Core Multiplication in Childhood

A dedicated, non-symbolic, system yielding imprecise representations of large quantities (approximate number system, or ANS) has been shown to support arithmetic calculations of addition and subtraction. In the present study, 5–7-year-old children without formal schooling in multiplication and division were given a task requiring a scalar transformation of large approximate numerosities, presented as arrays of objects. In different conditions, the required calculation was doubling, quadrupling, or increasing by a fractional factor (2.5). In all conditions, participants were able to represent the outcome of the transformation at above-chance levels, even on the earliest training trials. Their performance could not be explained by processes of repeated addition, and it showed the critical ratio signature of the ANS. These findings provide evidence for an untrained, intuitive process of calculating multiplicative numerical relationships, providing a further foundation for formal arithmetic instruction.Psycholog

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

Operational Momentum During Ordering Operations for Size and Number in 4-Month-Old Infants

An Operational Momentum (OM) effect is shown by 9-month-old infants during non-symbolic arithmetic, whereby they overestimate the outcomes to addition problems, and underestimate the outcomes to subtraction problems. Recent evidence has shown that this effect extends to ordering operations for size-based sequences in 12-month-olds. Here we provide evidence that OM occurs for ordering operations involving numerical sequences containing multiple quantity cues, but not size-based sequences, already at 4 months of age. Infants were tested in an ordinal task in which they detected and represented increasing or decreasing variations in physical and/or numerical size, and then responded to ordinal sequences that exhibited greater or lesser sizes/numerosities, thus following or violating the OM generated during habituation. Results showed that OM was absent during size ordering (Experiment 1), but was present when infants ordered arrays of discrete elements varying on numerical and non-numerical dimensions, if both number and continuous magnitudes were available cues to discriminate between with-OM and against-OM sequences during test trials (Experiments 2 vs. 3). The presence of momentum for ordering number only when provided with multiple cues of magnitude changes suggests that OM is a complex phenomenon that blends multiple representations of magnitude early in infancy

Dividing Attention Increases Operational Momentum

When adding or subtracting two quantities, adults often compute an estimated outcome that is larger or smaller, respectively, than the actual outcome, a bias referred to as “operational momentum”. The effects of attention on operational momentum were investigated. Participants viewed a display in which two arrays of objects were added, or one array was subtracted from another array, and judged whether a subsequent outcome (probe) array contained the correct or incorrect number of objects. In a baseline condition, only the arrays to be added or subtracted were viewed. In divided attention conditions, participants simultaneously viewed a sequence of colors or shapes, and judged which color (a non-spatial judgment) or shape (a spatial judgment) was repeated. Operational momentum occurred in all conditions, but was higher in divided attention conditions than in the baseline condition, primarily for addition problems. This pattern suggests that dividing attention, rather than decreasing operational momentum by decreasing attentional shifts, actually increased operational momentum. These results are consistent with a heightened use of arithmetic heuristics under conditions of divided attention

Parental construction of spatial associations: Origins of culturally-mediated left-to-right spatial associations in toddlers

The mapping of numbers in space to form a "mental number line" has been consistently found in adults in many different number situations. Typically, this mapping goes in a culturally-consistent direction mediated by the direction of writing, and has also been found to generalize to other non-numerical, ordinal stimuli such as the alphabet. The primary theory regarding the origins of this spatial-mapping is a causal role of the visuo-motor process of automatically scanning and reading language. Yet, more recent findings demonstrate that this directional orientation begins to develop prior to formal reading, suggesting that other earlier experiences might also be responsible for the structuring of this attentional bias. The current study investigates if and how caregivers structure the environment for their child in a culturally-congruent direction prior to any formal reading instruction. The structure of pointing behavior was observed and scored as caregivers to one- and two-year-olds described images in a slideshow task, told stories via placement of tiles with objects on them, and created scenes for their child using magnets. These children had not yet entered preschool, but were old enough for caregivers to have begun to extensively describe the environment to them. Caregivers showed a left-to-right directional preference when leading their child's attention in the slideshow task. Caregivers displayed a trend of left-to-right tile structuring during the tile placement task, and showed no preferred structuring in the magnet scene-construction task

Spatial recall for Experiment 2: Non-symbolic Number Arrays.

<p>Female and male participants’ performance in Experiment 2: Non-Symbolic Number at each string length (1 panel up to 10 panels), for the left-to-right structured and right-to-left structured spatial flow types. Error bars are the within-subject SEM.</p