Ordinality and Verbal Framing Influence Preschoolers' Memory for Spatial Structure.

During the preschool years, children are simultaneously undergoing a reshaping of their mental number line and becoming increasingly sensitive to the social norms expressed by those around them. In the current study, 4- and 5-year-old American and Israeli children were given a task in which an experimenter laid out chips with numbers (1-5), letters (A-E), or colors (Red-Blue, the first colors of the rainbow), and presented them with a specific order (initial through final) and direction (Left-to-right or Right-to-left). The experimenter either did not demonstrate the laying out of the chips (Control), emphasized the process of the left-to-right or right-to-left spatial layout (Process), or used general goal language (Generic). Children were then asked to recreate each sequence after a short delay. Children also completed a short numeracy task. The results indicate that attention to the spatial structuring of the environment was influenced by conventional framing; children exhibited better recall when the manner of layout was emphasized than when it was not. Both American and Israeli children were better able to recall numerical information relative to non-numerical information. Although children did not show an overall benefit for better recall of information related to the culture's dominant spatial direction, American children's tendency to recall numerical direction information predicted their early numeracy ability.

Eye Tracking Lateralized Spatial Associations in Early Childhood.

This experiment tests the age at which left-to-right spatial associations found in infancy shift to culture-specific spatial biases in later childhood, for both numerical and non-numerical information. Children ages 1 to 5 years (N=320) were tested within an eye-tracking paradigm which required passive viewing of a video portraying a spatial transposition. In this video, an item was hidden in a vertical set of locations, which were then surreptitiously rotated 90°. There were several conditions, which varied in the degree to which the locations were presented alongside ordinal (numerical, alphabetical) or non-ordinal (nonsense label) information. After transposition, a narrator prompted the child to visually search the array. The amount of time spent fixating in a location consistent with a left-to-right mapping or a right-to-left mapping was measured to gauge the degree and laterality of spatial associations. Overall, children looked more towards locations consistent with a left-to-right mapping. This effect fluctuated with age, dipping as children entered toddlerhood, increasing in 3- and 4-year-olds, and then disappearing at age 5. The ordinal nature of the stimuli (e.g., numerical or non-numerical) did not influence the laterality of the spatial associations. A follow-up experiment confirms that, like older preschoolers, adults (N=66) also exhibit no spontaneous left-to-right mapping bias in this paradigm, with no fluctuation as a result of condition. These data support the presence of a decrease in left-to-right processing around the age of two, as children recede from infantile spatial biases and progress to exhibiting culture-specific spatial biases in early childhood.

A left visual advantage for quantity processing in neonates.

Forty-eight newborn infants were tested in one of three multimodal stimulus conditions, in which auditory quantities were presented alongside visual object arrays in two test trials. These tests varied with respect to which side (either left or right) numerically matched the auditory number. The infants looked longer to the test trials in which the left side of the visual display exhibited a quantity that matched the presented auditory quantity. This study provides the first evidence for an untrained, innate bias for humans to preferentially process quantity information presented in the left field of vision.

Measuring Spontaneous Focus on Space in Preschool Children.

Previous work on children's Spontaneous Focus on Numerosity (SFON) has shown the value of measuring children's spontaneous attention within naturalistic interactions. SFON is the spontaneous tendency to focus attention on, and explicitly enumerate the exact number of, items in a set. This measure predicts later math skills above and beyond general IQ and other cognitive factors such as attention. The utility of SFON suggests that a parallel construct for space is a worthy pursuit; spatial cognition underlies many of our mathematical skills, especially as children are first learning these skills. We developed a measure of children's Spontaneous Focus on Space - the spontaneous tendency to attend to absolute and relative spatial components of the environment - and studied its relation to reasoning about the important spatial-numerical concept of proportions. Fifty-five 3- to 6-year-olds were tested at a local children's museums in New York City. Children participated in tasks designed to measure their spontaneous focus on space and number, and their ability to reason about spatial proportions. Results indicate that as children grow older, their Spontaneous Focus on Space becomes more complete and is positively related to proportional reasoning performance. These findings suggest that spatial awareness is rapidly increasing in the preschool years, alongside numerical awareness and spatial-numerical proportional reasoning.

Operational momentum for magnitude ordering in preschool children and adults.

When adding or subtracting quantities, adults tend to overestimate addition outcomes and underestimate subtraction outcomes. They also shift visuospatial attention to the right when adding and to the left when subtracting. These operational momentum phenomena are thought to reflect an underlying representation in which small magnitudes are associated with the left side of space and large magnitudes with the right side of space. Currently, there is limited research on operational momentum in early childhood or for operations other than addition and subtraction. The current study tested whether English-speaking 3- and 4-year-old children and college-aged adults exhibit operational momentum when ordering quantities. Participants were presented with two experimental blocks. In one block of trials, they were tasked with choosing the same quantity they had previously seen three times; in the other block, they were asked to generate the next quantity in a doubling sequence composed of three ascending quantities. A bias to shift attention to the right after an ascending operation was found in both age groups, and a bias to overestimate the next sequential quantity during an ascending ordering operation was found in adults under conditions of uncertainty. These data suggest that, for children, the spatial biases during operating are more pronounced than the mis-estimation biases. These findings highlight the spatial underpinnings of operational momentum and suggest that both very young children and adults conceptualize quantity along a horizontal continuum during ordering operations, even before formal schooling.

Children's spontaneous focus on number before and after guided parent-child interactions in a children's museum.

Little is known about whether and how parents can foster their children's spontaneous focus on number, an unprompted measure of attention to small numbers of objects that predicts later math achievement. In the current study, we asked 54 preschool-aged children and their parents to play together in a children's museum exhibit using either a numerical prompt or a nonnumerical prompt (control condition). Before and after playing with their parent, children completed assessments to measure individual differences in their tendency to spontaneously focus on number. After playing with their parent, children whose parents received the numerical prompt showed greater spontaneous focus on number compared to children whose parents received the control prompt. These findings suggest that when parents interact in an informal play setting with their children in ways that involve numerical content, it sharpens children's later spontaneous attention to numerical information. (PsycINFO Database Record

Observation of directional storybook reading influences young children's counting direction.

Even before formal schooling, children map numbers onto space in a directional manner. The origin of this preliterate spatial-numerical association is still debated. We investigated the role of enculturation for shaping the directionality of the association between numbers and space, focusing on counting behavior in 3- to 5-year-old preliterate children. Two studies provide evidence that, after observing reading from storybooks (left-to-right or right-to-left reading) children change their counting direction in line with the direction of observed reading. Just observing visuospatial directional movements had no such effect on counting direction. Complementarily, we document that book illustrations, prevalent in children's cultures, exhibit directionality that conforms to the direction of a culture's written language. We propose that shared book reading activates spatiotemporal representations of order in young children, which in turn affect their spatial representation of numbers.

The Early Construction of Spatial Attention: Culture, Space, and Gesture in Parent-Child Interactions.

American and Israeli toddler-caregiver dyads (mean age of toddler = 26 months) were presented with naturalistic tasks in which they must watch a short video (N = 97) or concoct a visual story together (N = 66). English-speaking American caregivers were more likely to use left to right spatial structuring than right to left, especially for well-ordered letters and numbers. Hebrew-speaking Israeli parents were more likely than Americans to use right to left spatial structuring, especially for letters. When constructing a pictorial narrative for their children, Americans were more likely to place pictures from left to right than Israelis. These spatial structure biases exhibited by caregivers are a potential route for the development of spatial biases in early childhood, before children have developed automatic reading and writing habits.

Number prompts left-to-right spatial mapping in toddlerhood.

Toddlers performed a spatial mapping task in which they were required to learn the location of a hidden object in a vertical array and then transpose this location information 90° to a horizontal array. During the vertical training, they were given (a) no labels, (b) alphabetical labels, or (c) numerical labels for each potential spatial location. After the array was transposed to become a horizontal continuum, the children who were provided with numerical labels during training and those who heard alphabetical labels and formed a strong memory for the vertical location, selectively chose the location corresponding to a left-to-right mapping bias. Children who received no concurrent ordinal labels during training were not able to transpose the array, and did not exhibit any spatial directionality bias after transposition. These results indicate that children exhibit more flexible spatial mapping than other animals, and this mapping is modulated depending on the type of concurrent ordinal information the child receives. (PsycINFO Database Record

The relationship between non-symbolic multiplication and division in childhood.

Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a + b - b = a). The current study examines children's ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and were then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8*4/4) or did not (e.g., 8*4/2). Children's performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a*b/b structure, suggesting that they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems.

How not to develop a sense of number.

The authors rightly point to the theoretical importance of interactions of space and number through the life span, yet propose a theory with several weaknesses. In addition to proclaiming itself unfalsifiable, its stage-like format and emphasis on the role of selective attention are at odds with what is known about the development of spatial-numerical associations in infancy.

Encouraging Spatial Talk: Using Children's Museums to Bolster Spatial Reasoning.

Longitudinal spatial language intervention studies have shown that greater exposure to spatial language improves children's performance on spatial tasks. Can short naturalistic, spatial language interactions also evoke improved spatial performance? In this study, parents were asked to interact with their child at a block wall exhibit in a children's museum. Some parents were instructed to emphasize formal shape terms, others to emphasize spatial goals, and some were not provided scripts. Children were presented with a series of spatial reasoning tasks before and after this parental interaction, and the amount and type of spatial language during the training session was coded for parents and children. We found that (a) parents significantly increased their spatial language use when prompted, (b) children and parents used different types of spatial language in each of the scripted conditions, and

Ratio abstraction over discrete magnitudes by newly hatched domestic chicks (Gallus gallus).

A large body of literature shows that non-human animals master a variety of numerical tasks, but studies involving proportional discrimination are sparse and primarily done with mature animals. Here we trained 4-day-old domestic chicks (Gallus gallus) to respond to stimuli depicting multiple examples of the proportion 4:1 when compared with the proportion 2:1. Stimuli were composed of green and red dot arrays; for the rewarded 4:1 proportion, 4 green dots for every red dot (e.g. ratios: 32:8, 12:3, and 44:11). The birds continued to discriminate when presented with new ratios at test (such as 20:5), characterized by new numbers of dots and new spatial configurations (Experiment 1). This indicates that chicks can extract the common proportional value shared by different ratios and apply it to new ones. In Experiment 2, chicks identified a specific proportion (2:1) from either a smaller (4:1) or a larger one (1:1), demonstrating an ability to represent the specific, and not relative, value of a particular proportion. Again, at test, chicks selectively responded to the previously reinforced proportion from new ratios. These findings provide strong evidence for very young animals' ability to extract, identify, and productively use proportion information across a range of different amounts.

Culturally inconsistent spatial structure reduces learning.

Human adults tend to use a spatial continuum to organize any information they consider to be well-ordered, with a sense of initial and final position. The directionality of this spatial mapping is mediated by the culture of the subject, largely as a function of the prevailing reading and writing habits (for example, from left-to-right for English speakers or right-to-left for Hebrew speakers). In the current study, we tasked American and Israeli subjects with encoding and recalling a set of arbitrary pairings, consisting of frequently ordered stimuli (letters with shapes: Experiment 1) or infrequently ordered stimuli (color terms with shapes: Experiment 2), that were serially presented in a left-to-right, right-to-left, or central-only manner. The subjects were better at recalling information that contained ordinal stimuli if the spatial flow of presentation during encoding matched the dominant directionality of the subjects' culture, compared to information encoded in the non-dominant direction. This phenomenon did not extend to infrequently ordered stimuli (e.g., color terms). These findings suggest that adults implicitly harness spatial organization to support memory, and this harnessing process is culturally mediated in tandem with our spatial biases.

Operational momentum and size ordering in preverbal infants.

Recent evidence has shown that, like adults and children, 9-month-old infants manifest an operational momentum (OM) effect during non-symbolic arithmetic, whereby they overestimate the outcomes to addition problems, and underestimate the outcomes to subtraction problems. Here we provide the first evidence that OM occurs for transformations of non-numerical magnitudes (i.e., spatial extent) during ordering operations. Twelve-month-old infants were tested in an ordinal task in which they detected and represented ascension or descension in physical size, and then responded to ordinal sequences that exhibited greater or lesser sizes. Infants displayed longer looking time to the size change whose direction violated the operational momentum experienced during habituation (i.e., the smaller sequence in the ascension condition and the larger sequence in the descension condition). The presence of momentum for ordering size during infancy suggests that continuous quantities are represented spatially during the first year of life.

Non-symbolic division in childhood.

The approximate number system (ANS) underlies representations of large numbers of objects as well as the additive, subtractive, and multiplicative relationships between them. In this set of studies, 5- and 6-year-old children were shown a series of video-based events that conveyed a transformation of a large number of objects into one-half or one-quarter of the original number. Children were able to estimate correctly the outcomes to these halving and quartering problems, and they based their responses on scaling by number, not on continuous quantities or guessing strategies. Children's performance exhibited the ratio signature of the ANS. Moreover, children performed above chance on relatively early trials, suggesting that this scaling operation is easily conveyed and readily performed. The results support the existence of a flexible and substantially untrained capacity to scale numerical amounts.

The impact of symbolic and non-symbolic quantity on spatial learning.

An implicit mapping of number to space via a "mental number line" occurs automatically in adulthood. Here, we systematically explore the influence of differing representations of quantity (no quantity, non-symbolic magnitudes, and symbolic numbers) and directional flow of stimuli (random flow, left-to-right, or right-to-left) on learning and attention via a match-to-sample working memory task. When recalling a cognitively demanding string of spatial locations, subjects performed best when information was presented right-to-left. When non-symbolic or symbolic numerical arrays were embedded in these spatial locations, and mental number line congruency prompted, this effect was attenuated and in some cases reversed. In particular, low-performing female participants who viewed increasing non-symbolic number arrays paired with the spatial locations exhibited better recall for left-to-right directional flow information relative to right-to-left, and better processing for the left side of space relative to the right side of space. The presence of symbolic number during spatial learning enhanced recall to a greater degree than non-symbolic number--especially for female participants, and especially when cognitive load is high--and this difference was independent of directional flow of information. We conclude that quantity representations have the potential to scaffold spatial memory, but this potential is subtle, and mediated by the nature of the quantity and the gender and performance level of the learner.

Culturally-Driven Biases in Preschoolers' Spatial Search Strategies for Ordinal and Non-Ordinal Dimensions.

Culturally-driven spatial biases affect the way people interact with and think about the world. We examine the ways in which spatial presentation of stimuli affects learning and memory in preschool-aged children in the USA and Israel. In Experiment 1, preschoolers in both cultures were given a spatial search task in which they were asked to utilize verbal labels (letters of the alphabet) to match the hiding locations of two monkeys. The labels were taught to the children in either a left-to-right or right-to-left fashion to assess whether performance on this task is affected by directionality of labeling. English-speaking children performed better on the spatial search task when locations were labeled in a left-to-right fashion, while Hebrew-speaking children exhibited higher performance when labels were taught in a right-to-left fashion. In Experiment 2, English-speaking preschoolers were given a modified task in which the verbal label was a non-ordinal stimulus type (colors). These children showed no subsequent advantage on the task for spatial presentations which were culturally-consistent (left-to-right) relative to culturally-inconsistent (right-to-left). These findings support the hypothesis that culturally-consistent spatial layout improves learning and memory, and that this benefit is reduced or absent when information lacks ordinal properties.