Can children use probability to guide their choices under uncertainty?

We encounter situations in our everyday lives where we need to make decisions under uncertainty. But what kind of information do we use and what abilities are helpful to us when making decisions under uncertainty? In three experiments (Total N = 180), I examined whether 3- to 7-year-olds could use numerical information (e.g., probability) to judge which of two situations presented with more or less uncertainty. Children were shown two games with different numbers of hiding locations. Using a within-subjects design, they were asked to select the game that would make it either easy or hard for someone else to find a coin that is hidden under one of the locations. Around the age of five, children selected the side with fewer hiding locations when asked to make it easy to find the coin and selected the side with more hiding locations when asked to make it hard to find the coin (Experiment 1). Findings from Experiment 2 suggest that children do this by considering the absolute number of hiding locations, rather than using perceptual cues like surface area (e.g., clutter). In Experiment 3, we simplified our procedure to examine whether younger children could make a similar inference. Findings reveal that even 4-year-olds were selecting the side with fewer hiding locations when asked which ball was easier to find and selecting the side with more hiding locations when asked which ball was harder to find. These results suggest that around age four, children can evaluate probability to make judgements about levels of uncertainty. Moreover, these results highlight that perhaps evaluating the probabilities of outcomes is a helpful tool when confronted with uncertainty

What association exists between arithmetic and other early numerical skills in toddlers? A study

openLe precoci capacità aritmetiche, l’acuità numerica e i principi del conteggio costituiscono parte delle fondamenta su cui si baseranno le competenze matematiche in età scolare, svolgendo un ruolo determinante anche per il successo scolastico negli anni successivi. Il presente lavoro ha voluto indagare tali competenze in bambini tra i 18 e i 36 mesi nell’ottica di voler dimostrare che è possibile approfondire il campo di conoscenza della cognizione numerica anche in bambini frequentanti l’asilo nido, con la prospettiva di fondo di voler sensibilizzare personale educativo e famiglie ad un tema su cui si sta arricchendo il bagaglio di conoscenza in possesso della comunità scientifica. Le competenze legate al numero sono il risultato dell’interazione fra capacità presenti fin dalla nascita e altre acquisite nel corso dello sviluppo, entrambe mediate dalla cultura di appartenenza e dagli stimoli forniti dall’ambiente in cui si viene cresciuti. Quando si parla di cognizione numerica si pensa ad aspetti che hanno a che fare sia con ciò che l’uomo possiede a livello ontogenetico che le acquisizioni che derivano dalle esperienze a cui quotidianamente viene sottoposto. Tra le competenze innate, il presente studio si è soffermato in particolare sulle abilità aritmetiche precoci che sono presenti già a pochi mesi di vita e che sono in continuo cambiamento nel corso dello sviluppo. Posseggono la caratteristica di essere sensibili alla ratio: i bambini in età prescolare sono in grado di compiere delle operazioni aritmetiche con accuratezza crescente all’aumentare del rapporto tra due numeri presentati (competenza che manterranno per tutto il corso della loro vita). Le analisi svolte sul campione che ha partecipato alla ricerca hanno evidenziato come sia presente una sensibilità alla ratio anche nella prima infanzia, ma in maniera differente rispetto a quanto la letteratura sottolinea dal momento che i bambini sono stati più accurati nel rispondere agli item in cui il rapporto era minore (1:2) rispetto a quando era maggiore (1:4) (F (1, 19) = 15.629, p= <.001). Inoltre, i bambini in età prescolare sanno anche confrontare le quantità di due insiemi differenti, capacità denominata acuità numerica: essa muta con il progredire dello sviluppo e presenta la stessa caratteristica di sensibilità alla ratio di cui si è accennato per le competenze aritmetiche. Le due abilità appena presentate, entrambe di carattere innato, hanno in comune il sistema cognitivo che sottostà alla loro attivazione: l’Approximate Number System. Infatti, dalle analisi, le prove che indagavano le competenze aritmetiche e l’acuità numerica sono risultate in correlazione fra loro (r= 0.694, p= <.001), a dimostrazione del fatto che è implicato lo stesso meccanismo. I bambini che hanno un’età compresa fra i 18 e i 36 mesi, però, posseggono anche altre competenze che rientrano nell’ambito della cognizione numerica. Nella prima infanzia i bambini dimostrano di possedere una serie di concetti che ruotano attorno al mondo dei numeri, tali concetti denominati “principi del conteggio” (Gelman & Gallistel, 1978) sono fortemente dipendenti dalle esperienze che i bambini vivono quotidianamente e a questa età iniziano a sperimentarli tramite le interazioni con i loro adulti di riferimento

The development of integrating number and proportion in probabilistic decision-making

The ability to integrate multiple pieces of information and use it to guide decision-making is an essential part of everyday reasoning. While it may not seem like it, the information in our environments is often numerical in nature. From simple decisions like which cashier line to stand in at the grocery store, to more consequential judgments like evaluating the chances of getting accepted into a competitive graduate program, numbers and proportions are everywhere. And while combining numerical information to make judgments and decisions sounds challenging, even young children have some of the requisite abilities to do so. In this dissertation, I describe and discuss a series of experiments that examine the developmental trajectories of integrating numerical and proportional information to make probability judgements and arrive at favourable outcomes in game-like scenarios. Chapter 2 examines whether 5- and 6-year-old children (N=160) and adults (N=68) can integrate two types of numerical information to make decisions in a probability game involving single- and multi-draw samples from different distributions. I presented children with a computer game in which they must maximize the number of green objects obtained. In order to do so successfully they were required to integrate the absolute number of draws with the proportion of targets to non-targets from which those draws are made. Across five studies, I established that 5- and 6-year-olds and adults can – under certain conditions –integrate two sources of numerical information to make decisions that maximize the odds of a favourable outcome. Chapter 3 examines the developmental origins of these integrative abilities by adapting the paradigm used in Chapter 2 to test infants (n=46). I presented them with two trial types: one where the correct response was to choose the lower draw number from the distribution with a higher proportion of target objects, and another where the correct response was to choose the higher draw number from the distribution with a lower proportion of target objects. Results from 10-12-month-olds revealed that infants were not able to combine the numerical and proportional information to make probability judgments and performed at chance levels with no effects of age or trial type. These results suggested that the ability to integrate both numerical and proportional information to make probability judgments is not yet a consistent hallmark of probabilistic reasoning within the age range we tested. Chapter 4 examines whether or not toddlers (n=40) would be successful on the same trial types used with infants. Results from 18-30-month-olds show that toddlers were able to correctly choose the larger draw number from the distribution with the lower proportion of target objects, but responded at rates no different than chance on the trial where the correct response was to choose the smaller draw number from the distribution with the larger proportion of target objects. Taken together, the results from these three sets of experiments suggest that adults and school-aged children are capable of integrating probability and number in a game-like probability task, and that these abilities may begin in toddlerhood. It appears that beginning in the second year of life, but likely not before then, human learners can consider both the distributions and the number of draws when reasoning about sampling and probability

Parallel Individuation Supports Numerical Comparisons in Preschoolers

While the approximate number system (ANS) has been shown to represent relations between numerosities starting in infancy, little is known about whether parallel individuation – a system dedicated to representing objects in small collections – can also be used to represent numerical relations between collections. To test this, we asked preschoolers between the ages of 2 ½ and 4 ½ to compare two arrays of figures that either included exclusively small numerosities ( 4). The ratios of the comparisons were the same in both small and large numerosity conditions. Experiment 1 used a between-subject design, with different groups of preschoolers comparing small and large numerosities, and found that small numerosities are easier to compare than large ones. Experiment 2 replicated this finding with a wider range of set sizes. Experiment 3 further replicated the small-large difference in a within-subject design. We also report tentative evidence that non- and 1-knowers perform better on comparing small numerosities than large numerosities. These results suggest that preschoolers can use parallel individuation to compare numerosities, possibly prior to the onset of number word learning, and thus support previous proposals that there are numerical operations defined over parallel individuation (e.g., Feigenson & Carey, 2003; https://doi.org/10.1111/1467-7687.00313)