Numerical Building Blocks: Exploring Domain-Specific Cognitive Predictors of Mathematics
Bibliographic record
Abstract
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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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".