Children dynamically update and extend the interface between number words and perceptual magnitudes.

As adults, we represent and think about number, space, and time in at least two ways: our intuitive-but imprecise-perceptual representations, and the slowly learned-but precise-number words. With development, these representational formats interface, allowing us to use precise number words to estimate imprecise perceptual experiences. We test two accounts of this developmental milestone. Either slowly learned associations are required for the interface to form, predicting that deviations from typical experiences (e.g., presentation of a novel unit or unpracticed dimension) will disrupt children's ability to map number words to their perceptual experiences or children's understanding of the logical similarity between number words and perceptual representations allows them to flexibly extend this interface to novel experiences (e.g., units and dimensions they have not yet learned how to formally measure). 5-11-year-olds completed verbal estimation and perceptual sensitivity tasks across three dimensions: Number, Length, and Area. For verbal estimation, they were given novel units (i.e., a three-dot unit called one "toma" for Number, a 44 px long line called one "blicket" for Length, a 111 px2 blob called one "modi" for Area) and asked to estimate how many tomas/blickets/modies they saw when shown a larger set of dots, lines, and blobs. Children could flexibly link number words to novel units across dimensions, demonstrating positive estimation slopes, even for Length and Area, which younger children had limited experience with. This suggests that the logic of structure mapping can be dynamically utilized across perceptual dimensions, even without extensive experience.

The malleable impact of non-numeric features in visual number perception.

Non-numeric stimulus features frequently influence observers' number judgments: when judging the number of items in a display, we will often (mis)perceive the set with a larger cumulative surface area as more numerous. These "congruency effects" are often used as evidence for how vision extracts numeric information and have been invoked in arguments surrounding whether non-numeric cues (e.g., cumulative area, density, etc.) are combined for number perception. We test whether congruency effects for one such cue - cumulative area - provide evidence that it is necessarily used and integrated in number perception, or if its influence on number is malleable. In Experiment 1, we replicate and extend prior work showing that the presence of feedback eliminates congruency effects between number and cumulative area, suggesting that the role of cumulative area in number perception is malleable rather than obligatory. In Experiment 2, we test whether this malleable influence is because of use of prior experiences about how number naturalistically correlates with cumulative area, or the result of response competition, with number and cumulative area actively competing for the same behavioral decision. We preserve cumulative area as a visual cue but eliminate response competition with number by replacing one side of the dot array with its corresponding Hindu-Arabic numeral. Independent of the presence or absence of feedback, we do not observe congruency effects in Experiment 2. These experiments suggest that cumulative area is not necessarily integrated in number perception nor a reflection of a rational use of naturalistic correlations, but rather congruency effects between cumulative area and number emerge as a consequence of response competition. Our findings help to elucidate the mechanism through which non-numeric cues and number interact, and provide an explanation for why congruency effects are only sometimes observed across studies.

Real models: The limits of behavioural evidence for understanding the ANS.

Clarke and Beck use behavioural evidence to argue that (1) approximate ratio computations are sufficient for claiming that the approximate number system (ANS) represents the rationals, and (2) the ANS does not represent the reals. We argue that pure behaviour is a poor litmus test for this problem, and that we should trust the psychophysical models that place ANS representations within the reals.

Visual illusions help reveal the primitives of number perception.

The human perceptual system is responsive to numerical information within visual and auditory scenes. For example, when shown 2 displays of dots, observers can instantly, albeit approximately, identify the set that is more numerous. Theories in perceptual and cognitive psychology have focused on 2 mechanisms for how vision accomplishes such a feat: Under the domain-specific encoding theory, number is represented as a primary visual feature of perception, much like motion or color, while under the domain-general theory, the visual system represents number indirectly, through a complex combination of features such as the size of the dots, their total cluster, and so forth. Evidence for the latter theory often comes from "congruency effects:" the finding that participants frequently select the side where the dots on the screen are denser, larger, or brighter, rather than the side that is actually more numerous. However, such effects could also stem from response conflicts between otherwise independent dimensions. Here, we test these 2 competing accounts by embedding numerical displays within visual illusions that create large conflicts between number and other non-numeric dimensions-including contour length, convex hull, and density-and contrast participants' performance on a number discrimination task (i.e., "Which side has more dots?") against a number estimation task (i.e., "How many dots are there?"), which should eliminate response conflicts. Across 3 experiments, we find that while contour length illusions only affect number perception in discrimination tasks, the influences of convex hull and density on number perception persist in both discrimination and estimation tasks, supporting a more domain-general account of number encoding. (PsycINFO Database Record (c) 2019 APA, all rights reserved).