A Meta-Analysis: Improvement of Students’ Algebraic Reasoning through Metacognitive Training
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
Although algebraic reasoning has been considered as an important factor influencing students’ mathematical performance, many students struggle to build concrete algebraic reasoning. Metacognitive training has been regarded as one effective method to develop students’ algebraic reasoning; however, there are no published meta-analyses that include an examination of the effects of metacognitive training on students’ algebraic reasoning. Therefore, the purpose of this meta-analysis was to examine the impact of metacognitive training on students’ algebraic reasoning. Eighteen studies with 22 effect sizes were selected for inclusion in the present meta-analysis. In the process of the analysis, one study was determined as an outlier; therefore, another meta-analysis was reconstructed without the outlier to calculate more robust results. The findings indicated that the overall effect size without an outlier equaled d=0.973 with SE=0.196. Q=20.201 (p<.05) and I2=0.997, which indicated heterogeneity of the studies. These results showed that the metacognitive training had a statistically significant positive impact on students’ algebraic reasoning.
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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.002 | 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