Developmental Differences in Understanding and Solving Simple Mathematics Word Problems

The hypothesis was tested that older chidren, fifth/sixth graders versus third graders, who are more accurate in word problem solution, would show evidence of problem differentiation consistent with schema theories of problem representation and solution. A mathematics word problem sorting task and an accuracy test were used to assess problem representation and accuracy of solution across 16 different problem types. Cluster analyses of sorting data revealed that older children demonstrated sorting patterns consistent with a refined schema theory. Younger children were both less accurate and less systematic in their sorting. Idealized sorting patterns representing schema theories as well as surface structure problem similarity were tested against actual sorting patterns. Regression analyses confirmed that the fifth/sixth graders' and third graders' sorting data were best fit by a schematic sort and by a surface structure sort, respectively. Additionally, an English versus Spanish language contrast showed no effect of language on either accuracy of solution or the sorting patterns of the math word problems.     

Meaningful processing of meaningless stimuli: the influence of perceptual experience on early visual processing of faces

The N170 is an event-related potential component associated with extrastriate visual mechanisms involved in detecting human faces and leading to their characteristic structural encoding. Consequently the N170 discriminates the processing of stimuli providing physiognomic information from the processing of other, similarly complex, visual patterns. We have used this effect to explore the top-down influence of newly acquired experience on the initial visual categorization of physiognomic stimuli. Schematic faces having the inner components mislocated did not elicit an N170 effect in naive participants. However, after normally configured versions of the schematic faces were exposed, suggesting what the ambiguous patterns represented, the same patterns elicited an N170 effect as conspicuous as that elicited by regular schematic faces. This priming effect, which changed the visual processing of distorted faces in extrastriate regions, could not be explained by post-perceptual decisions. Although accounts based on changes in focal attention, or within-vision constraints could not be categorically rejected, this outcome might suggest cognitive penetrability of early visual categorization.     

Do humans and baboons use the same information when categorizing human and baboon faces?

What information is used for sorting pictures of complex stimuli into categories? We applied a reverse correlation method to reveal the visual features mediating categorization in humans and baboons. Two baboons and 6 humans were trained to sort, by species, pictures of human and baboon faces on which random visual noise was superimposed. On ambiguous probe trials, a human-baboon morph was presented, eliciting "human" responses on some trials and "baboon" responses on others. The difference between the noise patterns that induced the two responses made explicit the information mediating the classification. Unlike the humans, the baboons based their categorization on information that closely matched that used by a theoretical observer responding solely on the basis of the pixel similarities between the probe and training images. We show that the classification-image technique and principal components analysis provide a method to make explicit the differences in the information mediating categorization in humans and animals.     

Deployment of attention to the configuration of features in facelike patterns by ten-week-old infants

Abstract

Three experiments were conducted to investigate the response of 10-week-old infants to the configuration of features in facelike patterns. In each experiment a series of preview trials was shown before. facelike patterns were presented on test trials. Preview stimuli were schematic drawings with non-facial configurations (Experiment 1), schematic drawings with facial configurations (Experiment 2), or photographs of men's and women's faces (Experiment 3). Test stimuli in all three experiments were facelike drawings that differed in the number and the configuration of their stimulus features.     

Schematic or Taxonomic Organisation of the Reality and the Development of Class Logic

The experiment studied the effect of various methods of organising reality (taxonomic vs. schematic) on success in inclusion and logical complementation tasks. Seventy-two nine-year-old children were divided into four groups on the basis of their logical structuring abilities. Using three sets of material (Animals, Plants, Means of Transportation), the subjects performed a sorting task and an evaluation task in which the taxonomic and schematic modes of organising reality were opposed. Contrary to our hypothesis, the “logical includers” did not exhibit a greater capacity for taxonomic organisation than the “empirical includers” of the same age, either in the sorting or the evaluation task. The development of success in class logic tasks therefore does not appear to be linked to a change in the preferred mode of categorisation (schematic → categorical) but to the restructuring and differentiation of each of the two modes of organisation, both of which are available to the child at an early age.     

Comparison of the geometric and the contrast models of similarity by presentation of visual stimuli to the left and the right visual fields

In this study we investigated by means of the "same-different" decision task the process of comparing visual stimuli (schematic faces, familiar objects, houseplants, and nonsense figures) when presented for 100-150 msec to the right or to the left visual hemifields. The analysis of incorrect "same" responses showed that the addition of a common component (e.g., glasses, buttons) to a pair of nonidentical stimuli increased the percentage of incorrect same responses whereas the addition of the same component to one stimulus only in the pair decreased the percentage of incorrect "same" responses. This pattern, which is in accordance with Tversky's contrast model of similarity, is incompatible with any geometric model. Second, for schematic faces the results revealed that the left hemisphere is more sensitive to common than to distinctive features, whereas the right hemisphere is more sensitive to distinctive than to common features. No such interaction was obtained for the other type of stimuli. The implications of these results for models of similarity and the difference between the present findings and the findings of Sergent (1984) are discussed.     

The effect of categorisation on sensitivity to second-order relations in novel objects

Adults appear to be more sensitive to configural information, including second-order relations (the spacing of features), in faces than in other objects. Superior processing of second-order relations in faces may arise from our experience of identifying faces at the individual level of categorisation (eg Bob versus John) but other objects at the basic level of categorisation (eg table versus chair; Gauthier and Tarr, 1997 Vision Research 37 1673- 1682). We simulated this learning difference with novel stimuli (comprised of blobs) by having two groups view the same stimuli but learn to identify the objects only at the basic level (based on the number of constituent blobs) or at both the basic level and individual level (based on the spacing, or second-order relations, of the blobs) of categorisation. Results from two experiments showed that, after training, observers in the individual-level training group were more sensitive to the second-order relations in novel exemplars of the learned category than observers in the basic-level training group. This is the first demonstration of specific improvement in sensitivity to second-order relations after training with non-face stimuli. The findings are consistent with the hypothesis that adults are more sensitive to second-order relations in faces than in other objects, at least in part, because they have more experience identifying faces at the individual level of categorisation.     

Feature frequency in concept learning: What is counted?

Frequency theories of concept learning assume that people count how often features occur among instances of a concept, but different versions make various assumptions about what features they count. According to the basic feature model, only basic features are counted, whereas according to the configural model, basic features and configural features (all combinations of basic features) are counted. Two experiments assessed the predictions of both versions of frequency theory. Subjects viewed schematic human faces, which included both positive and negative instances of the concept to be learned, and then provided typicality ratings, classification responses, and frequency estimates of configural features, basic features, and whole exemplars. Because both models assume that basic features are counted, they make the same predictions in many situations. Here, the basic feature estimation and whole exemplar tests were designed such that both models make the same predictions, whereas the typicality rating, classification, and confignral feature estimation tests were designed to distinguish between the models. The pattern of results clearly supported the basic feature version of frequency theory.     

Priming visual face-processing mechanisms: electrophysiological evidence

Accumulated evidence from electrophysiology and neuroimaging suggests that face perception involves extrastriate visual mechanisms specialized in processing physiognomic features and building a perceptual representation that is categorically distinct and can be identified by face-recognition units. In the present experiment, we recorded event-related brain potentials in order to explore possible contextual influences on the activity of this perceptual mechanism. Subjects were first exposed to pairs of small shapes, which did not elicit any face-specific brain activity. The same stimuli, however, elicited face-specific brain activity after subjects saw them embedded in schematic faces, which probably primed the subjects to interpret the shapes as schematic eyes. No face-specific activity was observed when objects rather than faces were used to form the context. We conclude that the activity of face-specific extrastriate perceptual mechanisms can be modulated by contextual constraints that determine the significance of the visual input.     

The effects of attention-directing training on recognition memory task performance of three-year-old children

Thirty-eight 3-year-old children served as subjects in an investigation of recognition memory in which schematic faces differing only in the orientation of the eyes were employed as stimuli. A pretest was administered to all children, after which the two experimental groups received training in either attention to the distinctive feature of the training stimuli (also schematic faces) by means of a matching task, or in labeling the faces according to how they looked (sleepy, happy, sad, mad) and in using the labels to perform a matching task. After the training session all children were given a posttest on recognition memory of the faces. The verbally trained group obtained significantly higher scores on the posttest than either the feature or control groups. These results indicate that although the children were able to discriminate the faces, evidenced in their ease of performance on the training tasks, they were not able to use this knowledge unless given training in attaching labels to the stimuli, which enabled them to store the information for later use. Results are discussed in light of Gibson's (1969) theory of the developmental interrelations of cognitive processes.     

Effects of object complexity and type on the gaze behavior of children with pervasive developmental disorder

The looking behavior of children with pervasive developmental disorder (PDD) and age- and IQ-matched normal control children was studied using infrared oculography. Stimuli varying in complexity and topic were presented to test whether children with PDD have specific abnormalities in looking behavior to complex stimuli and/or to faces. All children showed more and longer fixations on the complex objects than on the simple objects, especially the complex nonsense figure, but group differences were not found. The results show no evidence for specific abnormalities in looking behavior to either faces or to complex stimuli in high functioning children with PDD.     

Detecting emotional faces and features in a visual search paradigm: are faces special?

In 2 experiments, participants were presented schematic faces with emotional expressions (threatening, friendly) in a neutral-faces context or neutral expressions in an emotional-faces context. These conditions were compared with detection performance in displays containing key features of emotional faces not forming the perceptual gestalt of a face. Supporting the notion of a threat detection advantage, Experiment 1 found that threatening faces were faster detected than friendly faces, whereas no difference emerged between the corresponding feature conditions. Experiment 2 increased task difficulty with a backward masking procedure and found corresponding results. In neither of the studies was the threat detection advantage associated with reduced accuracy. However, features were, in general, detected faster than faces when task difficulty was high.     

How much does a shared name make things similar? Part 1. Linguistic labels and the development of similarity judgment

Most theoretical proposals considering effects of language on similarity assume that labels affect similarity in a qualitative all-or-nothing manner. This article proposes another theoretical alternative--a model of the label as a discrete attribute of an object. According to this model, the relative weight of labels decreases with the child's age. Predictions derived from the model were tested in 3 experiments. In these experiments, children aged 6-12 years were presented with triads of schematic faces and were asked to make similarity judgments. Similarity of faces within the triads was manipulated via systematic variation of distinct facial features. It was found that (a) labels contribute to similarity judgment in a quantifiable manner, (b) labels' weight decreased with age, and (c) effects of labels are likely to stem from the cross-modality of labels. These results are discussed in relation to theories of development of categorization.     

Does recognition memory improve with age?

In order to test the hypothesis that recognition is a developmentally stable component of the memory system, age differences in recognition of faces were examined while controlling for nonmemory factors that might contribute to differences between the groups. Three groups of children (mean ages: 3 years, 4 months; 4 years, 9 months; and 6 years, 11 months) and a group of college students were tested on a recognition task and a similar matching task. The results indicated no change in recognition across the preschool years but an improvement from the later preschool period to the first grade. Further analyses indicated that this improvement was not due to changes in decision criteria or perceptual skills. These findings call into question the view that recognition is a developmentally invariant component of the memory system.     

Feature saliency and recognition memory for schematic faces

Memory for schematic faces was studied using a recognition memory paradigm. Ss indicated whether two faces, separated by delays of 6, 12, or 18 sec, were the same or different. Theoretical interest centered on the effects of component feature saliency on response bias and detectability. The main results were that there were fewer misses and more false alarms on the more salient features. Analysis showed that the main effect of feature saliency was on response bias, not detectability.     

Development of classification: The use of similarity and dimensional relations

Findings about perceptual development indicate that overall similarity is the primary perceptual relation by which young children compare complex objects. Traditional studies of classification, however, did not focus on children's organizational use of holistic relations but rather on their ability to classify by dimensions or criterial attributes. The results from such traditional studies suggest that young children are deficient classifiers. The present research investigated the possibility, contrary to the traditional view, that 4- to 6-year-old children are competent and systematic classifiers at least by overall similarity. In three experiments, preschoolers and kindergarteners classified various sets of multidimensional stimuli that could be organized into categories by overall similarity or by dimensional attributes. Consistent with the research in perceptual development, the children were highly attentive to overall similarity. However, the preschoolers in particular showed marked difficulty in using this relation to form categories of more than two objects. The children's difficulties were highly reminiscent of traditional claims about early classification. Analyses of the classification strategies used by the children, however, suggest that even the youngest children understood the purpose of a classification. The developmentla changes appear to be in the ability to execute a classification. Importantly, type of classification strategy was independent of type of category organization. Individual children used the same strategies both when classifying by overall similarity and by dimensional attributes. These results strongly suggest that it is the classification skills themselves, and not just the ability to classify by particular relations, that change with age.     

Hierarchical categorization by bilingual Latino children: does a basic-level bias exist?

Research has shown that children classify most easily at the basic level where objects in the same category look similar enough to each other to be grouped together but are distinct enough from objects in other categories to be discriminated (e.g., animal/bird/duck). In this article, the authors report on 2 experiments they conducted to determine whether children maintain this basic category bias when the perceptual similarity of stimuli at different hierarchical levels is equalized. Pictures within and across 3 hierarchical levels were made perceptually equivalent and shown to 71 Latino children who were bilingual in Spanish and English. In Experiment 1, the pictures used as exemplars could be categorized on any of the 3 hierarchical levels. In Experiment 2, example pictures unambiguously defined the level of categorization that would be accurate, and linguistic cues were given that might assist in the selection of the correct category. In both experiments, the children sorted pictures from all 3 levels equally well, but they found it harder to justify their sorting of superordinate pictures. English competence predicted sorting on the more ambiguous sorting task in Experiment 1; and English competence predicted verbal justifications in both experiments, even though the experiments were conducted in Spanish. Competence in Spanish or English was an equally good predictor of sorting in the better defined sorting task in Experiment 2. These findings indicate that a superordinate level deficiency remains after perceptual differences are eliminated and that the deficiency is cognitive in nature. Differences in the performances of children who differed in bilingualism support the hypothesis that a threshold of proficiency in both languages is an important determinant of the effect of bilingualism on categorization.     

Memory for Faces in Children with Autism

Previous research has established that children with Autistic Disorder have deficits in aspects of social cognition and in verbal memory, but research on social memory is limited. Twenty-four autistic boys aged 7 to 12 years and normal controls matched for verbal mental age were administered parallel social and nonsocial matching and memory tasks. Results showed that the children with autism were impaired relative to the normal children on the social (face) memory task only. Furthermore, of the four experimental tasks, the social memory task had the highest and most consistent correlations with measures of social development and adaptive skills. Whereas the normal children used the special status of faces to recall them more easily than objects, the children with autism showed equal recall of objects and faces.