranges (0-8 work units, 0-20 pennies), with means in the middle of those ranges. This casts some doubt on Leventhal and Anderson's (1970) contention that 5-year-olds distort their memory of relative work to cognitively eliminate the inequity generated by their previous selfish allocations. The second theory, appropriate from about 7 to 12 years, is best labeled ordinal. The child of this period, as the present RPP results suggest, transfers a relational concept from one dimension to another but does not form and compare ratios. Moral and legal curriculum (taxes, torts) on distributive justice should focus on serial order relationships between dimensions. The person who does the most work gets the most reward. Ordinal stands in opposition to the multiple norm interpretation. Previous researchers (Chertkoff & Esser 1977; Leventhal & Anderson 1970) have argued that allocations which fall between those predicted by equality and proportional norms represent the individual's internal compromise between two norms. Such an interpretation implies the rather remarkable (for this age group) activity of calculating proportional and equality solutions and averaging them-a ratio of a ratio operation. Ordinal explains the many in-between results in this age group (table 1) without assuming nearly so much activity. The third theory, appropriate after about 12 years, is proportional theory. However, researchers should probably note two caveats. First, the present RPP results suggest that many 13-year-olds give final solutions to logico-mathematical problems consistent with an understanding of ratio proportionality. Our clinical investigation, however, revealed that many of these solutions were reached by a nonratio process of recursion. For example, in the RPP 24 item, 13-year-olds could determine that the longer blue train carried 18 marbles by dividing groups of eight marbles (the total number of train cars) into piles of six and two, then repeating the process until all the marbles were exhausted, then counting the marbles in the larger pile. This gave proportional answers This content downloaded from 207.46.13.83 on Fri, 13 May 2016 06:37:44 UTC All use subject to http://about.jstor.org/terms 1042 Child Development without proportional thought. Second, seemingly proportional allocations could be shown before proportional thought competence by using a completed equity design (Brickman & Bryan 1976), in which the experimenter manipulates work and reward and then asks subjects to rate the consequent equitable or equal allocation in terms of fairness. This design asks the subject to react to an already accomplished equitable allocation, rather than creating one. Proportional theory is not the only theory which implies the formation and comparison of ratios that has been, perhaps erroneously, applied to the social judgments of children under 13 years old. For example, Anderson's (1973) cognitive algebra theory has been used to predict the toy preference judgments of children from 4 to 12 years old without reference to ability changes in that age range (Butzin & Anderson 1973). The present research, particularly the RPP data, is inconsistent with such an approach, as is other social perception work (Kuhn & Brannock 1977; Kun, Parsons, & Ruble 1974) which suggests that preadolescent social judgments are best characterized as additive rather than multiplicative. As hypothesized, there is a strong relationship between the RPP and allocation data when both are expressed as scores. This raises the question: Is one logically necessary for or the cause of the other? Researchers influenced by Piaget (1968) and Kohlberg (1967; Lee 1971; Tomlinson-Keasey & Keasey 1974) have published evidence that moral judgments are built upon, and subsequent to, more basic logical thought structures. Damon (1975) adopted this perspective in his study of positive justice judgments. Vygotsky (1962) argued that formally instructed, scientific concepts precede analogous spontaneous concepts from everyday life. On the other hand, the position of the French sociological school (Durkheim & Mauss 1963) is that logical concepts (e.g., space) derive from analogous social concepts (e.g., property or territory). The present data fall short of causal explanation for two reasons: mediation and lack of temporal priority. The logico-allocation relationship is mediated by age, such that the overall relationship is not replicated within each age group. Future research should include subjects from age groups straddling the transitions between the three theory periods rather than, as in the present study, groups solidly in the middle of the periods. Such transitional data would be more likely to reveal an unmediated logico-allocation relationship because, unlike the present data, all the subjects would not have had a chance to reach the mature ability characteristic of the period on both dimensions. This strategy, together with longitudinal, panel data, might reveal whether the logical or the allocative behavior characteristic of the period is prior. Although the present design failed to rule out age as a mediator or to determine whether the logical or the allocative is prior, it does constitute a distinct advance over previous research on logico-moral synchrony (Damon 1975; Lee 1971; Tomlinson-Keasey & Keasey 1974). In previous work, global stages of logical judgments (e.g., formal operations on Piaget's balance and combination tasks) were related to global stages on moral judgments (e.g., Kohlberg's principled moral stage) with no specific hypothesized thought structure common to both. Furthermore, the two stage responses, logical and moral, frequently made very different demands on the child's language and memory. Moral measures are usually verbal, logical measures more motor, creating d6calage problems. In the present research, the logical and allocative reflect the same underlying structure presented in a manner that made the same demands of language and memory.