Bibliographic record
Abstract
What are the roles of cardinal and ordinal processing in the development of arithmetic?In the present dissertation, cardinal knowledge is defined as the ability to determine the quantity of number symbols whereas ordinal knowledge is defined as the ability to determine the relative relationship among number symbols.This dissertation includes two studies examining the development of the relations among cardinal, ordinal and arithmetic skills, both concurrently and predictively, for children in the early grades of elementary school.In both studies, children completed a number comparison task (e.g., which number is bigger, 4 or 5?) as an index of their cardinal knowledge.They also completed two novel order tasks: (a) missing number (e.g., which number is missing, 1 _ 3 4?), and (b) number ordering (i.e., order the three digits from the smallest to the largest, e.g., 4 5 3 or 2 7 9).Furthermore, children completed two measures of inhibitory control.Last, children's arithmetic skill (e.g., solving problems such as 4 + 5 or 7 + 6) was measured.In Study 1, I evaluated the internal consistency and validity of the novel order measures for children entering grades 1 to 3 (n = 70).In Study 2, multi-group path analysis showed that for children in grade 1 (n = 66), number ordering was strongly predicted by number comparison, but not by the missing number task or inhibitory control.Moreover, performance on the number comparison and missing number task independently predicted addition.Further, performance on the number comparison task uniquely predicted the growth of addition.In contrast, for children in grade 2 (n = 80), variance in the number ordering task was shared among the number comparison, missing number, and inhibitory control tasks.Number ordering uniquely predicted addition iii concurrently and it also predicted the growth of addition.I interpret the different patterns of results from grades 1 to 2 as reflecting different ongoing processes of integration of symbolic numerical associations.These findings suggest that development of number competence involves the integration of cardinal, ordinal, and arithmetic associations in an extensive network of relations among numbers.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".