Development of children's ability to judge relative numerosity

Three- to seven-year-old chilren were trained through reinforcement to select either the more or less numerous of two rows of squares. One group was shown rows in which number covaried with row length, one group saw rows in which number covaried with row density, and a third group saw rows in which number did not covary with other dimensions. The children's operational stage was assessed by a number conservation test. All children successfully judged relative numerosity when number covaried with length or with density, but only concrete operational children were successful when number did not covary with other dimensions. Preoperational children are thus not able to base judgments of relative numerosity solely on number.     

Oppel-Kundt illusion in three-dimensional space

A three-dimensional form of the Oppel-Kundt illusion was examined. Subjects viewed arrays consisting of two parallel rows of lights. For one group the rows consisted of equal numbers of lights (2, 3, or 4), while for a second group the row nearest the subject always had the greater number of lights. Subjects viewed these arrays from two vantage points, one directly in front of the array and the other displaced laterally. For each array subjects adjusted the extent of the far array until they felt the two rows were the same length. Both the nature of the array and the viewpoint had a significant influence on the perceived length of the far row. The size of the near row was overestimated significantly more when the array was viewed from the central position and also when the number of lights in the near row exceeded that of the far row. These results confirm that a lateral viewing position decreases the perspective effect and indicate that the Oppel-Kundt illusion can occur with three-dimensional stimuli.     

Perceptual completion and object-based representations in short-term visual memory

Object-based representations in visual short-term memory (VSTM) were examined using a change detection memory task. A display comprising two rows of four differently colored elements was followed by a probe display in which only one of the rows reappeared. On same trials, the probed row was identical to the corresponding row in the memory display. On different trials, two of the elements in the probed row had their colors exchanged. In each memory display, a task-irrelevant visual element appeared between the two rows, with the potential to function as an occluder. Performance was enhanced when perceptual completion meant that four, rather than eight, objects were perceived in the memory display and when the probe display revealed that the occluded elements continued behind the occluder. It appears that several forms of representation can co-occur to support VSTM, one of which is object based.     

Evocation and characterization of percepts of apparent motion on the face

The percepts evoked by sequential stimulation of sites in close spatial proximity (<2.5 cm) on the face were studied. Both method-of-limits and magnitude-estimation procedures were used to identify and characterize alterations in the percepts produced by systematic changes in the temporal and spatial parameters of the sequence. Each site was stimulated by a vertically oriented row of miniature vibrating probes. Apparent motion was consistently perceived when the delay between the onsets of sequentially activated rows (interstimulus onset interval, or ISOI) fell within a relatively narrow range of values, the lower limit of which approximated 5 msec. Both the upper limit and the perceived smoothness and continuity of the motion percepts (goodness of motion) increased with the duration for which each row stimulated the skin over the range evaluated, 15–185 msec. For the successive activation of only two rows, goodness of motion was not influenced by changes in their separation from 0.4 to 2.5 cm. The ISOI values at which magnitude estimates of goodness of motion were highest increased with the duration for which each row stimulated the skin. As such, maximum goodness of motion decreased with increases in the apparent velocity of motion. When the number of sequentially activated rows was increased from two to four or more, the quality of the motion percepts improved. For the successive activation of multiple closely spaced rows, values of ISOI at which numerical estimates of goodness of motion were highest approximated integral fractions of the duration for which each row stimulated the skin. In this situation, the probes rose and fell in a regular, step-locked rhythm to simulate an edge-like or rectangular object moving across the skin. The goodness of motion so attained was relatively independent of the apparent velocity of motion.     

Vicario's illusion of sloping steps reexamined

If a few parallel horizontal rows of dots are set diagonally, like steps, across the visual field, the inner rows appear not to be horizontal but sloping up to one side; the effect holds as long as the vertical distances between the rows do not exceed a given visual angle. This illusion, described by Vicario in 1978, was never explained. An experiment is reported in which the illusion was still visible at row separations well in excess of the spatial limits originally considered, provided the stimulus elements were enlarged. The maximum illusion was obtained for length ratios (interrow distance to size of dots) identical to those which have been shown to produce the largest effects in a number of illusions of area and length. This suggests that Vicario's illusion is similar to other illusions of extent, and that it can be explained by a neural extent-coding model.     

Attention and information storage in visual short-term memory

Schioldborg, P. Attention and information storage in visual short-term memory. Scand. J. Psychol., 1973, 14, 1–3.- Information retrieval from STM was examined with Sperling's (1960) method. Of nine letters displayed in rows of three, the number of letters correctly reported from each row differed significantly, the mean being 2.4, 2.2, and 1.6 letters for the middle, upper, and lower row, respectively. By increasing exposure time, number of correctly reported letters increased for each row at equal rate. However, by increasing the delay period of the selection signal, number of letters decreased at different rates, the reduction being 48%, 24%, and 10% for the lower, upper, and middle row respectively. The results are assumed to reflect differences in the initial attention level for the individual item; the smaller this level, the lower the level of information processing and the faster the erasure from STM.     

Spatial problem solving and functional relations

Three experiments investigated the role of object knowledge on participants' ability to solve a spatial arrangement problem. The task was to rearrange six real-world three-dimensional objects so that their relative locations agreed with a given set of rules. The aim of the experiments was to tease out the relative extent to which object association, orientation, and object-specific functional relations affect performance on arrangement tasks. When the problem was presented vertically (objects arranged in piles), participants solved functional canonical versions of the problem significantly quicker than functional non-canonical versions both between (Experiments 1a and 2), and within subjects (Experiment 3). When the arrangement problem was presented horizontally (objects arranged flat in two rows), no significant differences in solution times were found between conditions (Experiments 1b and 2). Overall the results provide evidence for the importance of object-specific functional relations as a predictor of the solution time of spatial arrangement problems, although some differences were noted between single and multiple presentation of problems when specific rules within problems were rotated. The importance of functional information in memory as a constraint on the building of mental models and problem spaces is discussed.     

Inducing a blockmodel structure of two-mode binary data using seriation procedures

We show that seriation of the rows and columns of a two-mode, binary matrix can be an effective method for producing a reordering of the matrix that reveals a blockmodel structure of the data. The objective criterion of the seriation process is based on Robinson patterning of matrix elements. The key advantages of the proposed method are: (a) it can be used in conjunction with existing two-mode blockmodeling algorithms by facilitating selection of the number of classes for the rows and columns of the matrix and the appropriate types of ideal blocks; (b) the model uses a well-grounded index based on Robinson structure, (c) guaranteed optimal solutions can be obtained for problems of practical size, and (d) the seriation method is frequently capable of producing a solution that has a substantive interpretation with respect to the orderings of the row objects and column items.     

The effects of number of responses on pause length with temporal variables controlled

A change in the size of a fixed-ratio schedule involves a simultaneous change in number of responses, in time to complete the ratio (work time), and in the interval between successive reinforcements (interreinforcement interval). Previous studies have suggested the importance of work time and the interreinforcement interval in controlling the length of the post-reinforcement pause. The present study sought to determine whether number of responses is also a significant factor. Pigeons were trained on a multiple fixed-ratio x fixed-ratio 2 plus timeout schedule in which the size of the fixed-ratio x was manipulated. When the work times (Experiment I) or interreinforcement intervals (Experiment II) were equated for the two components, the pause before the fixed-ratio x was longer than the pause before the fixed-ratio 2 plus timeout. As fixed-ratio x size increased, the relative difference in the lengths of the two types of pauses also increased. Because the fixed-ratio x component contained a larger number of responses than the fixed-ratio 2 plus timeout component, the relatively longer pause preceding the fixed-ratio x indicates that number of responses played a significant role in determining the length of the post-reinforcement pause.     

Why preschoolers are reluctant to count spontaneously

Two experiments are reported which examine children's counting and its role in reasoning about the relative numerosity of two arrays. In the first experiment, children's number judgements were compared under different conditions designed to evaluate the importance of three different cues to number—length and density of rows, small number perception and counting. Children were found to count very rarely unless specifically asked to do so. Experiment 2 investigated some possible reasons why children who count readily in some situations are reluctant to count spontaneously in this number judgement task. Spontaneous counting in 4-year-olds increased in one condition only: when they were given feedback as to the correctness of their previous judgements. This feedback showed that basing judgements on number as counted was always correct whereas length and density judgements were only sometimes correct. Preschoolers' preference for length as a cue to number may therefore be due to their belief that length is a more reliable cue than counting, rather than to their ignorance about the link between counting and numerical reasoning.     

Normalization of irrelevant dimensions in stimulus comparisons

When subjects compared two multidimensional stimuli with respect to a single (relevant) dimension in a same-different task, variation in the irrelevant dimension systematically affected reaction times. For same trials, reaction times increased monotonically with the amount of disparity between the stimuli on the irrelevant dimension. The dimensions were heights and widths of ellipses or hues and tints of color patches. The results were interpreted in terms of a normalization process that internally transforms the irrelevant dimensions of the two stimuli until they are equal. The amount of normalization, and hence same reaction time, increased with increasing disparity on the irrelevant dimension. These results suggest that in order to decide that two objects are equivalent in some criterial respect, it is often necessary to normalize irrelevant disparities.     

Effects of viewing time,fixations, and viewing strategies on visual memory for briefly presented natural objects

We investigated the impact of viewing time and fixations on visual memory for briefly presented natural objects. Participants saw a display of eight natural objects arranged in a circle and used a partial report procedure to assign one object to the position it previously occupied during stimulus presentation. At the longest viewing time of 7,000 ms or 10 fixations, memory performance was significantly higher than at the shorter times. This increase was accompanied by a primacy effect, suggesting a contribution of another memory component—for example, visual long-term memory (VLTM). We found a very limited beneficial effect of fixations on objects; fixated objects were only remembered better at the shortest viewing times. Our results revealed an intriguing difference between the use of a blocked versus an interleaved experimental design. When trial length was predictable, in the blocked design, target fixation durations increased with longer viewing times. When trial length was unpredictable, fixation durations stayed the same for all viewing lengths. Memory performance was not affected by this design manipulation, thus also supporting the idea that the number and duration of fixations are not closely coupled to memory performance.     

Stereoscopic illusion based on the proximity principle

A class of ambiguous random-dot stereograms were created that share the following interesting property: Although the binocular disparity forms a periodic 'sawtooth' waveform as a function of row number (the disparity is constant for a given row), these stimuli yield a monotonically increasing depth percept along the rows. The random-dot pattern of each row is periodic along the horizontal direction for the purpose of producing an ambiguous depth percept. It is this ambiguity that makes it possible for the periodic stimulus to give rise to a monotonic percept. This monotonic percept is substantially enhanced when the rows are shown in temporal sequence instead of all being displayed together. Experiments are reported which indicate that this illusion is due to the proximity, or pulling, effect in stereopsis.     

Getting a tool gives wings: overestimation of tool-related benefits in a motor imagery task and a decision task

Two experiments examine whether people overestimate the benefits provided by tool use in motor tasks. Participants had to move different quantities of objects by hand (two at a time) or with a tool (four at a time). The tool was not within reach so participants had to get it before moving the objects. In Experiment 1, the task was performed in a real and an imagined situation. In Experiment 2, participants had to decide for each quantity, whether they preferred moving the objects by hand or with the tool. Our findings indicated that people perceive tool actions as less costly in terms of movement time than they actually are (Experiment 1) and decide to use a tool even when it objectively provides less time-based benefits than using the hands (Experiment 2). Taken together, the data suggest that people overestimate the benefits provided by tool use.     

Curve tracing: A possible basic operation in the perception of spatial relations

The two experiments in this study suggest that fast internal tracing of curves is employed by the visual system in the perception of certain shape properties and spatial relations. The experimental task in the first experiment was to determine, as rapidly as possible, whether two Xs lay on the same curve or on different curves in a visual display. Mean response time for “same” responses increased monotonically with increasing distance along the curve between the Xs. The task in the second experiment was to decide either that a curve joining two Xs was unbroken or that the curve had a gap. Decision times again increased as the length of the curve joining the Xs was increased. The results of both experiments suggest that people can trace curves in a visual display internally at high speed (the average rate of tracing was about 40° of visual angle per second). Curve tracing may be an important visual process used to integrate information from different parts of a visual display.     

Attention capture by faces

We report three experiments that investigate whether faces are capable of capturing attention when in competition with other non-face objects. In Experiment 1a participants took longer to decide that an array of objects contained a butterfly target when a face appeared as one of the distracting items than when the face did not appear in the array. This irrelevant face effect was eliminated when the items in the arrays were inverted in Experiment 1b ruling out an explanation based on some low-level image-based properties of the faces. Experiment 2 replicated and extended the results of Experiment 1a. Irrelevant faces once again interfered with search for butterflies but, when the roles of faces and butterflies were reversed, irrelevant butterflies no longer interfered with search for faces. This suggests that the irrelevant face effect is unlikely to have been caused by the relative novelty of the faces or arises because butterflies and faces were the only animate items in the arrays. We conclude that these experiments offer evidence of a stimulus-driven capture of attention by faces.     

A contribution to the study of phenomenal causation

In his studies of the perception of causality, Michotte describes a number of “impressions” concomitant with precisely defined experimental conditions, of which “Launching” and “Triggering” are two of the most important. Two major factors influencing the nature of the impressions are the relative speeds of the two rectangles representing objects participating in dynamic inter-relationships, and the length of path of the more passive of the two objects. This investigation was an attempt to discover the quantitative relationships obtaining between these two independent variables and the dependent variable of the subjects' responses to the experimental conditions.     

Evidence of amodal representation of small numbers across visuo-tactile modalities in 5-month-old infants

Two experiments investigated 5-month-old infants’ amodal sensitivity to numerical correspondences between sets of objects presented in the tactile and visual modes. A classical cross-modal transfer task from touch to vision was adopted. Infants were first tactually familiarized with two or three different objects presented one by one in their right hand. Then, they were presented with visual displays containing two or three objects. Visual displays were presented successively (Experiment 1) or simultaneously (Experiment 2). In both experiments, results showed that infants looked longer at the visual display which contained a different number of objects from the tactile familiarization phase. Taken together, the results revealed that infants can detect numerical correspondences between a sequence of tactile and visual stimulation, and they strengthen the hypothesis of amodal and abstract representation of small numbers of objects (two or three) across sensory modalities in 5-month-old infants.     

Do First Graders Make Efficient Use of External Number Representations? The Case of the Twenty-Frame

External number representations are commonly used throughout the first years of instruction. The twenty-frame is a grid that contains two rows of 10 dots each, and within each row, dots are organized in two groups of five. The assumption is that children can make use of these structures for enumerating the dots, rather than relying on one-by-one counting. We compared first-grade children's performance on two types of computerized enumeration tasks, in which between one and 20 dots were presented in random arrangements or on a twenty-frame. The number of dots was a strong predictor of response times and accuracy rates in the enumeration task with random arrangements but not in the twenty-frame task. Performance on the twenty-frame task was correlated with performance on a number and arithmetic test, even when other cognitive variables were statistically controlled. We discuss these findings in the light of theories on utilizing external representations to support numerical learning.