1 < 2 and 2 < 3: non-linguistic appreciations of numerical order

Directionality in the interrelations between approximate number, verbal number, and mathematics in preschool-aged children

A fundamental question in numerical development concerns the directional relation between an early-emerging non-verbal approximate number system (ANS) and culturally acquired verbal number and mathematics knowledge. Using path models on longitudinal data collected in preschool children (M_age  = 3.86 years; N = 216; 99 males; 80.8% White; 10.8% Multiracial, 3.8% Latino; 1.9% Black; collected 2013-2017) over 1 year, this study showed that earlier verbal number knowledge was associated with later ANS precision (average β = .32), even after controlling for baseline differences in numerical, general cognitive, and language abilities. In contrast, earlier ANS precision was not associated with later verbal number knowledge (β = -.07) or mathematics abilities (average β = .10). These results suggest that learning about verbal numbers is associated with a sharpening of pre-existing non-verbal numerical abilities.

Anchoring Effect of Performance Feedback on Accuracy of Metacognitive Monitoring in Preschool Children

Preschool children are generally inaccurate at evaluating past and predicting future performance. The present study examines the effect of performance feedback on the accuracy of preschoolers' predictive judgments and tests whether performance feedback acts as an anchor for postdictive judgments. In Experiment 1, preschool children (n = 40) solved number patterns, and in Experiment 2 they solved object patterns (n = 59). The results in both experiments revealed, firstly, that children receiving performance feedback made more accurate predictive judgments and lowered their certainty after their incorrect answer. Secondly, the children relied on performance feedback more than on actual task experience when making postdictive judgments, indicating that performance feedback was used as an anchor for subsequent postdictive judgments.

Spatial complexity facilitates ordinal mapping with a novel symbol set

The representation of number symbols is assumed to be unique, and not shared with other ordinal sequences. However, little research has examined if this is the case, or whether properties of symbols (such as spatial complexity) affect ordinal learning. Two studies were conducted to investigate if the property of spatial complexity affects learning ordinal sequences. In Study 1, 46 adults made a series of judgements about two novel symbol sets (Gibson and Sunúz). The goal was to find a novel symbol set that could be ordered by spatial complexity. In Study 2, 84 adults learned to order nine novel symbols (Sunúz) with a paired comparison task, judging which symbol was 'larger' (whereby the larger symbol became physically larger as feedback), and were then asked to rank the symbols. Participants were assigned to either a condition where there was a relationship between spatial complexity and symbol order, or a condition where there was a random relationship. Of interest was whether learning an ordered list of symbols would be facilitated by the spatial complexity of the novel symbols. Findings suggest spatial complexity affected learning ability, and that pairing spatial complexity with relational information can facilitate learning ordinal sequences. This suggests that the implicit cognitive representation of number may be a more general feature of ordinal lists, and not exclusive to number per se.

Representation of different exact numbers of prey by a spider-eating predator

Our objective was to use expectancy-violation methods for determining whether Portia africana, a salticid spider that specializes in eating other spiders, is proficient at representing exact numbers of prey. In our experiments, we relied on this predator's known capacity to gain access to prey by following pre-planned detours. After Portia first viewed a scene consisting of a particular number of prey items, it could then take a detour during which the scene went out of view. Upon reaching a tower at the end of the detour, Portia could again view a scene, but now the number of prey items might be different. We found that, compared with control trials in which the number was the same as before, Portia's behaviour was significantly different in most instances when we made the following changes in number: 1 versus 2, 1 versus 3, 1 versus 4, 2 versus 3, 2 versus 4 or 2 versus 6. These effects were independent of whether the larger number was seen first or second. No significant effects were evident when the number of prey changed between 3 versus 4 or 3 versus 6. When we changed prey size and arrangement while keeping prey number constant, no significant effects were detected. Our findings suggest that Portia represents 1 and 2 as discrete number categories, but categorizes 3 or more as a single category that we call 'many'.

How Parents Read Counting Books and Non-numerical Books to Their Preverbal Infants: An Observational Study

Studies have stressed the importance of counting with children to promote formal numeracy abilities; however, little work has investigated when parents begin to engage in this behavior with their young children. In the current study, we investigated whether parents elaborated on numerical information when reading a counting book to their preverbal infants and whether developmental differences in numerical input exist even in the 1st year of life. Parents and their 5–10 months old infants were asked to read, as they would at home, two books to their infants: a counting book and another book that did not have numerical content. Parents’ spontaneous statements rarely focused on number and those that did consisted primarily of counting, with little emphasis on labeling the cardinality of the set. However, developmental differences were observed even in this age range, such that parents were more likely to make numerical utterances when reading to older infants. Together, results are the first to characterize naturalistic reading behaviors between parents and their preverbal infants in the context of counting books, suggesting that although counting books promote numerical language in parents, infants still receive very little in the way of numerical input before the end of the 1st year of life. While little is known regarding the impact of number talk on the cognitive development of young infants, the current results may guide future work in this area by providing the first assessment of the characteristics of parental numerical input to preverbal infants.