Infants Distinguish Between Two Events Based on Their Relative Likelihood

Heuristic strategy of intuitive statistical inferences in 7- to 10-year-old children

Intuitive statistical inferences refer to making inferences about uncertain events based on limited probabilistic information, which is crucial for both human and non-human species' survival and reproduction. Previous research found that 7- and 8-year-old children failed in intuitive statistical inference tasks after heuristic strategies had been controlled. However, few studies systematically explored children's heuristic strategies of intuitive statistical inferences and their potential numerical underpinnings. In the current research, Experiment 1 (N = 81) examined 7- to 10-year-olds' use of different types of heuristic strategies; results revealed that children relied more on focusing on the absolute number strategy. Experiment 2 (N = 99) and Experiment 3 (N = 94) added continuous-format stimuli to examine whether 7- and 8-year-olds could make genuine intuitive statistical inferences instead of heuristics. Results revealed that both 7- and 8-year-olds and 9- and 10-year-olds performed better in intuitive statistical inference tasks with continuous-format stimuli, even after focusing on the absolute number strategy had been controlled. The results across the three experiments preliminarily hinted that the ratio processing system might rely on the approximate number system. Future research could clarify what specific numerical processing mechanism may be used and how it might support children's statistical intuitions.

Minimally counterintuitive stimuli trigger greater curiosity than merely improbable stimuli

Curiosity plays a key role in directing learning throughout the lifespan. Prior work finds that violations of expectations can be powerful triggers of curiosity in both children and adults, but it is unclear which expectation-violating events induce the greatest curiosity and how this might vary over development. Some theories have suggested a U-shaped function such that stimuli of moderate extremity pique the greatest curiosity. However, expectation-violations vary not only in degree, but in kind: for example, some things violate an intuitive theory (e.g., an alligator that can talk) and others are merely unlikely (e.g., an alligator hiding under your bed). Combining research on curiosity with distinctions posited in the cognitive science of religion, we test whether minimally counterintuitive (MCI) stimuli, which involve one violation of an intuitive theory, are especially effective at triggering curiosity. We presented adults (N = 77) and 4- and 5-year-olds (N = 36) in the United States with stimuli that were ordinary, unlikely, MCI, and very counterintuitive (VCI) and asked which one they would like to learn more about. Adults and 5-year-olds chose Unlikely over Ordinary and MCI over Unlikely, but not VCI over MCI, more often than chance. Our results suggest that (i) minimally counterintuitive stimuli trigger greater curiosity than merely unlikely stimuli, (ii) surprisingness has diminishing returns, and (iii) sensitivity to surprisingness increases with age, appearing in our task by age 5.

Statistical learning in infancy predicts vocabulary size in toddlerhood

During the first 2 years of life, an infant's vocabulary grows at an impressive rate. In the current study, we investigated the impact of three challenges that infants need to overcome to learn new words and expand the size of their vocabulary. We used longitudinal eye-tracking data (n = 118) to assess sequence learning, associative learning, and probability processing abilities at ages 6, 10, and 18 months. Infants' ability to efficiently solve these tasks was used to predict vocabulary size at age 18 months. We demonstrate that the ability to make audio-visual associations and to predict sequences of visual events predicts vocabulary size in toddlers (accounting for 20% of the variance). Our results indicate that statistical learning in some, but not all, domains have a role in vocabulary development.

The Number Sense Represents (Rational) Numbers

On a now orthodox view, humans and many other animals possess a "number sense," or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique-the arguments from congruency, confounds, and imprecision-and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for number, such as "numerosities" or "quanticals," as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g. 7), but also non-natural rational numbers (e.g. 3.5). It does not represent irrational numbers (e.g. √2), however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research.

A description-experience gap in statistical intuitions: Of smart babies, risk-savvy chimps, intuitive statisticians, and stupid grown-ups

Comparison of different lines of research on statistical intuitions and probabilistic reasoning reveals several puzzling contradictions. Whereas babies seem to be intuitive statisticians, surprisingly capable of statistical learning and inference, adults' statistical inferences have been found to be inconsistent with the rules of probability theory and statistics. Whereas researchers in the 1960s concluded that people's probability updating is "conservatively" proportional to normative predictions, probability updating research in the 1970s suggested that people are incapable of following Bayes's rule. And whereas animals appear to be strikingly risk savvy, humans often seem "irrational" when dealing with probabilistic information. Drawing on research on the description-experience gap in risky choice, we integrate and systematize these findings from disparate fields of inquiry that have, to date, operated largely in parallel. Our synthesis shows that a key factor in understanding inconsistencies in statistical intuitions research is whether probabilistic inferences are based on symbolic, abstract descriptions or on the direct experience of statistical information. We delineate this view from other conceptual accounts, consider potential mechanisms by which attributes of first-hand experience can facilitate appropriate statistical inference, and identify conditions under which they improve or impair probabilistic reasoning. To capture the full scope of human statistical intuition, we conclude, research on probabilistic reasoning across the lifespan, across species, and across research traditions must bear in mind that experience and symbolic description of the world may engage systematically distinct cognitive processes.

First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals

Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty-five 6- to 8-year-old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children's numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills.

Play enhances visual form perception in infancy-an active training study

Motor experiences and active exploration during early childhood may affect individual differences in a wide range of perceptual and cognitive abilities. In the current study, we suggest that active exploration of objects facilitates the ability to process object forms and magnitudes, which in turn impacts the development of numerosity perception. We tested our hypothesis by conducting a preregistered active exploration intervention with 59 8-month-old infants. The minimal intervention consisted of actively playing with and exploring blocks once a day for 8 weeks. In order to control for possible training effects on attention, we used book reading as a control condition. Pre- and post-test assessments using eye-tracking showed that block play improved visual form perception, where infants became better at detecting a deviant shape. Furthermore, using three control tasks, we showed that the intervention specifically improved infants' ability to process visual forms and the effect could not be explained by a domain general improvement in attention or visual perception. We found that the intervention did not improve numerosity perception and suggest that because of the sequential nature of our hypothesis, a longer time frame might be needed to see improvements in this ability. Our findings indicate that if infants are given more opportunities for play and exploration, it will have positive effects on their visual form perception, which in turn could help their understanding of geometrical concepts.