Developmental sequences in class reasoning and propositional reasoning

Bateson and Wright on Number and Quantity: How to Not Separate Thinking from Its Relational Context

As part of his explication of the epistemological error made in separating thinking from its ecological context, Bateson distinguished counts from measurements. With no reference to Bateson, the measurement theory and practice of Benjamin Wright also recognizes that number and quantity are different logical types. Describing the confusion of counts and measures as schizophrenic, like Bateson, Wright, a physicist and certified psychoanalyst, showed mathematically that convergent stochastic processes informing counts are predictable in ways that facilitate methodical measurements. Wright’s methods experimentally evaluate the complex symmetries of nonlinear and stochastic numeric patterns as a basis for estimating interval quantities. These methods also retain connections with locally situated concrete expressions, mediating the data display by contextualizing it in relation to the abstractly communicable and navigable quantitative unit and its uncertainty. Decades of successful use of Wright’s methods in research and practice are augmented in recent collaborations of metrology engineers and psychometricians who are systematically distinguishing numeric counts from measured quantities in new classes of knowledge infrastructure. Situating Wright’s work in the context of Bateson’s ideas may be useful for infrastructuring new political, economic, and scientific outcomes.

New tools, new insights: Kohlberg’s moral judgement stages revisited

In this paper, four sets of data, collected by four different research teams over a period of 30 years are examined. Common item equating, which yielded correlations from .94 to .97 across datasets, was employed to justify pooling the data for a new analysis. Probabilistic conjoint measurement (Rasch analysis) was used to model the results. The detailed analysis of these pooled data confirms results reported in previous research about the ordered acquisition of moral stages and the relationship between moral stages and age, education, and sex. New findings include: (1) empirical evidence that transitions between “childhood” and “adult” stages of development involve similar mechanisms; (2) support for the notion of stages as qualitatively distinct modes of reasoning that display properties consistent with a notion of structure d’ensemble; and (3) evidence of a stage between Kohlberg’s stages 3 and 4. Consistent with reports from earlier research, the relationship between age and moral development is curvilinear. The relationship between educational attainment and moral development is linear, suggesting that educational environments have an equivalent impact across the course of development. Older males have slightly higher scores than older females after age and education are taken into account (accounting for 0.3% of the variance in moral ability).

An Application of Configural Frequency Analysis

Development of class reasoning was investigated using configural frequency analysis (CFA). We administered class inclusion, vicariant inclusion, and law of duality tasks to a sample of 540 Chinese second through fifth graders. In each task, children were asked to compare two classes and make a choice from four alternative answers while the number of classes was not given. Results showed that (1) children’s performance on both class inclusion and vicariant inclusion tasks improved significantly from Grade 2 to Grade 3 and from Grade 3 to Grade 4, but children did not tend to give correct answers to class inclusion items until Grade 4 and to vicariant inclusion items until Grade 5; (2) children from Grades 2 to 5 performed poorly on the law of duality task, but fifth graders were more likely to respond correctly than the general population; and (3) second graders tended to give wrong answers such as “equal number” and “not sure.” A discussion of the development of class reasoning followed.

The Relationship Between Deductive Reasoning Ability, Test Anxiety, and Standardized Test Scores in a Latino Sample

One Hundred and Twelve Latino students from Philadelphia participated in this study, which examined the development of deductive reasoning across adolescence, and the relation of reasoning to test anxiety and standardized test scores. As predicted, 11th and ninth graders demonstrated significantly more advanced reasoning than seventh graders. Error response patterns revealed a steady, age-related increase in the ability to use falsification strategies. Test anxiety was not related to reasoning performance. These results are discussed in terms of developmental theories of deductive reasoning. Negative correlations between deductive reasoning and standardized test scores for 11th graders are discussed in light of accountability standards required by the No Child Left Behind Act.

“ Good Education Is… ” The Development of Evaluative Thought Across the Life Span

The author uses a cognitive developmental approach to investigate educational conceptions, addressing the question, How does evaluative reasoning about education change over the course of cognitive development? The author conducted independent analyses of the developmental level and conceptual content of 246 interview performances of individuals aged 5 to 86 years. The developmental level of the interview performances was assessed with a content-general scoring system, the Hierarchical Complexity Scoring System. A Rasch analysis of the results revealed 6 developmental levels and provided support for invariant sequence, developmental spurts and plateaus, and similar developmental patterns for childhood and adulthood levels. The results of the subsequent analysis of the propositional content of the same interview texts were used to produce qualitative descriptions of changes in evaluative reasoning about education across the 6 levels identified in the data. Finally, descriptions constructed in this way, although richer and less prone to reification, were shown to be conceptually analogous to the stage definitions produced by other cognitive developmental researchers. The implications of the method and findings are discussed.

Age, memory load, and individual differences in working memory as determinants of class-inclusion reasoning

We studied the effects of individual differences in speak-span scores and variations in memory demands on the class-inclusion performance of 10-, 13-, and 15-year-old children. The speak-span task was an age-appropriate modification of Daneman and Carpenter's (1980) reading-span task and was considered to be a measure of global resources. The age variable was assumed to be a global index of skill development, and some of the specific skills hypothesized to be important in class-inclusion reasoning were estimated using a mathematical model. The results from both regression analyses and the mathematical model indicated that differences in age, speak span, and memory load all affected performance. Surprisingly, the effects of speak span and memory load were independent. However, the effects of each of these variables depended on the age level of the participants. Based on these findings, we argued that (a) resources vary continuously with age, (b) both skill level and global resources should be varied in developmental studies of problem solving, and (c) resource theories (e.g., Norman & Shallice, 1986) should be modified to account for developmental change.