A Piagetian perspective on mathematical construction

In this paper, we offer a Piagetian perspective on the construction of the logico-mathematical schemas which embody our knowledge of logic and mathematics. Logico-mathematical entities are tied to the subject's activities, yet are so constructed by reflective abstraction that they result from sensorimotor experience only via the construction of intermediate schemas of increasing abstraction. The ‘axiom set’ does not exhaust the cognitive structure (schema network) which the mathematician thus acquires. We thus view ‘truth’ not as something to be defined within the closed ‘world’ of a formal system but rather in terms of the schema network within which the formal system is embedded. We differ from Piaget in that we see mathematical knowledge as based on social processes of mutual verification which provide an external drive to any ‘necessary dynamic’ of reflective abstraction within the individual. From this perspective, we argue that axiom schemas tied to a preferred interpretation may provide a necessary intermediate stage of reflective abstraction en route to acquisition of the ability to use formal systems in abstracto.     

Converging operations on a basic level in event taxonomies

Research on object concepts has identified one level of abstraction as "basic" in cognition and communication. We investigated whether concepts for routine social events have a basic level by replicating the converging operations used to investigate object concepts. In Experiment 1, subjects were presented with event names from a taxonomy and were asked to list the actions comprising the event. Many more actions were listed at the middle than at the highest taxonomic level, without a further increase at the most specific level, paralleling the pattern of superordinate-, basic-, and subordinate-level object concepts. From these action lists, brief stories were composed for each event. In Experiment 2, subjects made pairwise similarity judgments on the stories. The mean similarity of events increased with specificity, as expected. But differentiation of categories (within-category similarity compared to between-category similarity) was highest for super-ordinates, contrary to results with object categories. In Experiment 3, subjects were fastest in recognizing actions as belonging to events named at the basic level. In Experiment 4, subjects predominantly chose basic-level terms to name stories. We conclude that event taxonomies do show basic-level structure, albeit a less sharply defined and less stable structure than in object taxonomies. The benefits and hazards of extending models of object concepts to other entities, such as social events, are discussed.     

Negatively biased recall in children with self-reported symptoms of depression

This study investigated differences in depressed and nondepressed children's recall of positively and negatively reinforced behavior. Twenty-six children with self-reported symptoms of depression in the fourth through sixth grades were compared with a matched sample of 26 nondepressed children to determine if there was a negative bias in depressed children's recall. Subjects first generated guesses of the most common associations to each of a series of 40 words. Later, when compared with their nondepressed peers, the children with depressive symptomology were less accurate in recalling which words they had answered correctly and remembered fewer of their own correct responses. They also did more poorly when asked to recall the correct answers that had been provided by the investigator. The two groups did not differ, however, in their recall of which items had been answered incorrectly or in their recall of their previous wrong responses. These results suggest that children with self-reported depressive symptomology do not remember negative experiences more than do nondepressed children; rather, they recall positive experiences less well. Selective forgetting of positively reinforced behavior could be a serious handicap for depressed children in school. It could also play an important role in the maintenance and perhaps even the etiology of depressive symptomatology in children.We wish to thank Bruce Compas for his helpful comments on an earlier draft of this paper.     

Acquiring English at different ages: The English displacement effect and other findings

An analysis of the language backgrounds of 237 persons in a psychology department subject pool is presented. Specific findings indicate that (a) only about two-thirds of the subjects were native speakers of English, (b) native English speakers can be divided into several different groups on the basis of bilingual background and age of acquisition of their second language, (c) the number of native English speakers who would be considered ideal for psycholinguistic experiments in English (e.g., monolinguals and bilinguals who acquired a second language in or after adolescence) is only about a third of the sample, (d) nonnative English speakers appear to have their native, non-English-language abilities reduced as a function of their acquisition of English; that is, English appears to displace other languages that a person knows (the English displacement effect), and (e) age of English acquisition is shown to be an important factor, by correlating negatively with rated English abilities and reported Scholastic Aptitude Test (SAT) scores, and positively with rated ability in a non-English language.Portions of this research were first presented at the 59th annual meeting of the Eastern Psychological Association in Buffalo, New York, April 1988. I gratefully thank Doris Aaronson for the numerous comments she made on earlier versions of this paper.     

Image statistics and the perception of apparent motion

The short- and long-range apparent motion processes are discussed in terms of the statistical properties of images. It is argued that the short-range process, exemplified by the random-dot kinematogram, is primarily sensitive to the dipole statistics, whereas the long-range process, exemplified by illusory occlusion, is treated by the visual system primarily in terms of the tripole and higher statistical correlation functions. The studies incorporate the balanced dot, which is a unique stimulus element that permits high pass filtering while preserving detailed positional information. Low spatial frequencies are shown to be critical for texture segregation in random-dot kinematograms, independent of the grain size or number density of texture elements. Illusory path perception in the long-range process is shown not to require low spatial frequencies, but is sensitive rather to global temporal phase coherency. These results are interpreted in terms of the respective roles of the power and phase spectra in perceptual organization. The construction of balanced dots is discussed in detail.     

Cognition and metacognition at extreme altitudes on Mount Everest

The FACTRETRIEVAL2 test battery, which assesses both retrieval of general information from memory and metacognition about that retrieval, was administered to people before and after a recent expedition to Mount Everest and at extreme altitudes above 6,400 m (higher than any mountain in North America or Europe). The major findings were as follows: First, the same extreme altitudes already known to impair learning did not affect either accuracy or latency of retrieval, and this robustness of retrieval occurred for both recall and forced-choice recognition. Second, extreme altitude did affect metacognition: The climbers showed a decline in their feeling of knowing both while at extreme altitude and after returning to Kathmandu (i.e., both an effect and an aftereffect of extreme altitude). Third, extreme altitude had different effects than alcohol intoxication (previously assessed by Nelson. McSpadden, Fromme, & Marlatt, 1986). Alcohol intoxication affected retrieval without affecting metacognition, whereas extreme altitude affected metacognition without affecting retrieval; this different pattern for extreme altitude versus alcohol intoxication implies that (a) hypoxia does not always yield the same outcome as alcohol intoxication and (b) neither retrieval nor metacognition is strictly more sensitive than the other for detecting changes in independent variables.     

Predicate-argument structure as a link between linguistic and nonlinguistic representations

We present a study wherein a severe Broca's aphasic patient was trained to learn symbols representing both pure transitive and dative predicates--predicates differing in argument structure--in a visually based artificial language (c-ViC). We found a decrease in performance when two symbols, rather than one, were used to depict these "verbs." However, this decrease in performance was more pronounced for symbols representing pure transitive verbs--those that allow only one argument structure--than for symbols representing dative verbs--those that allow two different argument structures. Also, dative "verbs" yielded better performance when they were inserted in more complex, three-argument "sentences" than when they were inserted in two-argument "sentences." The opposite pattern was found for pure transitives. These results are discussed in terms of our claim that argument structure serves as a point of connection between linguistic information and non-linguistic visual information and in terms of the possibility that argument structure entries are shaped by the form in which visual information is parsed.     

How to study the kinetic depth effect experimentally

Sperling, Landy, Dosher, and Perkins (1989) proposed an objective 3D shape identification task with 2D artifactual cues removed and with full feedback (FB) to the subjects to measure KDE and to circumvent algorithmically equivalent KDE-alternative computations and artifactual non-KDE processing. (1) The 2D velocity flow-field was necessary and sufficient for true KDE. (2) Only the first-order (Fourier-based) perceptual motion system could solve our task because the second-order (rectifying) system could not simultaneously process more than two locations. (3) To ensure first-order motion processing, KDE tasks must require simultaneous processing at more than two locations. (4) Practice with FB is essential to measure ultimate capacity (aptitude) and, thereby, to enable comparisons with ideal observers. Experiments without FB measure ecological achievement--the ability of subjects to extrapolate their past experience to the current stimuli.     

Selfish genes vs. selfish people: Sociobiology as origin myth

The sociobiological version of human evolution is criticized as excessively reductionistic and focused on reproductive competition. An alternative version of evolutionary psychology is proposed based on the premise that the most important feature of human evolutionary history is selection for small group living. The structural requirements of group survival can account for fundamentally social motives characteristic of the human species such as cooperation, conformity, and group loyalty.Adapted from a symposium presentation at the annual meeting of the Society for Experimental Social Psychology, October 13, 1990, Buffalo, New York.     

The GRIMS. A psychometric instrument for the assessment of marital discord

Research in marital therapy has been disadvantaged by the lack of a good, short and recent psychometric questionnaire to objectively assess the state of a marriage for research, demographic and clinical purposes. The Golombok Rust Inventory of Marital State (GRIMS) is a companion questionnaire to the Golombok Rust Inventory of Sexual Satisfaction (GRISS), and concentrates on aspects other than the sexual in a dyadic relationship between two adults living together. It is a 28 item psychometrically constructed inventory designed to produce a single scale along which changes in a marriage may develop as marital therapy progresses. It has been shown to be valid for this purpose, and to have a good reliability.