An attempt to understand students' understanding of basic algebra

This paper reports the results obtained with a group of 24 14-year-old students when presented with a set of algebra tasks by the Leeds Modelling System, LMS. These same students were given a comparable paper-and-pencil test and detailed interviews some four months later. The latter studies uncovered several kinds of student misunderstandings that LMS had not detected. Some students had profound misunderstandings of algebraic notation: Others used strategies such as substituting numbers for variables until the equation balanced. Additionally, it appears that the student errors fall into several distinct classes: namely, manipulative, parsing, clerical, and “random.” LMS and its rule database have been enhanced as the result of this experiment, and LMS is now able to diagnose the majority of the errors encountered in this experiment. Finally, the paper gives a process-oriented explanation for student errors, and re-examines related work in cognitive modelling in the light of the types of student errors reported in this experiment. Misgeneralization is a mechanism suggested to explain some of the mal-rules noted in this study.     

Role of referent concreteness in the acquisition of passive sentence comprehension through abstract modeling

The present experiment tested the hypothesis that development of syntactic comprehension through verbal modeling is enhanced by referent concreteness as a contextual influence. Young children heard a model narrate a series of events in passive form while the model either performed the corresponding activities, showed pictures portraying the same activities, or displayed no referential aids. In accord with prediction, verbal modeling with enactive referents produced higher levels of comprehension of passives than modeling with pictorial referents or modeling without referential aids. Modeling with pictorial referents and modeling without referents did not differ in overall efficacy. However, modeling alone produced results that were less consistent across different measures of comprehension. Children who lacked understanding of passives were more dependent on concrete referents than those who had some initial comprehension of the linguistic form. The results suggest that verbal modeling with pictorial referents and verbal modeling alone facilitate comprehension of passives, whereas verbal modeling with enactive referents promotes learning. Findings of a supplemental experiment reveal that the effects of verbal modeling on comprehension are enhanced when syntactic forms occur in a meaningful verbal context.     

Remembering information related to one's self

How does memory for an incident vary depending on whether, and how, the person relates the information to himself? Trait adjectives are better remembered if they were judged in reference to oneself rather than judged for meaning or sound. Our first experiment found a similar mnemonic advantage of referring a described episode or object to some event from one's life. Pleasant events were remembered better than unpleasant ones. A second experiment found incidental memory for trait adjectives was equally enhanced by judging each directly in reference to one's self-concept or indirectly by retrieving an episode either from one's life or from one's mother's life. Contrariwise, memory was poorer when traits were judged in reference to a less familiar person. Thus, good memory depends on relating the inputs to a well-differentiated memory structure.     

Moral outrage and pragmatism: Explanations for collective action

Two explanations for collective behavior were contrasted. The first, exemplified by relative deprivation theory, stresses the importance of feelings of moral outrage and perceived economic injustice. The second focuses on more pragmatic considerations, such as the availability of resources for mobilization. The present study examines these explanations for collective behavior in a laboratory setting. Subjects were members of a disadvantaged group. In a 3 × 2 factorial design two independent variables were manipulated. The magnitude of pay inequality between the disadvantaged group and a more advantaged group was manipulated to be large, moderate, or small. Mobilization resources available to the disadvantaged group were manipulated to be either present or absent. In accord with predictions based on relative deprivation theory, as the magnitude of the inequality increased, stronger feelings of deprivation were expressed. However, contrary to relative deprivation theory, larger magnitudes of inequality and stronger feelings of deprivation were not associated with greater willingness to engage in legitimate or illegitimate forms of collective behavior. Instead, as predicted by some critics of relative deprivation theory, willinginess to engage in illegitimate forms of collective behavior was affected only by a gragmatic consideration: the presence or absence of mobilization resources.     

Developmental trends in the use of perceptual and conceptual attributes in grouping,clustering, and retrieval

In Experiment I, two tasks were administered to children aged 4, 5, and 9 in order to investigate preference for perceptual versus conceptual attributes in grouping of common objects, and in various aspects of memory. The grouping task revealed a clear chronological progression: color and form determined the youngest children's grouping about equally; form dominated in the 5-year-olds; and most of the oldest children grouped primarily by conceptual attributes. In the memory task, three lists—one organized by color, one by form, one by superordinate category—were presented for free, followed by cued recall. Clustering showed the developmental shift from color to form to concept, while cued recall showed conceptual superiority at all ages. Experiment II replicated the memory task, yielding the same results. The results were discussed in terms of the relative abstractness and predictability of conceptual versus perceptual attributes and the difficulty of abstraction in encoding and the function of predictability in retrieval.     

The gestures of a gorilla: language acquisition in another pongid

A female lowland gorilla, Koko, has been engaged in an ongoing language program since July 1972 when she was 1 year old. During the first 30 months of training she acquired a vocabulary of 100 words in American Sign Language which she spontaneously combined into meaningful and often novel statements of up to 11 signs in length. The gorilla is using a rapidly expanding vocabulary of signs to express semantic and possibly grammatical relations similar to those expressed by human children in the early stages of language acquisition. Patterns of generalization, gradual increase in mean length of utterance, and innovative use of gestural language are discussed in relation to data available on children and chimpanzees.