Professional Education
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Master of Science, University of Wisconsin Madison (2019)
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Ph.D., University of Wisconsin - Madison, Educational Psychology, Human Development (2021)
All Publications
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Developmental Changes in Nonsymbolic and Symbolic Fractions Processing: A Cross-Sectional fMRI Study.
Developmental science
2025; 28 (5): e70042
Abstract
A substantial body of research has demonstrated that human and nonhuman animals have perceptually-based abilities to process magnitudes of nonsymbolic ratios (e.g., ratios composed by juxtaposing two-line segments). In prior work, we have extended the neuronal recycling hypothesis to include neurocognitive architectures for nonsymbolic ratio processing, proposing that these systems might support symbolic fractions acquisition. We tested two key propositions: (1) children should show neural sensitivity to nonsymbolic fractions before receiving formal fractions instruction, and (2) they should leverage this foundation by recruiting neural architectures for nonsymbolic fractions processing for symbolic fractions. We compared nonsymbolic and symbolic fractions processing among 2nd-graders (n = 28, ages 7.5-8.8), who had not yet received formal symbolic fractions instruction, and 5th-graders (n = 33, ages 10.3-11.9), who had. During fMRI scanning, children performed ratio comparison tasks, determining which of two nonsymbolic or symbolic fractions was larger. Both cohorts showed behavioral and neural evidence of processing nonsymbolic and symbolic fractions magnitudes, with performance modulated by numerical distance between stimuli. Consistent with our predictions, 2nd-graders recruited a right parietal-frontal network for nonsymbolic fractions but not for symbolic fractions, whereas 5th-graders recruited a bilateral parietal-frontal network for both, overlapping with but extending beyond that of 2nd-graders. Furthermore, nonsymbolic-symbolic neural similarity in the intraparietal sulcus was greater for 5th-graders than for 2nd-graders. These results present the first developmental neuroimaging evidence that neural substrates for nonsymbolic ratios exist before formal learning, which may be recycled to process symbolic fractions. SUMMARY: 2nd-graders, prior to formal fractions instructions, already recruit a right parietal-frontal network when comparing nonsymbolic fractions. 5th-graders, who have received some formal fractions instruction, recruit this same network not only for nonsymbolic fractions, but also for symbolic fractions. These findings are consistent with the neuronal recycling account, which posits that symbolic fraction processing builds on neural substrates originally used for nonsymbolic fraction processing. These findings suggest that pedagogical strategies focus on supporting this recycling process may enhance students' understanding of symbolic fractions.
View details for DOI 10.1111/desc.70042
View details for PubMedID 40607583
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Short-term number sense training recapitulates long-term neurodevelopmental changes from childhood to adolescence.
Developmental science
2024: e13524
Abstract
Number sense is fundamental to the development of numerical problem-solving skills. In early childhood, children establish associations between non-symbolic (e.g., a set of dots) and symbolic (e.g., Arabic numerals) representations of quantity. The developmental estrangement theory proposes that the relationship between non-symbolic and symbolic representations of quantity evolves with age, with increased dissociation across development. Consistent with this theory, recent research suggests that cross-format neural representational similarity (NRS) between non-symbolic and symbolic quantities is correlated with arithmetic fluency in children but not in adolescents. However, it is not known if short-term training (STT) can induce similar changes as long-term development. In this study, children aged 7-10 years underwent a theoretically motivated 4-week number sense training. Using multivariate neural pattern analysis, we investigated whether short-term learning could modify the relation between cross-format NRS and arithmetic skills. Our results revealed a significant correlation between cross-format NRS and arithmetic fluency in distributed brain regions, including the parietal and prefrontal cortices, prior to training. However, this association was no longer observed after training, and multivariate predictive models confirmed these findings. Our findings provide evidence that intensive STT during early childhood can promote behavioral improvements and neural plasticity that resemble and recapitulate long-term neurodevelopmental changes that occur from childhood to adolescence. More generally, our study contributes to our understanding of the malleability of number sense and highlights the potential for targeted interventions to shape neurodevelopmental trajectories in early childhood. RESEARCH HIGHLIGHTS: We tested the hypothesis that short-term number sense training induces the dissociation of symbolic numbers from non-symbolic representations of quantity in children. We leveraged a theoretically motivated intervention and multivariate pattern analysis to determine training-induced neurocognitive changes in the relation between number sense and arithmetic problem-solving skills. Neural representational similarity between non-symbolic and symbolic quantity representations was correlated with arithmetic skills before training but not after training. Short-term training recapitulates long-term neurodevelopmental changes associated with numerical problem-solving from childhood to adolescence.
View details for DOI 10.1111/desc.13524
View details for PubMedID 38695515
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Integrated number sense tutoring remediates aberrant neural representations in children with mathematical disabilities.
bioRxiv : the preprint server for biology
2024
Abstract
Number sense is essential for early mathematical development but it is compromised in children with mathematical disabilities (MD). Here we investigate the impact of a personalized 4-week Integrated Number Sense (INS) tutoring program aimed at improving the connection between nonsymbolic (sets of objects) and symbolic (Arabic numerals) representations in children with MD. Utilizing neural pattern analysis, we found that INS tutoring not only improved cross-format mapping but also significantly boosted arithmetic fluency in children with MD. Critically, the tutoring normalized previously low levels of cross-format neural representations in these children to pre-tutoring levels observed in typically developing, especially in key brain regions associated with numerical cognition. Moreover, we identified distinct, 'inverted U-shaped' neurodevelopmental changes in the MD group, suggesting unique neural plasticity during mathematical skill development. Our findings highlight the effectiveness of targeted INS tutoring for remediating numerical deficits in MD, and offer a foundation for developing evidence-based educational interventions.
View details for DOI 10.1101/2024.04.09.587577
View details for PubMedID 38645139
View details for PubMedCentralID PMC11030345
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More than the sum of its parts: Exploring the development of ratio magnitude versus simple magnitude perception
DEVELOPMENTAL SCIENCE
2021; 24 (3): e13043
Abstract
Humans perceptually extract quantity information from our environments, be it from simple stimuli in isolation, or from relational magnitudes formed by taking ratios of pairs of simple stimuli. Some have proposed that these two types of magnitude are processed by a common system, whereas others have proposed separate systems. To test these competing possibilities, the present study examined the developmental trajectories of simple and relational magnitude discrimination and relations among these abilities for preschoolers (n = 42), 2nd-graders (n = 31), 5th-graders (n = 29), and adults (n = 32). Participants completed simple magnitude and ratio discrimination tasks in four different nonsymbolic formats, using dots, lines, circles, and irregular blobs. All age cohorts accurately discriminated both simple and ratio magnitudes. Discriminability differed by format such that performance was highest with line and lowest with dot stimuli. Moreover, developmental trajectories calculated for each format were similar across simple and ratio discriminations. Although some characteristics were similar for both types of discrimination, ratio acuity in a given format was more closely related with ratio acuities in alternate formats than to within-format simple magnitude acuity. Results demonstrate that ratio magnitude processing shares several similarities to simple magnitude processing, but is also substantially different.
View details for DOI 10.1111/desc.13043
View details for Web of Science ID 000581927100001
View details for PubMedID 33030291
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Developmental changes in the relationship between magnitude acuities and mathematical achievement in elementary school children
EDUCATIONAL PSYCHOLOGY
2017; 37 (7): 873-887
View details for DOI 10.1080/01443410.2015.1127332
View details for Web of Science ID 000404843600007