Approximate multiplication in young children prior to multiplication instruction.

Prior work indicates that children have an untrained ability to approximately calculate using their approximate number system (ANS). For example, children can mentally double or halve a large array of discrete objects. Here, we asked whether children can perform a true multiplication operation, flexibly attending to both the multiplier and multiplicand, prior to formal multiplication instruction. We presented 5- to 8-year-olds with nonsymbolic multiplicands (dot arrays) or symbolic multiplicands (Arabic numerals) ranging from 2 to 12 and with nonsymbolic multipliers ranging from 2 to 8. Children compared each imagined product with a visible comparison quantity. Children performed with above-chance accuracy on both nonsymbolic and symbolic approximate multiplication, and their performance was dependent on the ratio between the imagined product and the comparison target. Children who could not solve any single-digit symbolic multiplication equations (e.g., 2 × 3) on a basic math test were nevertheless successful on both our approximate multiplication tasks, indicating that children have an intuitive sense of multiplication that emerges independent of formal instruction about symbolic multiplication. Nonsymbolic multiplication performance mediated the relation between children's Weber fraction and symbolic math abilities, suggesting a pathway by which the ANS contributes to children's emerging symbolic math competence. These findings may inform future educational interventions that allow children to use their basic arithmetic intuition as a scaffold to facilitate symbolic math learning.

Rational number representation by the approximate number system.

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known "connectedness illusion" to provide evidence that these ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers.

Contextual coherence increases perceived numerosity independent of semantic content.

Number perception emerges from multiple stages of visual processing. Understanding how systematic biases in number perception occur within a hierarchy of increasingly complex feature representations helps uncover the multistage processing underlying our visual number sense. Recent work demonstrated that reducing coherence of low-level visual attributes, such as color and orientation, systematically reduces perceived number. Here, we ask when in the visual processing hierarchy coherence affects numerosity perception and specifically whether the coherence effect is exclusive to low-level visual features or instead whether it can be driven by contextual or semantic relationships. We tested adults in an ordinal numerical comparison task with contextual coherence mathematically manipulated using a statistical model of visual object co-occurrence. Across several experiments, we found that arrays with high contextual coherence were perceived as numerically larger than arrays with low contextual coherence. This contextual coherence effect was not attenuated even when we reduced objects to texforms (unrecognizable images that preserve midlevel visual features) or removed semantic content from the images through box scrambling and diffeomorphic warping. Together, these results suggest that visual coherence derived from natural statistics of object co-occurrence systematically alters perceived numerosity at low-level visual processing, even before later stages at which items can be explicitly categorized and identified. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Increasing entropy reduces perceived numerosity throughout the lifespan.

Numerical illusions may provide a powerful window into the mechanisms that give rise to our visual number sense. Recent research has shown that similarly oriented elements appear more numerous than randomly oriented elements in an array. Here we examine whether the orientation coherence illusion is a more general byproduct of the effect of entropy on numerical information-processing. Participants engaged in an ordinal numerical comparison task where the color entropy of arrays was manipulated. We found that arrays with low color entropy were perceived as more numerous than arrays with high color entropy (Experiments 1 and 2), suggesting that the coherence illusion on numerosity perception is not specific to a particular visual property (e.g., orientation) but instead that the entropy of visual arrays more generally affects numerical processing. In Experiment 3, we explored the developmental trajectory of the color entropy effect in children aged 5 to 17 and found that the strength of the coherence illusion increases into adulthood, raising intriguing questions as to how perceptual experiences influence the progression of this numerosity illusion. We consider a recently proposed resource-rational model as a framework for understanding the entropy effect on numerosity perception under an information-theoretic perspective.

Missing the joke: Reduced rereading of garden-path jokes during mind-wandering.

Mind-wandering (i.e., thoughts irrelevant to the current task) occurs frequently during reading. The current study examined whether mind-wandering was associated with reduced rereading when the reader read the so-called garden-path jokes. In a garden-path joke, the reader's initial interpretation is violated by the final punchline, and the violation creates a semantic incongruity that needs to be resolved (e.g., "My girlfriend has read so many negative things about smoking. Therefore, she decided to quit reading."). Rereading text prior to the punchline can help resolve the incongruity. In a main study and a preregistered replication, participants read jokes and nonfunny controls embedded in filler texts and responded to thought probes that assessed intentional and unintentional mind-wandering. Results were consistent across the two studies: When the reader was not mind-wandering, jokes elicited more rereading (from the punchline) than the nonfunny controls did, and had a recall advantage over the nonfunny controls. During mind-wandering, however, the additional eye movement processing and the recall advantage of jokes were generally reduced. These results show that mind-wandering is associated with reduced rereading, which is important for resolving higher level comprehension difficulties. (PsycInfo Database Record (c) 2020 APA, all rights reserved).