Canada

Recent work has suggested that cross-notation understanding (e.g., 2/5 vs. 0.25) is important for math outcomes. In this study, equivalent fraction, decimal, and percent stimuli were used to examine individual differences in cross-notation and within-notation comparison in undergraduate students (N=183). Hierarchical linear regression analyses suggested that cross-notation magnitude comparison accuracy added explanatory power beyond that of within-notation magnitude comparison accuracy in predicting fraction arithmetic calculation and estimation skills, as well as ACT scores. Additionally, participants did not perceive equivalent rational numbers as equivalent when expressed in different notations (e.g., percentages were perceived as larger than equivalent fractions or decimals). Undergraduate students were also randomly assigned to one of two number line interventions: one focused on emphasizing connections among fractions, decimals, and percentages and another focused on developing fraction magnitude representations. Both interventions yielded improvements in rational number understanding, but there were some greater benefits of the cross-notation intervention.

CogSci 2022

Monster Math Race: Chasing Integrated Number Sense

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Join us for CogSci2022! Our 44th Annual Conference will be centered around the theme of diversity, with an accompanying range of keynotes and invited speakers who themselves highlight the diversity of our field. Our three symposia are Cognition across Diverse Populations, Cognition within Diverse Societies, and Global Challenges for Cognitive Science. The conference is being offered in a fully hybrid environment for onsite and online attendees.
 
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The 44th Annual Meeting of the Cognitive Science Society highlighted research on the theme Cognitive Diversity in addition to the full breadth and diversity of research topics offered by the society’s membership. 





Because of its importance in academic achievement, especially in mathematics, training cognitive flexibility at school is a major issue. The present research investigates the effectiveness of a school-based intervention to improve proportion arithmetic problem solving. The study was conducted with 5th graders of 10 classes from 5 high-priority education schools in the Paris region. Students of the control and experimental groups took part in 8 learning sessions about proportion problem solving. The experimental group’s training focused on comparing and flexibly categorizing the problems in the hopes to help students achieve a deeper understanding of proportion problems. Results show that training flexible categorization allowed the experimental group to progress more than the control group, in both categorization and solving tasks. The educational implications of our results are discussed.

Training flexible categorization to improve arithmetic problem solving: A school-based intervention with 5th graders

This exploratory study provides evidence that middle-grade students' symbolic fraction knowledge relates to grounded and embodied cognitive learning processes such as spatial ability and anxiety. These findings (N = 89) are consistent with several previous findings on fraction knowledge and mathematics learning more generally while highlighting several novel associations. Three key findings include: 1) mental rotation and spatial visualization are specifically predictive of fraction knowledge scores; 2) spatial anxiety may moderate the relationship between spatial ability and fraction knowledge scores; and 3) fraction knowledge is not only grounded in processes operating at biological and cognitive timescales individually, but components of these processes are interconnected. Though exploratory, these findings may provide the foundations for future work exploring the mechanisms behind these associations.


Expanding Understandings of Embodied Mathematical Cognition in Students' Fraction Knowledge

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.


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

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.

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