Canada

This study investigated how the different components of mathematical language, quantitative language (e.g., more) and spatial language (e.g., after) relate to children’s performance in different domains of mathematics (numerical competencies, measurement, geometry). Our sample included 75 preschool children (Mage = 4 years 10 months). Children received measures of mathematical language and mathematical ability. We also assessed their general language and spatial skill, and investigated to which extent associations between mathematical language and mathematical abilities remained when these general skills were controlled for. Results indicated that both quantitative and spatial language were correlated with children’s numerical competencies, measurement and geometry scores. We further observed that spatial language, but not quantitative language, was a unique predictor of children’s mathematical abilities, particularly of their numerical competencies and their geometry performance, suggesting that spatial language is more critical than quantitative language. This relation between spatial language and mathematical ability disappeared when general language and spatial skill, were taken into account. Follow-up analyses further indicated that spatial language partially mediated the association between these general abilities and mathematical abilities. These findings present evidence on the link between distinct types of mathematical language and different mathematical abilities, and they emphasize the role of spatial language in children’s mathematical abilities.


CogSci 2022

Understanding mathematical development in preschool children: the association between mathematical language and mathematical abilities

technical paper

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Based on prior work, we predicted that traditional, 2-D counting books would be better than tactile counting books at promoting young children's numeracy. However, the first author suspected that the effect of tactility on learning would differ for Black versus non-Black children. To test this, we examined data from an existing project on preschoolers' learning from shared counting book reading. Participants included 325 preschoolers, ages 2 to 6, 41% of whom were Black. Findings suggest that race moderates the effect of tactility on numeracy. Non-Black children conformed to the original hypothesis that non-tactile counting books would be best for promoting children's numeracy, but Black children did not. This finding is important because much of the research on children's early numeracy is conducted with homogeneous, convenience samples, so theories and predictions are being built on incomplete data. Without studying diverse samples, the field risks making inaccurate conclusions about how children learn.


Race moderates the effect of tactility on children's learning from counting books

Following Griffiths and Tenenbaum (2006), we explore whether people use relevant social information to improve their already nearly optimal predictions about quantities in everyday events. We tested this question in two experiments involving quantities in three domains: cake baking times, movie runtimes, and podcast lengths. In Experiment 1, we found that participants were sensitive to the difference between relevant and irrelevant social information. In Experiment 2, we found that people consistently used relevant social information to adjust their predictions in the expected directions. We introduce an optimal social prediction model but find that it does not consistently perform better at accounting for our participants' social predictions than an optimal non-social prediction model. We conclude by discussing whether people use social information for prediction in an optimal way.


Do people use social information to improve predictions about everyday events?

Robots are extraordinary, category-defying entities. Machines that move autonomously, store and communicate information, display emotions, and cultivate social relationships pose a challenge to our most basic assumptions about what kinds of things exists in the world and how we should reason about them. As such, studies of lay people’s beliefs about robots offer new insights into the ordinary functioning of folk ontologies. In this paper, I propose that there are two ontological questions that human reasoners must grapple with in making sense of robots, or any other entity: Which kind of thing is it? and Which causal forces act on it? Each question highlights a distinct way in which robots are extraordinary—albeit, not exceptional—entities for the human cognitive system. A meditation on the dynamic interplay between these two ontological questions provides a new theoretical framework for understanding conceptual change at both the individual and the cultural-historical level.


Extraordinary entities: Insights into folk ontology from studies of lay people’s beliefs about robots

We investigated whether the representation of relational categories is different from that of featural categories. Earlier work has suggested an extreme-value hypothesis: when a category is defined in terms of a relation, exemplars with exaggerated values along this stimulus dimension are judged as better members of the category. Featural categories, on the other hand, are not exaggerated. To test this hypothesis, we trained participants to categorize two fictional diseases defined either by a deterministic relation or a deterministic feature. After the categorization task was mastered up to a predefined learning criterion, we provided a graphical user interface that enabled participants to construct good examples of the acquired categories by adjusting the stimulus attributes. We constructed a novel index of relational exaggeration based on residual deviations from a non-exaggerated response strategy. These results supported the extreme-value hypothesis. This replicates and extends an earlier quasi-experimental study (Du et al., 2021).


Exaggeration of Stimulus Attributes in the Representation of Relational Categories

Intuitive conceptions are prevalent among young learners and can impose constraints to knowledge acquisition. Even though the data suggests that instruction does not eradicate them, this phenomenon has rarely been quantified. In this study we raise the question of how robust intuitive conceptions are. Moreover, we look at their persistence long after instruction of the studied notions. Production tasks concerning the four elementary arithmetic operations were used for measuring the degree to which they prevail and impose constraints among adults, 131 bachelor students as well as 168 high-school teachers and 57 mathematics teachers. The findings revealed that in most cases (88.93%) participants evoked examples that are congruent with an intuitive conception. This was observed for all the arithmetic operations and populations involved in the study. Even when explicitly prompted to find incongruent cases, they failed on two thirds of the cases. The educational entailments of these findings are discussed.


How robust and persistent are intuitive conceptions? Insights from production tasks

This study addresses the interaction between language and event cognition. Previous research has shown that viewers follow perceptual and conceptual features of event structure, and these features influence how they process events. Here, we examine whether events are processed in different ways when preceded by descriptions that contrast in lexical aspect. In our experiment, viewers watched fifteen short movie clips and were asked to indicate whether they saw an interruption. Interruptions occurred in either the midpoint or the late point of the events. We found that telic vs. atelic sentences shown prior to the movie clips influenced event construal and hence the detection of interruptions at midpoints vs. endpoints. This novel finding supports a mapping between lexical aspect in language and temporal structure-building in event apprehension. Our study provides direct experimental evidence for the role of language as a top-down conceptual cue in event processing.

Linguistic aspect constrains event apprehension

How people learn about events often varies with some events perceived in their entirety and others are inferred based on the available evidence. Here, we investigate how children and adults linguistically encode the sources of their event knowledge. We focus on Turkish – a language that obligatorily encodes source of information for past events using two evidentiality markers. Children (4- to 5-year-olds and 6- to 7- year-olds) and adults watched and described events that they directly saw or inferred based on visual cues with manipulated degrees of indirectness. Overall, participants modified the evidential marking in their descriptions depending on (a) whether they saw or inferred the event and (b) the indirectness of the visual cues giving rise to an inference. There were no differences across age groups. These findings suggest that Turkish-speaking adults’ and children’s use of evidential markers are sensitive to the indirectness of the inferential evidence for events.

Linguistic Encoding of Inferential Evidence for Events

Like verbal discourse, visual narratives use various techniques to motivate readers to infer unstated events. One technique of sponsoring bridging inferences in visual sequences is to replace climactic events with an “onlooker”, a bystander viewing the off-panel climax reacting with textual and/or bodily cues to varying degrees. In two self-paced reading experiments, we explored how onlookers sponsored inferencing. Experiment 1 compared five types of onlookers ranging from a passive face with no cues to explicit facial or textual cues, and Experiment 2 investigated the effect of zooming in on onlookers’ bodily cues. Less explicit onlookers are processed faster, but at the next panel all onlookers required equal updating costs and zooms elicited further costs. Moreover, textual cues facilitated understanding. Overall, these findings show that complexity and explicitness of information in visual narratives affect subsequent event inferencing.

A Closer Look at Bridging Inferences: Onlookers and Framing in Visual Narratives

Recent evidence indicates that children represent and learn multiple meanings of ambiguous words from early in development (e.g., mail letter, alphabetic letter). This raises the question of which naturalistic factors might allow young children to resolve lexical ambiguities. Previous research has shown that children’s processing of ambiguous words is facilitated by verb-related information. However, it is still unclear whether such facilitation comes from bottom-up (lexical associations) or top-down information sources (verb-event structures). In this study, we leveraged a large sense-annotated child-directed speech corpus to disentangle the effect of bottom-up lexical and top-down event structure cues. Preliminary results show that 4-year-olds might rely on verb-event structures when these are put in competition with lexical association. We discuss implications for theories of sentence parsing and word learning.

The Role of Verb-Event Structure in Children’s Lexical Ambiguity Resolution

Over the last few decades, Causal Model Theory (CMT) has become a dominant framework for human causal-based reasoning, including categorization and inference. CMT prescribes how people should reason about probabilistic events in terms of causal models. In typical causal-based categorization experiments, subjects are provided with verbal descriptions of causally linked features, generally including probabilistic information. Another line of research focuses on perceived or experienced causal events, rather than on verbal descriptions. In this work we asked whether effects which are consistent with CMT, and that have been obtained with verbal descriptions, generalize to visually perceived events. In two experiments, we presented subjects with videos of a 3D A→B causal event rather than verbal descriptions. In Exp. 1, we found that subjects who saw the causal event did not show the coherence effect in categorization (i.e., subjects tend to rate the null ¬A¬B event as a category member). However, subjects who did see the null event during training did show the effect. In Exp. 2, we ruled out the possibility that Exp. 1’s results were simply an effect of how frequently events were experienced during training. We conclude that a one-shot perceived causal event is not sufficient for people to show causal-based reasoning as CMT predicts.


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Understanding mathematical development in preschool children: the association between mathematical language and mathematical abilities

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