An examination of third- and fourth-graders’ equivalence knowledge after classroom instruction
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The present correlational study examined third- and fourth-graders’ (N = 56) knowledge of mathematical equivalence after classroom instruction on the equal sign. Three distinct learning trajectories of student equivalence knowledge were compared: those who did not learn from instruction (Never Solvers), those whose performance improved after instruction (Learners), and those who had strong performance before instruction and maintained it throughout the study (Solvers). Learners and Solvers performed similarly on measures of equivalence knowledge after instruction. Both groups demonstrated high retention rates and defined the equal sign relationally, regardless of whether they had learned how to solve equivalence problems before or during instruction. Never Solvers had relatively weak arithmetical (nonsymbolic) equivalence knowledge and provided operational definitions of the equal sign after instruction.
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.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it