Numerical Building Blocks: Exploring Domain-Specific Cognitive Predictors of Mathematics
Notice bibliographique
Résumé
This dissertation includes three studies examining individual differences in domainspecific quantitative skills as predictors of adults' mathematical performance.Quantitative skills included subitizing, counting, approximate number system (ANS), and symbolic skills.Subitizing is the ability to quickly and exactly enumerate small sets without counting (1 to 3 or 4), whereas the ANS facilitates discrimination between large quantities.Given the evidence for their presence among human infants and other animals, the subitizing and approximate number systems are considered core quantitative systems-leading to theories that one or both systems scaffold the acquisition of symbolic quantity representations.Counting is the process of enumerating sets beyond the subitizable range to determine exact quantity; learning to count is the first step in acquiring the symbolic system.The present research was framed by three theoretical accounts, each of which emphasize the subitizing, counting, or approximate number system as the key contributor to mathematical success.Compared to the ANS literature, very little research has examined subitizing and counting skills in relation to mathematics performance with adult samples.To address this issue, the current research included subitizing, counting, and ANS-as well as symbolic skills.These domain-specific quantitative skills were examined in relation to each other and as relative contributors to mathematics outcomes via path analyses (Studies 1 and 2) and structural equation modeling (Study 3).ANS skill did not uniquely predict mathematical outcomes requiring exact calculation, but did predict symbolic and nonsymbolic number line performance.Counting predicted symbolic quantitative skills, but not mathematical outcomes.Subitizing emerged as a predictor of arithmetic fluency across all three studies, but did iii not predict other mathematical outcomes.As hypothesized, symbolic quantitative skill tended to be the strongest predictor of all mathematical outcomes, except for nonsymbolic number line.Experiential factors also predicted mathematical outcomes across all three studies.These findings suggest that the subitizing system scaffolds the development of counting and symbolic quantitative skills, and continues to predict arithmetic fluency in adulthood.It is recommended that future research explore the role of subitizing in the development of symbolic quantitative skills, to gain understanding of this developmental trajectory.Many thanks to my graduate advisor, Jo-Anne LeFevre.When I applied to graduate school, I had no idea how lucky I was be to be accepted by a supervisor like you.I am so glad that I ended up in the field of mathematical cognition, which has proved to be both challenging and fruitful.It's amazing to think about how much I have learned and experienced since I entered the LeFevre Mathlab.Jo-Anne: You are such a wonderful mentor.You are so hard-working, but in my opinion the best thing about you is that you understand how to foster the talents of your graduate students.You encourage us to excel and be the best that we can be, but you also display so much empathy and caring when we need it.Best academic mom ever!I may be leaving the SS Mathlab, but you will always be my Captain Picard!
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Comment cette classification a été obtenuedéplier
Prédiction machine sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Le volet Gemma est une étiquette directe du modèle pour chaque travail de la base, lue sur la notice réduite au titre. Le volet Codex est un classifieur appris des 10 348 étiquettes directes de Codex et calibré sur les taux pondérés de l'échantillon; les champs sans appui suffisant ne portent aucun appel Codex. Le mode candidate est l'union des deux volets; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont pas des étiquettes humaines.
Scores du classifieur distillé par catégorie (deux têtes)
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,001 | 0,007 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,001 | 0,001 |
| Études des sciences et des technologies | 0,000 | 0,000 |
| Communication savante | 0,001 | 0,001 |
| Science ouverte | 0,000 | 0,001 |
| Intégrité de la recherche | 0,000 | 0,001 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,003 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule source (Gemma direct ou Codex distillé), pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».